Finite Group Databasebeta

← C₅×C₁₁×D₂₈₁ #44525612

Subgroups — C₅×C₁₁×D₂₈₁ #44525612

Order 30910.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₈₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₂₈₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₂₈₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₂₈₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	D₂₈₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₂₈₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×C₁₁	—	281	1	no	maximal, Hall
9	C₅×C₁₁	D₂₈₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁	—	281	1	no	Hall
11	C₁₁	C₅×D₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	281	1	no	Hall
13	C₅	C₁₁×D₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	281	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₂₈₁
commutator, cosocle, hypocenter	C₂₈₁	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₂₈₁	C₂
LCS	G ▷ C₂₈₁
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₂₈₁	C₂	semidirect
2. C₁₁×D₂₈₁	C₅	direct (N × H)
3. C₁₁×C₂₈₁	C₂×C₅	semidirect
4. C₅×D₂₈₁	C₁₁	direct (N × H)
5. C₅×C₂₈₁	C₂×C₁₁	semidirect
6. D₂₈₁	C₅×C₁₁	direct (N × H)
7. C₂₈₁	C₂×C₅×C₁₁	semidirect
9. C₅×C₁₁	D₂₈₁	direct (N × H)
11. C₁₁	C₅×D₂₈₁	direct (N × H)
13. C₅	C₁₁×D₂₈₁	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×C₁₁×C₂₈₁	2
C₁₁×D₂₈₁	5
C₅×D₂₈₁	11
C₂×C₅×C₁₁	281