Subgroup

Template:GroupsIn group theory, a branch of mathematics, given a group $G$ under a binary operation, a subset $H$ of $G$ is called a subgroup of $G$ if the elements $H$ also forms a group under the binary operation.

The situation could arise in which the subset $H$ does not comply with the binary operation. In that case, H would not be a subgroup.

For example, the even numbers are a subgroup of the integers, with addition as the binary operation.