A group of order $pqr$ (primes $p > q > r$) has a subgroup of order $qr$
4402
Group of order $pqr$, $p < q < r$ primes
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 $d$.
102429
There are 2 groups of order 6 (up to isomorphism)
125640
Group of order $p^2$ is abelian.
38853
Cyclic group of prime order
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
39976
If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
57427
Group of order $8p$ is solvable, for any prime $p$
123796
Order of automorphism group of a $p$-group is divisible by $p$.
83710
Order of a homomorphism of groups
75670
Questions around the number of subgroups of a $p$-group
61550
Existence of elements of order $p^k$ in a finite group
90591
On the group of all complex roots of unity whose orders are powers of $p$, prime number
13734
Show that every group of prime order is cyclic
39469
If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
14895
Reference for the subgroup structure of $\rm{PSL}_2(q)$