Every Finite Group of order greater than one possesses a finite series of Subgroups, called acomposition series, such that
where is a maximal subgroup of . The Quotient Groups , , ...,, are called composition quotient groups.See also Finite Group, Jordan-Hölder Theorem, Quotient Group, Subgroup
References
Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 26, 1993.