Prove, that $ K $ needn't be normal subgroup of $ G $
97928
Normal subgroup of a normal subgroup
58251
To show every sylow p-subgroup is normal in G
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
116737
An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
7973
Groups of order $pq$ have a proper normal subgroup
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
26449
$|G|=24$ prove that $G$ is not simple
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
44165
the image of normal subgroups
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
2174
Proving that HK is a subgroup when K 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 $G$.
99999
A question on identifying normal subgroups of $S_4$
11003
Proving that $G/N$ is an abelian group