### Definition of Subgroup

1. Noun. A distinct and often subordinate group within a group.

Generic synonyms: Group, Grouping
Specialized synonyms: Bench

2. Noun. (mathematics) a subset (that is not empty) of a mathematical group.
Category relationships: Math, Mathematics, Maths
Generic synonyms: Group, Mathematical Group

### Definition of Subgroup

1. n. A subdivision of a group, as of animals.

### Definition of Subgroup

1. Noun. A group within a larger group; a group whose members are some, but not all, of the members of a larger group. ¹

2. Noun. (group theory) A subset ''H'' of a group ''G'' that is itself a group and has the same binary operation as ''G''. ¹

3. Verb. To divide or classify into subgroups ¹

¹ Source: wiktionary.com

### Definition of Subgroup

1. to divide into smaller groups [v -ED, -ING, -S]

### Subgroup Pictures

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### Lexicographical Neighbors of Subgroup

 subgrantedsubgranteesubgranteessubgrantingsubgrantssubgranularsubgraphsubgraphssubgraywackesubgraywackes subgreywackesubgreywackessubgridsubgridssubgrosssubgroup (current term)subgroupedsubgroupingsubgroupingssubgroupoid subgroupoidssubgroupssubgumsubgumssubhadronicsubhallucinogenicsubhalosubhaloessubhalossubharmonic

### Literary usage of Subgroup

Below you will find example usage of this term as found in modern and/or classical literature:

1. The Encyclopedia Americana: A Library of Universal Knowledge (1918)
"These substitutions form a subgroup of G called the group belonging to 0. On the other hand, let H be a subgroup of G. Any rational function 0(ri, . ..."

2. An Introduction to the Theory of Groups of Finite Order by Harold Hilton (1908)
"But r = l (mod p), and hence 8 = 1 (mod p). Therefore the proof by induction holds good. Ex. 2. A subgroup H of order p&+l normal in G contains a subgroup ..."

3. Theory and Applications of Finite Groups by George Abram Miller, Hans Frederick Blichfeldt, Leonard Eugene Dickson (1916)
"If a 0-subgroup of the group G involves, a non-invariant subgroup or a non-invariant operator, this subgroup or operator cannot be transformed into all its ..."

4. Theory and Applications of Finite Groups by George Abram Miller, Hans Frederick Blichfeldt, Leonard Eugene Dickson (1916)
"Moreover, there is at least one maximal subgroup of G which does not include any given one of the independent generators of a particular set of independent ..."

5. Primitive Groups by William Albert Manning (1921)
"If H is invariant in a subgroup of G of order ah (a > 1) , H fixes ... If H is not an invariant subgroup of a subgroup of G, H displaces n — 1 letters. ..."

6. Guide to the Boris I. Nicolaevsky Collection in the Hoover Institution Archives by Anna M. Bourguina, Michael Jakobson (1989)
"The work was carried out by Michael Jakobson, who established subgroups 247-297 in accordance with modern archival principles and arranged each subgroup ..."

7. The Americana: A Universal Reference Library, Comprising the Arts and ...by Frederick Converse Beach, George Edwin Rines by Frederick Converse Beach, George Edwin Rines (1912)
"These substitutions form a subgroup of G called the group belonging to <j>. ... main R" for which the group of (i) is the palest invariant subgroup of G ..."