Proving a group of order 343 is not simple
101735
A finite $p$-group cannot be simple unless it has order $p$
15341
Non-abelian finite group in which more than half of the elements have order $2$
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
141188
Groups of order $56$
83710
Order of a homomorphism of groups
26449
$|G|=24$ prove that $G$ is not simple
15526
Question on groups of order $pq$
108309
An example of a non-abelian group of order $p^3$
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
132127
Proving a direct product of groups is a group
88344
Order of a group and subsequent subgroups
126113
Prove the existence of order 4 subgroups of order 8 groups
129157
An exercise on isomorphic groups of order 24
146760
Prove that H is a subgroup of G
104112
Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
52089
Group of $2n$ elements, $n$ odd, is not simple
12066
Group of order pq is not simple