Showing the group of Inner Automorphism are a normal subgroup of the Automorphisms
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
145809
Automorphism group of a lie algebra as a lie subgroup of $GL(\frak g)$
39866
Automorphism group of the quaternion group
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
7108
Normal subgroup of prime index
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
65900
Show that a finite group with certain automorphism is abelian
142413
Normal Subgroups of $SU(n)$
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
97928
Normal subgroup of a normal subgroup
146278
Automorphism group of direct product of groups
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
49257
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
152603
Group isomorphic to its automorphism group
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
44165
the image of normal subgroups