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1-automorphism-invariant subgroup, 2-subnormal subgroup, 3-subnormal subgroup, 4-subnormal subgroup, Abelian normal subgroup, C-closed normal subgroup, C-closed subgroup, Characteristic subgroup of group of prime power order, Completely distinguished subgroup, Cyclonormal subgroup, Direct projection-invariant subgroup, Fixed-point subgroup of a subgroup of the automorphism group, Intersection of Sylow subgroups, Intersection-transitively automorph-conjugate subgroup, Large subgroup, Malnormal subgroup, Quasiautomorphism-invariant subgroup, Retraction-invariant subgroup, Subgroup-cofactorial automorphism-invariant subgroup, Transfer-closed fully invariant subgroup