There is no simple group of order $pq^2$.
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
15341
Non-abelian finite group in which more than half of the elements have order $2$
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
15526
Question on groups of order $pq$
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
49366
Group of order 30 can't be simple
49162
Classify all groups with order $pq$, $p$ is not equal to $q$
109060
Group containing no subgroup of index 2
157853
$Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
129830
A group with no proper non-trivial subgroups
52089
Group of $2n$ elements, $n$ odd, is not simple
151029
The number of non normal subgroups of a group cannot be $1$?
118022
Show that a group of order $180$ is not simple.
101735
A finite $p$-group cannot be simple unless it has order $p$
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
41572
$G/Z$ cannot be isomorphic to quaternion group
111703
If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple