Group Theory innG is normal subgroup of autG
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
37379
Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$.
6134
Some Subgroup of Dihedral Group is Normal
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
58694
Which non-abelian finite groups have the property that every subgroup is normal?
151699
Group of inner automorphisms of a group $G$
137691
What are the self-normalizing subgroups of $S_n$?
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
152603
Group isomorphic to its automorphism group
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
125244
Equivalent definitions of normal subgroups