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Abelian normal subgroup, Characteristic-potentially characteristic subgroup, Cofactorial automorphism-invariant subgroup, Complemented normal subgroup, Endomorphism kernel, Homomorph-containing subgroup, Intermediately characteristic subgroup, Intermediately endomorphism kernel, Isomorph-containing subgroup, Isomorph-free subgroup, Normal subgroup having no nontrivial homomorphism to its quotient group, Normal-extensible automorphism-invariant subgroup, Potentially fully invariant subgroup