Explore Subgroup on MathWorld

A subgroup is a subset of a mathematical group that is also a group.

Subgroup is a college-level concept that would be first encountered in an abstract algebra course covering group theory.


Group: A mathematical group is a set of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property.
Subset: A subset is a portion of a set. Subsets can also consist of the entire set or be empty.

Classroom Articles on Group Theory

  • Abelian Group
  • Group Theory
  • Cyclic Group
  • Normal Subgroup
  • Dihedral Group
  • Simple Group
  • Finite Group
  • Symmetric Group
  • Group Action
  • Symmetry Group
  • Group Representation

  • Classroom Articles on Abstract Algebra (Up to College Level)

  • Abstract Algebra
  • Gaussian Integer
  • Algebra
  • Ideal
  • Algebraic Number
  • Isomorphism
  • Boolean Algebra
  • Quaternion
  • Field
  • Ring
  • Finite Field