Group in which every characteristic subgroup is fully invariant

Definition
A group in which every characteristic subgroup is fully characteristic is a group with the property that every characteristic subgroup of it is fully characteristic -- it is invariant under all endomorphisms of the group.

Stronger properties

 * Weaker than::Simple group
 * Weaker than::Characteristically simple group
 * Weaker than::Abelian group whose automorphisms additive generate its endomorphism ring
 * Weaker than::Group in which every normal subgroup is fully invariant