Subgroup with finite index contains a normal group
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
48273
If a maximal subgroup is normal, it has prime index
61373
A normal subgroup that is not a characteristic
97928
Normal subgroup of a normal subgroup
15630
Normal subgroup of prime order is characteristic
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
123677
Normal subgroups of infinite symmetric group
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
115204
Show that SO(n) is a normal subgroup of O(n)
51352
Subgroups of a finite abelian group
113925
Normal Subgroup Counterexample
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
47731
Intersection of all $p$-Sylow subgroups is normal
139096
$|AxA|$ is a constant implies normal subgroup
70373
Intersection of normal subgroups proof
35602
If a subgroup has smallest prime index, then it is normal
6134
Some Subgroup of Dihedral Group is Normal