Prove that $Q_8$ has a subgroup $H$ of order $2$ and $H$ is normal in $Q_8$
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
15706
"Every Group of order $216$ contains a normal subgroup of order $27$ or $9$
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
28722
Prove that $H$ is a abelian subgroup of odd order
146760
Prove that H is a subgroup of G
53409
Show group of order $4n + 2$ has a subgroup of index 2.
75568
Subgroup of index $2$ is Normal
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
12502
The center of a non-Abelian group of order 8
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
80186
How to show that $K\leq S_4$ is a normal subgroup?
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists