Quotient-subisomorph-containing subgroup

Definition
The following are some equivalent definitions of quotient-subisomorph-containing subgroup.

Weaker properties

 * Stronger than::Weakly image-closed fully invariant subgroup
 * Stronger than::Fully invariant subgroup
 * Stronger than::Strictly characteristic subgroup
 * Stronger than::Characteristic subgroup

Related properties

 * Homomorph-containing subgroup