A group $G$ of order $pq$ (for $p < q$), $p$ and $q$ are prime numbers. Prove: $G$ cannot have two different subgroups of order $q$.
7973
Groups of order $pq$ have a proper normal subgroup
152904
Groups with Same Number Of Elements and Subgroups
57427
Group of order $8p$ is solvable, for any prime $p$
8746
Groups of order $pq$ without using Sylow theorems
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
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?
113357
Groups of order $pqr$ and their normal subgroups
38853
Cyclic group of prime order
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
103423
Normal subgroup where G has order prime
19016
Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
4402
Group of order $pqr$, $p < q < r$ primes
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
122970
A question on $p$-groups, and order of its commutator subgroup.
3213
There exists only two groups of order $p^2$ up to isomorphism.