diff --git a/src/sage/groups/libgap_wrapper.pyx b/src/sage/groups/libgap_wrapper.pyx
index edcd50dfa4f..d2305a655b4 100644
--- a/src/sage/groups/libgap_wrapper.pyx
+++ b/src/sage/groups/libgap_wrapper.pyx
@@ -345,6 +345,39 @@ class ParentLibGAP(SageObject):
         """
         return self._libgap._repr_()
 
+    def minimal_normal_subgroups(self):
+        """
+        Return the nontrivial minimal normal subgroups ``self``.
+
+        EXAMPLES::
+
+            sage: SL(2,GF(49)).minimal_normal_subgroups()
+            [Subgroup with 1 generators (
+             [6 0]
+             [0 6]
+             ) of Special Linear Group of degree 2 over Finite Field in z2 of size 7^2]
+        """
+        return [self._subgroup_constructor(gap_subgroup)
+                for gap_subgroup in self._libgap.MinimalNormalSubgroups()]
+
+    def maximal_normal_subgroups(self):
+        """
+        Return the maximal proper normal subgroups of ``self``.
+
+        This raises an error if `G/[G, G]` is infinite, yielding infinitely
+        many maximal normal subgroups.
+
+        EXAMPLES::
+
+            sage: SL(2,GF(49)).minimal_normal_subgroups()
+            [Subgroup with 1 generators (
+             [6 0]
+             [0 6]
+             ) of Special Linear Group of degree 2 over Finite Field in z2 of size 7^2]
+        """
+        return [self._subgroup_constructor(gap_subgroup)
+                for gap_subgroup in self._libgap.MaximalNormalSubgroups()]
+
     @cached_method
     def gens(self):
         """
diff --git a/src/sage/groups/perm_gps/permgroup.py b/src/sage/groups/perm_gps/permgroup.py
index 4de29a5c8e0..208758282b2 100644
--- a/src/sage/groups/perm_gps/permgroup.py
+++ b/src/sage/groups/perm_gps/permgroup.py
@@ -4116,6 +4116,37 @@ def isomorphism_type_info_simple_group(self):
         else:
             raise TypeError("group must be simple")
 
+    def minimal_normal_subgroups(self):
+        """
+        Return the nontrivial minimal normal subgroups ``self``.
+
+        EXAMPLES::
+
+            sage: G = PermutationGroup([(1,2,3),(4,5)])
+            sage: G.minimal_normal_subgroups()
+            [Subgroup generated by [(4,5)] of (Permutation Group with generators [(4,5), (1,2,3)]),
+             Subgroup generated by [(1,2,3)] of (Permutation Group with generators [(4,5), (1,2,3)])]
+        """
+        return [self.subgroup(gap_group=gap_subgroup)
+                for gap_subgroup in self._libgap_().MinimalNormalSubgroups()]
+
+    def maximal_normal_subgroups(self):
+        """
+        Return the maximal proper normal subgroups of ``self``.
+
+        This raises an error if `G/[G, G]` is infinite, yielding infinitely
+        many maximal normal subgroups.
+
+        EXAMPLES::
+
+            sage: G = PermutationGroup([(1,2,3),(4,5)])
+            sage: G.maximal_normal_subgroups()
+            [Subgroup generated by [(1,2,3)] of (Permutation Group with generators [(4,5), (1,2,3)]),
+             Subgroup generated by [(4,5)] of (Permutation Group with generators [(4,5), (1,2,3)])]
+        """
+        return [self.subgroup(gap_group=gap_subgroup)
+                for gap_subgroup in self._libgap_().MaximalNormalSubgroups()]
+
     ######################  Boolean tests #####################
 
     def is_abelian(self):