diff --git a/ipaddress.py b/ipaddress.py
index 20f33cb..263bcad 100644
--- a/ipaddress.py
+++ b/ipaddress.py
@@ -776,8 +776,7 @@
         if not isinstance(other, _BaseNetwork):
             raise TypeError("%s is not a network object" % other)
 
-        if not (other.network_address >= self.network_address and
-                other.broadcast_address <= self.broadcast_address):
+        if not other.subnet_of(self):
             raise ValueError('%s not contained in %s' % (other, self))
         if other == self:
             return
@@ -788,12 +787,10 @@
 
         s1, s2 = self.subnets()
         while s1 != other and s2 != other:
-            if (other.network_address >= s1.network_address and
-                other.broadcast_address <= s1.broadcast_address):
+            if other.subnet_of(s1):
                 yield s2
                 s1, s2 = s1.subnets()
-            elif (other.network_address >= s2.network_address and
-                  other.broadcast_address <= s2.broadcast_address):
+            elif other.subnet_of(s2):
                 yield s1
                 s1, s2 = s2.subnets()
             else:
@@ -975,6 +972,26 @@
         return (self.network_address.is_multicast and
                 self.broadcast_address.is_multicast)
 
+    @staticmethod
+    def _is_subnet_of(a, b):
+        try:
+            # Always false if one is v4 and the other is v6.
+            if a._version != b._version:
+                raise TypeError(f"{a} and {b} are not of the same version")
+            return (b.network_address <= a.network_address and
+                    b.broadcast_address >= a.broadcast_address)
+        except AttributeError:
+            raise TypeError(f"Unable to test subnet containment "
+                            f"between {a} and {b}")
+
+    def subnet_of(self, other):
+        """Return True if this network is a subnet of other."""
+        return self._is_subnet_of(self, other)
+
+    def supernet_of(self, other):
+        """Return True if this network is a supernet of other."""
+        return self._is_subnet_of(other, self)
+
     @property
     def is_reserved(self):
         """Test if the address is otherwise IETF reserved.
@@ -1410,7 +1427,8 @@
         if address_less is NotImplemented:
             return NotImplemented
         try:
-            return self.network < other.network
+            return (self.network < other.network or
+                    self.network == other.network and address_less)
         except AttributeError:
             # We *do* allow addresses and interfaces to be sorted. The
             # unassociated address is considered less than all interfaces.
@@ -2100,7 +2118,8 @@
         if address_less is NotImplemented:
             return NotImplemented
         try:
-            return self.network < other.network
+            return (self.network < other.network or
+                    self.network == other.network and address_less)
         except AttributeError:
             # We *do* allow addresses and interfaces to be sorted. The
             # unassociated address is considered less than all interfaces.
@@ -2294,4 +2313,4 @@
     _sitelocal_network = IPv6Network('fec0::/10')
 
 
-IPv6Address._constants = _IPv6Constants
+IPv6Address._constants = _IPv6Constants
\ No newline at end of file
diff --git a/test_ipaddress.py b/test_ipaddress.py
index 5f08f0c..a4fdc7e 100644
--- a/test_ipaddress.py
+++ b/test_ipaddress.py
@@ -92,7 +92,6 @@
                 y = pickle.loads(pickle.dumps(x, proto))
                 self.assertEqual(y, x)
 
-
 class CommonTestMixin_v4(CommonTestMixin):
 
     def test_leading_zeros(self):
@@ -119,7 +118,7 @@
 
     def test_bad_packed_length(self):
         def assertBadLength(length):
-            addr = bytes(length)
+            addr = b'\0' * length
             msg = "%r (len %d != 4) is not permitted as an IPv4 address"
             with self.assertAddressError(re.escape(msg % (addr, length))):
                 self.factory(addr)
@@ -139,11 +138,11 @@
         self.assertInstancesEqual(3232235521, "::c0a8:1")
 
     def test_packed(self):
-        addr = bytes(12) + bytes.fromhex("00000000")
+        addr = b'\0'*12 + bytes.fromhex("00000000")
         self.assertInstancesEqual(addr, "::")
-        addr = bytes(12) + bytes.fromhex("c0a80001")
+        addr = b'\0'*12 + bytes.fromhex("c0a80001")
         self.assertInstancesEqual(addr, "::c0a8:1")
-        addr = bytes.fromhex("c0a80001") + bytes(12)
+        addr = bytes.fromhex("c0a80001") + b'\0'*12
         self.assertInstancesEqual(addr, "c0a8:1::")
 
     def test_negative_ints_rejected(self):
@@ -158,7 +157,7 @@
 
     def test_bad_packed_length(self):
         def assertBadLength(length):
-            addr = bytes(length)
+            addr = b'\0' * length
             msg = "%r (len %d != 16) is not permitted as an IPv6 address"
             with self.assertAddressError(re.escape(msg % (addr, length))):
                 self.factory(addr)
@@ -477,6 +476,56 @@
 class NetworkTestCase_v4(BaseTestCase, NetmaskTestMixin_v4):
     factory = ipaddress.IPv4Network
 
