$H$ is a subgroup of $G$ with $\phi(H) = H$ $\forall \phi \in Aut(G) \Rightarrow $ $H$ is normal in $G$
63780
to show characteristic subgroup is normal in G
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
45277
The alternating group is a normal subgroup of the symmetric group
15630
Normal subgroup of prime order is characteristic
142413
Normal Subgroups of $SU(n)$
102622
K is a subgroup of G. Show that K is not a normal subgroup
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
23533
All subgroups normal $\implies$ abelian group
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
139096
$|AxA|$ is a constant implies normal subgroup
11043
A normal subgroup is the union of conjugacy classes.
103423
Normal subgroup where G has order prime
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
97928
Normal subgroup of a normal subgroup
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
11731
Normal subgroups of $S_4$