Group of order $108$ not simple using Sylow theorems on Sylow-$2$-subgroups
65972
Show that a group of order $108$ has a normal subgroup of order $9$ or $27$.
2731
Groups of even order have an element whose order is 2.
55719
Order of general- and special linear groups over finite fields.
90449
Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
108250
A group of order $595$ has a normal Sylow 17-subgroup.
8066
Sort-of-simple non-Hopfian groups
53409
Show group of order $4n + 2$ has a subgroup of index 2.
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
101735
A finite $p$-group cannot be simple unless it has order $p$
141458
How many subgroups or order 8 an abelian Group of order 72 can have
42096
Direct product of Sylow subgroups
112165
Classification of groups of order 12
152630
showing that a group of order 45 is abelian
52089
Group of $2n$ elements, $n$ odd, is not simple
90329
Prove there is no simple group of order $729$
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 $D_p$
76732
Number of non-isomorphic groups of order 21