Special subgroup of a group of order $n$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
50762
If $S_n$ has cyclic subgroups of these orders or not?
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
97928
Normal subgroup of a normal subgroup
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
134353
A group of order $108$ has a proper normal subgroup of order $\geq 6$.
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
113357
Groups of order $pqr$ and their normal subgroups
131516
Subgroup generated by n-th powers of elements
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
55719
Order of general- and special linear groups over finite fields.
7973
Groups of order $pq$ have a proper normal subgroup