Composition Series

Every Finite Group $G$ of order greater than one possesses a finite series of Subgroups, called a composition series, such that

$$I\subset H_s \subset \ldots \subset H_2 \subset H_1 \subset G,$$

where $H_{i+1}$ is a maximal subgroup of $H_i$. The Quotient Groups $G/H_1$, $H_1/H_2$, ..., $H_{s-1}/H_s$, $H_s$ 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.