Subgroup Meaning
/ˈsʌbˌɡɹuːp/Definition, CEFR level B1, pronunciation, examples, and quiz.
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Definition
nounA group within a larger group; a group whose members are some, but not all, of the members of a larger group.
nounA subset H of a group G that is itself a group and has the same binary operation as G.
Sentence Examples
Every subgroup of an abelian group is abelian.
The group has only one subgroup.
CEFR Practice Quiz
Within the class, a small ____ of students preferred math over science.
CEFR Practice Quiz (Alternate)
Researchers were divided into a small ____ to focus specifically on the environmental impact study.
Word Origin & History
From sub- + group.
Literary Quotations & Historical Citations
"The most important application of dysprosium and terbium, which belong to a subgroup known as the heavy rare earths, is in devices called neodymium boron magnets, or neo magnets for short."
— 2025 July 18, Timothy McLaughlin, “A Rebel Army Is Building a Rare-Earth Empire on China's Border. The Kachin Independence Organization fought for decades in obscurity. Now it's supplying essential minerals to manufacturers around the world”, in Bloomberg Businessweek, archived from the original on 18 Jul 2025:
"Much of the information about a group can be gleaned from a study of its subgroups. For these reasons it is important to study the subgroup structure of the almost simple groups, and in particular their maximal subgroups."
— 1990, Peter B. Kleidman, Martin W. Liebeck, The Subgroup Structure of the Finite Classical Groups, Cambridge University Press, page 1:
"A subgroup H of an algebraic group G is called algebraic if H is an algebraic subvariety of G. Algebraic subgroups defined over k (as algebraic subvarieties) are called k-subgroups. An algebraic subgroup of an algebraic group is called k-closed or closed over k (resp. k-defined or defined over k) if it is k-closed (resp. k-defined) as an algebraic subvariety."
— 1991, Gregori A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, page 13:
"This is applied in Chapter 9 to prove the first congruence subgroup theorem, which asserts that g.z = z for all z in the center of the Drinfel'd double D(H) and all g in the principal congruence subgroup."
— 2012, Yorck Sommerhäuser, Yongchang Zhu, Hopf Algebras and Congruence Subgroups, American Mathematical Society, page 3:
Explore More B1 Vocabulary Words
CEFR Practice Quiz
Within the class, a small ____ of students preferred math over science.
CEFR Practice Quiz (Alternate)
Researchers were divided into a small ____ to focus specifically on the environmental impact study.