Finite Group Databasebeta

← C₃×C₅×C₂₃×C₃₁ #24924119

Subgroups — C₃×C₅×C₂₃×C₃₁ #24924119

Order 10695.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₃×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅×C₃₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₃₁	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₂₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₃₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₃	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
10	C₃₁	C₃×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₃	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₃×C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₅×C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×C₂₃×C₃₁	C₃	direct (N × H)
2. C₃×C₂₃×C₃₁	C₅	direct (N × H)
3. C₂₃×C₃₁	C₃×C₅	direct (N × H)
4. C₃×C₅×C₃₁	C₂₃	direct (N × H)
5. C₃×C₅×C₂₃	C₃₁	direct (N × H)
6. C₅×C₃₁	C₃×C₂₃	direct (N × H)
7. C₅×C₂₃	C₃×C₃₁	direct (N × H)
8. C₃×C₃₁	C₅×C₂₃	direct (N × H)
9. C₃×C₂₃	C₅×C₃₁	direct (N × H)
10. C₃₁	C₃×C₅×C₂₃	direct (N × H)
11. C₂₃	C₃×C₅×C₃₁	direct (N × H)
12. C₃×C₅	C₂₃×C₃₁	direct (N × H)
13. C₅	C₃×C₂₃×C₃₁	direct (N × H)
14. C₃	C₅×C₂₃×C₃₁	direct (N × H)