Group in which every nontrivial normal subgroup contains a minimal normal subgroup

Definition
A group in which every nontrivial normal subgroup contains a minimal normal subgroup is a group with the property that any nontrivial normal subgroup of the group contains a minimal normal subgroup.

Stronger properties

 * Weaker than::Finite group
 * Weaker than::Artinian group
 * Weaker than::Group satisfying minimum condition on normal subgroups