2-subnormal subgroup, Almost normal subgroup, C-normal subgroup, C-subnormal subgroup, Central factor, Characteristic subgroup, Complemented normal subgroup, Conjugate-commensurable subgroup, Conjugate-comparable subgroup, Direct factor, Hypernormalized subgroup, Invariant random subgroup, Maximal normal subgroup, Modular subgroup, NE-subgroup, Nearly normal subgroup, Nilpotent quotient-by-core subgroup, Paranormal subgroup, Permutable subgroup, Polynormal subgroup, Pronormal subgroup, R-normal subgroup, Seminormal subgroup, Serial subgroup, Subgroup invariant under conjugation by a generating set, Subnormal subgroup, Transitively normal subgroup, Weakly normal subgroup, Weakly pronormal subgroup

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