If G is a group of order $pq$, where $p$ and $q$ are primes. How do I prove that any nontrivial subgroup of $G$ must be cyclic?
79995
G is group of order pq, pq are primes
54195
Do groups of prime order have one subgroup?
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
138108
If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.
22301
If $G$ has no proper subgroup, then $G$ is cyclic of prime order
8746
Groups of order $pq$ without using Sylow theorems
34552
Proper subgroups of non-cyclic p-group cannot be all cyclic?
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
65968
Prove that any two cyclic groups of the same order are isomorphic?
107716
Show that $G$ is cyclic
88440
Is G a CLT group if its order is product of distinct prime?
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
104080
Group with order $pq$ has subgroups of order $p$ and $q$
50762
If $S_n$ has cyclic subgroups of these orders or not?