example for not being a subgroup
124732
Finding a nonempty subset that is not a subgroup
61373
A normal subgroup that is not a characteristic
140563
Concrete examples of group actions.
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
113925
Normal Subgroup Counterexample
58076
Subgroup generated by a set
157330
Showing the image of a subgroup is a subgroup.
99309
Groups of order $n^2$ that have no subgroup of order $n$
91021
Torsion elements of a group aren't necessarily a subgroup
135701
An example of a group such that $G \cong G \times G$
122266
equivalent definition of normal subgroup
149029
3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
150207
Non isomorphic subgroups of cyclic groups
128428
Why is the set of commutators not a subgroup?