If $G$ is a group of order $pq$, where $p$ and $q$ are distinct primes, prove that $G$ has subgroups of order $p$ and $q$?
104080
Group with order $pq$ has subgroups of order $p$ and $q$
103423
Normal subgroup where G has order prime
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
145563
In an abelian group, the elements of finite order form a subgroup.
51352
Subgroups of a finite abelian group
50157
order of a sylow p-subgroup
62017
Distinct Sylow P subgroups
122970
A question on $p$-groups, and order of its commutator subgroup.
148904
Groups of order $p^3$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
38853
Cyclic group of prime order
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
70001
Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
3439
Other proofs that subgroups of $A_5$ have order at most 12