Quotient group with normal subgroup dividing the order of another group
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
50157
order of a sylow p-subgroup
43651
Normal subgroups and factor groups
115746
Find the order of a subgroup of $S_5$ generated by two elements
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
63499
Groups of prime squared order
3907
Abelian quotient group
80186
How to show that $K\leq S_4$ is a normal subgroup?
142413
Normal Subgroups of $SU(n)$
134353
A group of order $108$ has a proper normal subgroup of order $\geq 6$.
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
124237
Group equals union of three subgroups
7973
Groups of order $pq$ have a proper normal subgroup
110390
Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.