$|G| > 1$ and not prime implies existence of a subgroup other than two trivial subgroups
88344
Order of a group and subsequent subgroups
41231
Subgroups of (Z,+) of order n
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
139096
$|AxA|$ is a constant implies normal subgroup
133770
Subgroups of finite abelian groups.
132704
If G is not commutative, then is there always a subgroup that is not a normal subgroup?
80381
Groups with "few" subgroups
135701
An example of a group such that $G \cong G \times G$
27436
Does $G\cong G/H$ imply that $H$ is trivial?
103423
Normal subgroup where G has order prime
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
59902
Example of $2$ non-isomorphic groups that have the same quotients
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
22301
If $G$ has no proper subgroup, then $G$ is cyclic of prime order