Prove a subgroup is normal
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
51747
Showing that the intersection of all subgroups of order $n$ is normal
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
20386
Any subgroup of index $p$ in a $p$-group is normal.
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
61373
A normal subgroup that is not a characteristic
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
125498
Check whether subgroup is normal in $ S_4$
97928
Normal subgroup of a normal subgroup
103423
Normal subgroup where G has order prime
38095
The Commutator Subgroup is Normal.
122266
equivalent definition of normal subgroup
137691
What are the self-normalizing subgroups of $S_n$?
103002
Group equals union of two subgroups
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
125244
Equivalent definitions of normal subgroups