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Abelian normal subgroup, Central factor, Central subgroup, Complemented central factor, Complemented normal subgroup, Conjugacy-closed normal subgroup, Direct factor, Hereditarily normal subgroup, Homomorph-containing subgroup, Intermediately characteristic subgroup, Intermediately endomorphism kernel, Isomorph-containing subgroup, Isomorph-free subgroup, Normal Sylow subgroup, Normal subgroup having no nontrivial homomorphism to its quotient group, SCAB-subgroup, Transitively normal subgroup