Definition:Subgroup

If $$G$$ is a group and $$H \subseteq G$$ where $$H$$ is also a group under the operation of $$G,$$ then $$H$$ is called a subgroup of $$G$$. This is represented symbolically as $$H \le G$$.

One may verify if a subset of a group $$G$$ is a subgroup by using either the one-step or two-step subgroup test or by checking for each individual group property.