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Central factor is not finite-intersection-closed, Central factor is not quotient-transitive, Characteristicity does not satisfy image condition, Characteristicity does not satisfy intermediate subgroup condition, Characteristicity is not finite-relative-intersection-closed, Conjugacy-closedness is not join-closed, Direct factor is not upper join-closed, Full invariance does not satisfy intermediate subgroup condition, Intermediate characteristicity is not transitive, Isomorph-freeness is not transitive, Lattice-complemented is not transitive, Marginality does not satisfy intermediate subgroup condition, Normality is not transitive, Permutably complemented does not satisfy transfer condition, Permutably complemented is not finite-intersection-closed, Permutably complemented is not transitive, Pronormality is not centralizer-closed, Transitive normality is not quotient-transitive