If $H$ is a normal subgroup of group $G$ of odd order and $|H|=5$ . show that $H \subseteq Z(G)$
58205
$ N $ normal in a finite group $ G $, $ |N| = 5 $ and $ |G| $ odd. Why is $ N \subseteq Z(G) $?
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
70373
Intersection of normal subgroups proof
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
34902
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
28722
Prove that $H$ is a abelian subgroup of odd order
80186
How to show that $K\leq S_4$ is a normal subgroup?
65972
Show that a group of order $108$ has a normal subgroup of order $9$ or $27$.
97928
Normal subgroup of 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 $n!$
142413
Normal Subgroups of $SU(n)$
113357
Groups of order $pqr$ and their normal subgroups
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
51747
Showing that the intersection of all subgroups of order $n$ is normal
44165
the image of normal subgroups
11731
Normal subgroups of $S_4$
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$