In the mathematical subject known as group theory, given a group G under a binary operation *, we say that some subset H of G's a subgroup of G if H also forms a group under the operation *. More precisely, H's a subgroup of G if the restriction of * to H x H's a group operation on H. This's usually represented notationally by H ≤ G, read as "H's a subgroup of G". A proper subgroup of a group G's a subgroup H which's a proper subset of G (for example H ≠ G). The trivial subgroup of… (More on Subgroup)