subgroup

[suhb-groop]
noun
1.
a subordinate group; a division of a group.
2.
Chemistry. a division of a group in the periodic table.
3.
Mathematics. a subset of a group that is closed under the group operation and in which every element has an inverse in the subset.

Origin:
1835–45; sub- + group

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World English Dictionary
subgroup (ˈsʌbˌɡruːp)
 
n
1.  a distinct and often subordinate division of a group
2.  a mathematical group whose members are members of another group, both groups being subject to the same rule of combination

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
The subgroup of people with mild cognitive impairment also improved.
Meanwhile, neither subgroup of rats on low-fat chow gained any significant excess weight.
It is a subgroup of the isometry group of the space concerned.
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