subgroup

nouns

a distinct and often subordinate group within a group
is a type of (narrower)
any number of entities (members) considered as a unit
(mathematics) a subset (that is not empty) of a mathematical group
domain category
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
is a type of (narrower)
a set that is closed, associative, has an identity element and every element has an inverse