Composition subgroup

Symbol-free definition
A subgroup of a group is termed a composition subgroup if there is a composition series starting at the subgroup and ending at the whole group.

Stronger properties

 * Sub-(maximal normal) subgroup:

Weaker properties

 * Serial subgroup:

Metaproperties
Any composition subgroup of a composition subgroup is a composition subgroup -- we can concatenate the two composition series.