Finite Group Databasebeta

← C₅×C₂₃×C₃₁⋊C₃ #24924121

Subgroups — C₅×C₂₃×C₃₁⋊C₃ #24924121

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, complemented, Hall
2	C₂₃×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃₁⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₃	—	31	1	no	maximal, Hall
6	C₅×C₃₁	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
7	C₅×C₂₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃₁⋊C₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₃	—	31	1	no	Hall
10	C₃₁	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
11	C₂₃	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	—	31	1	no	Hall
13	C₅	C₂₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₂₃

Complements

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

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