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2-subnormal subgroup, Abelian normal subgroup, Almost normal subgroup, Ascendant subgroup, Central factor, Central subgroup, Image-closed characteristic subgroup, Image-closed fully invariant subgroup, Nearly normal subgroup, Normal Sylow subgroup, Normal subgroup, Permutable subgroup, Permutably complemented subgroup, Pronormal subgroup, Self-normalizing subgroup, Subgroup, Sylow subgroup, Transitively normal subgroup, Verbal subgroup