Normalizer of some subgroup of a group is necessarily normal subgroup of the group.
87454
Counterexample for the normalizer being a normal subgroup
137691
What are the self-normalizing subgroups of $S_n$?
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
44165
the image of normal subgroups
125498
Check whether subgroup is normal in $ S_4$
86872
normalized subgroup by another subgroup
157819
Every group of order $56$ has a proper non - trivial normal subgroup?
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
54911
The preimage of a normal subgroup under a group homomorphism is normal
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
63780
to show characteristic subgroup is normal in G
105610
Normalizer of upper triangular group in ${\rm GL}(n,F)$