Is centralizer a normal subgroup?
37971
Prove that the center of a group is a normal subgroup
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
123610
How to show that the commutator subgroup is a normal subgroup
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
111375
Normality of subgroups and Sylow groups under homomorphisms...
139611
Can a normal subgroup of a finite nonabelian group be nonabelian?
61373
A normal subgroup that is not a characteristic
115182
Centre of symmetric group algebra
6134
Some Subgroup of Dihedral Group is Normal
105610
Normalizer of upper triangular group in ${\rm GL}(n,F)$
35602
If a subgroup has smallest prime index, then it is normal
38095
The Commutator Subgroup is Normal.
142413
Normal Subgroups of $SU(n)$
63780
to show characteristic subgroup is normal in G
94999
A subgroup with an index of 2 is normal to the group.
51747
Showing that the intersection of all subgroups of order $n$ is normal