does a group of order $pqr$ where $p$,$q$ and $r$ are primes and $p<q<r$ always have a normal subgroup of order $qr$?
113357
Groups of order $pqr$ and their normal subgroups
104080
Group with order $pq$ has subgroups of order $p$ and $q$
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
70001
Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
15706
"Every Group of order $216$ contains a normal subgroup of order $27$ or $9$
63499
Groups of prime squared order
110390
Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
20386
Any subgroup of index $p$ in a $p$-group is normal.
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?
7108
Normal subgroup of prime index
38853
Cyclic group of prime order
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
51196
A group of order $p^2q^2$ is never simple
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
88440
Is G a CLT group if its order is product of distinct prime?