Class two normal subgroup

Definition
A subgroup of a group is termed a class two normal subgroup if it is a normal subgroup and is also nilpotent, with nilpotence class at most two.

Stronger properties

 * Weaker than::Abelian normal subgroup
 * Weaker than::Central subgroup
 * Weaker than::Critical subgroup
 * Weaker than::Class two characteristic subgroup
 * Weaker than::Commutator-in-center subgroup
 * Weaker than::Aut-abelian normal subgroup

Weaker properties

 * Stronger than::Nilpotent normal subgroup