Intermediately conjugacy-closed-to-retract

Definition
A subgroup of a group is termed intermediately conjugacy-closed-to-retract if, whenever it is a defining ingredient::conjugacy-closed subgroup in any intermediate subgroup, it is also a defining ingredient::retract of that intermediate subgroup, i.e., it has a normal complement in the intermediate subgroup.

Stronger properties

 * Weaker than::Sylow subgroup:
 * Weaker than::Retract