+    def test_subnet_of(self):
+        # containee left of container
+        self.assertFalse(
+            self.factory('10.0.0.0/30').subnet_of(
+                self.factory('10.0.1.0/24')))
+        # containee inside container
+        self.assertTrue(
+            self.factory('10.0.0.0/30').subnet_of(
+                self.factory('10.0.0.0/24')))
+        # containee right of container
+        self.assertFalse(
+            self.factory('10.0.0.0/30').subnet_of(
+                self.factory('10.0.1.0/24')))
+        # containee larger than container
+        self.assertFalse(
+            self.factory('10.0.1.0/24').subnet_of(
+                self.factory('10.0.0.0/30')))
+
+    def test_supernet_of(self):
+        # containee left of container
+        self.assertFalse(
+            self.factory('10.0.0.0/30').supernet_of(
+                self.factory('10.0.1.0/24')))
+        # containee inside container
+        self.assertFalse(
+            self.factory('10.0.0.0/30').supernet_of(
+                self.factory('10.0.0.0/24')))
+        # containee right of container
+        self.assertFalse(
+            self.factory('10.0.0.0/30').supernet_of(
+                self.factory('10.0.1.0/24')))
+        # containee larger than container
+        self.assertTrue(
+            self.factory('10.0.0.0/24').supernet_of(
+                self.factory('10.0.0.0/30')))
+
+    def test_subnet_of_mixed_types(self):
+        with self.assertRaises(TypeError):
+            ipaddress.IPv4Network('10.0.0.0/30').supernet_of(
+                ipaddress.IPv6Network('::1/128'))
+        with self.assertRaises(TypeError):
+            ipaddress.IPv6Network('::1/128').supernet_of(
+                ipaddress.IPv4Network('10.0.0.0/30'))
+        with self.assertRaises(TypeError):
+            ipaddress.IPv4Network('10.0.0.0/30').subnet_of(
+                ipaddress.IPv6Network('::1/128'))
+        with self.assertRaises(TypeError):
+            ipaddress.IPv6Network('::1/128').subnet_of(
+                ipaddress.IPv4Network('10.0.0.0/30'))
+
 
 class NetmaskTestMixin_v6(CommonTestMixin_v6):
     """Input validation on interfaces and networks is very similar"""
@@ -540,6 +589,42 @@
 class NetworkTestCase_v6(BaseTestCase, NetmaskTestMixin_v6):
     factory = ipaddress.IPv6Network
 
+    def test_subnet_of(self):
+        # containee left of container
+        self.assertFalse(
+            self.factory('2000:999::/56').subnet_of(
+                self.factory('2000:aaa::/48')))
+        # containee inside container
+        self.assertTrue(
+            self.factory('2000:aaa::/56').subnet_of(
+                self.factory('2000:aaa::/48')))
+        # containee right of container
+        self.assertFalse(
+            self.factory('2000:bbb::/56').subnet_of(
+                self.factory('2000:aaa::/48')))
+        # containee larger than container
+        self.assertFalse(
+            self.factory('2000:aaa::/48').subnet_of(
+                self.factory('2000:aaa::/56')))
+
+    def test_supernet_of(self):
+        # containee left of container
+        self.assertFalse(
+            self.factory('2000:999::/56').supernet_of(
+                self.factory('2000:aaa::/48')))
+        # containee inside container
+        self.assertFalse(
+            self.factory('2000:aaa::/56').supernet_of(
+                self.factory('2000:aaa::/48')))
+        # containee right of container
+        self.assertFalse(
+            self.factory('2000:bbb::/56').supernet_of(
+                self.factory('2000:aaa::/48')))
+        # containee larger than container
+        self.assertTrue(
+            self.factory('2000:aaa::/48').supernet_of(
+                self.factory('2000:aaa::/56')))
+
 
 class FactoryFunctionErrors(BaseTestCase):
 
@@ -1405,14 +1490,35 @@
                         ipaddress.ip_address('::2'))
 
     def testInterfaceComparison(self):
-        self.assertTrue(ipaddress.ip_interface('1.1.1.1') <=
-                        ipaddress.ip_interface('1.1.1.1'))
-        self.assertTrue(ipaddress.ip_interface('1.1.1.1') <=
-                        ipaddress.ip_interface('1.1.1.2'))
-        self.assertTrue(ipaddress.ip_interface('::1') <=
-                        ipaddress.ip_interface('::1'))
-        self.assertTrue(ipaddress.ip_interface('::1') <=
-                        ipaddress.ip_interface('::2'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.1/24') ==
+                        ipaddress.ip_interface('1.1.1.1/24'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.1/16') <
+                        ipaddress.ip_interface('1.1.1.1/24'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.1/24') <
+                        ipaddress.ip_interface('1.1.1.2/24'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.2/16') <
+                        ipaddress.ip_interface('1.1.1.1/24'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.1/24') >
+                        ipaddress.ip_interface('1.1.1.1/16'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.2/24') >
+                        ipaddress.ip_interface('1.1.1.1/24'))
+        self.assertTrue(ipaddress.ip_interface('1.1.1.1/24') >
+                        ipaddress.ip_interface('1.1.1.2/16'))
+
+        self.assertTrue(ipaddress.ip_interface('::1/64') ==
+                        ipaddress.ip_interface('::1/64'))
+        self.assertTrue(ipaddress.ip_interface('::1/64') <
+                        ipaddress.ip_interface('::1/80'))
+        self.assertTrue(ipaddress.ip_interface('::1/64') <
+                        ipaddress.ip_interface('::2/64'))
+        self.assertTrue(ipaddress.ip_interface('::2/48') <
+                        ipaddress.ip_interface('::1/64'))
+        self.assertTrue(ipaddress.ip_interface('::1/80') >
+                        ipaddress.ip_interface('::1/64'))
+        self.assertTrue(ipaddress.ip_interface('::2/64') >
+                        ipaddress.ip_interface('::1/64'))
+        self.assertTrue(ipaddress.ip_interface('::1/64') >
+                        ipaddress.ip_interface('::2/48'))
 
     def testNetworkComparison(self):
         # ip1 and ip2 have the same network address
@@ -1948,4 +2054,4 @@
 
 
 if __name__ == '__main__':
-    unittest.main()
+    unittest.main()
\ No newline at end of file