Prove that $SO_2$ is a normal subgroup of $O_2$
115204
Show that SO(n) is a normal subgroup of O(n)
45580
Intersection of conjugate subgroups is normal
123677
Normal subgroups of infinite symmetric group
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
154878
Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
116786
normal subgroups of Alternating group
142938
Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
89508
Existence of normal subgroups for a group of order $36$
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
156154
Sylow 2 subgroups of S4
54911
The preimage of a normal subgroup under a group homomorphism is normal
51359
Prove that every subgroup of an abelian group is a normal subgroup.
49666
Generalization of index 2 subgroups are normal
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$