Normal subgroup-lattice automorphism-invariant subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is a normal subgroup-lattice automorphism-invariant subgroup if $$H$$ is a normal subgroup of $$G$$ and is invariant under all the lattice automorphisms of the lattice of normal subgroups of $$G$$.

Related properties

 * Lattice automorphism-invariant subgroup