Finite Group Databasebeta

← C₅×C₃₇×D₃₁ #26039739

Subgroups — C₅×C₃₇×D₃₁ #26039739

Order 11470.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₃₇	—	31	1	no	maximal, Hall
5	C₅×D₃₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₃₇	D₃₁	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₃₁	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃₇	—	31	1	no	Hall
9	D₃₁	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃₇	C₅×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	31	1	no	Hall
13	C₅	C₃₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₃₇	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₃₇	C₂	semidirect
2. C₃₇×D₃₁	C₅	direct (N × H)
3. C₃₁×C₃₇	C₂×C₅	semidirect
5. C₅×D₃₁	C₃₇	direct (N × H)
6. C₅×C₃₇	D₃₁	direct (N × H)
7. C₅×C₃₁	C₂×C₃₇	semidirect
9. D₃₁	C₅×C₃₇	direct (N × H)
10. C₃₇	C₅×D₃₁	direct (N × H)
11. C₃₁	C₂×C₅×C₃₇	semidirect
13. C₅	C₃₇×D₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₃₁×C₃₇	2
C₃₇×D₃₁	5
C₂×C₅×C₃₇	31
C₅×D₃₁	37