20D10 4 20D15 2 20D30 2 05C25 1 20D20 1 20D35 1 20E15 1 20E34 1 20F19,20F22 1 Finite soluble group; \(PT\)-group; permutable subgroup; complete graph 1 Hall \(S\)-permutably embedded subgroup 1 PST-group 1 S-permutable subgroup 1 Sylow subgroup 1 \(P\sigma T\)-group 1 \(S\)-permutable closure 1 \(S\)-permutable subgroup 1 \(\sigma\)-nilpotent group 1 \(\sigma\)-permutable subgroup 1 \(\sigma\)-soluble group 1 abnormal subgroups 1 contranormal subgroup 1 finite group 1 locally graded group 1 maximal subgroup 1 normal subgroups 1 permutable subgroups 1 pronormal subgroups 1 radical group 1 seminormal subgroup 1