Intersection of normal subgroups is normal
70373
Intersection of normal subgroups proof
99999
A question on identifying normal subgroups of $S_4$
44165
the image of normal subgroups
125244
Equivalent definitions of normal subgroups
99114
Subgroups of index 3 are normal
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
19720
A normal subgroup intersects the center of the $p$-group nontrivially
113925
Normal Subgroup Counterexample
102622
K is a subgroup of G. Show that K is not a normal subgroup
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
139096
$|AxA|$ is a constant implies normal subgroup
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
14666
What are the non-trivial normal subgroups of $O(3)$?
35602
If a subgroup has smallest prime index, then it is normal
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q