Complemented fully invariant subgroup

Definition
A subgroup of a group is termed a complemented fully invariant subgroup if it satisfies the following equivalent conditions:


 * 1) It is both a conjunction involving::permutably complemented subgroup  and a fully invariant subgroup.
 * 2) It is both a conjunction involving::lattice-complemented subgroup  and a fully invariant subgroup.
 * 3) It is both a complemented normal subgroup and a fully invariant subgroup.

Stronger properties

 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup
 * Weaker than::Fully invariant direct factor
 * Weaker than::Complemented homomorph-containing subgroup

Weaker properties

 * Stronger than::Fully invariant subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Normal subgroup
 * Stronger than::Complemented characteristic subgroup
 * Stronger than::Complemented normal subgroup