Check whether subgroup is normal in $ S_4$
99999
A question on identifying normal subgroups of $S_4$
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
113925
Normal Subgroup Counterexample
2174
Proving that HK is a subgroup when K is normal
48273
If a maximal subgroup is normal, it has prime index
76943
Existence of subgroup of order six in $A_4$
99114
Subgroups of index 3 are normal
54911
The preimage of a normal subgroup under a group homomorphism is normal
14666
What are the non-trivial normal subgroups of $O(3)$?
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
94999
A subgroup with an index of 2 is normal to the group.
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
57883
Example of a Subgroup That Is Not Normal
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
57227
Maximal normal $\pi$-subgroups and torsion subgroups
70373
Intersection of normal subgroups proof