Show that a subgroup $K$ is normal
29453
An epimorphism from $S_{4}$ to $S_{3}$ having the kernel isomorphic to Klein four-group
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
45580
Intersection of conjugate subgroups is normal
38095
The Commutator Subgroup is Normal.
125244
Equivalent definitions of normal subgroups
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
20386
Any subgroup of index $p$ in a $p$-group is normal.
54911
The preimage of a normal subgroup under a group homomorphism is normal
22444
Normal subgroups of dihedral groups
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
103423
Normal subgroup where G has order prime
11731
Normal subgroups of $S_4$
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
51747
Showing that the intersection of all subgroups of order $n$ is normal
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.