Subgroups — C₃×C₃⋊(D₂₈₁⋊C₅) #38760613

Order 25290.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₈₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(D₂₈₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₂₈₁⋊C₅	—	3	1	no	maximal
4	C₃×D₈₄₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₂₈₁⋊C₅	—	2	1	no	—
6	C₃×C₂₈₁⋊C₅	D₃	1	1	yes	characteristic, complemented
7	C₃×C₂₈₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₂₈₁⋊C₅	—	3	1	no	Hall
9	C₃²×C₂₈₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₈₄₃	C₃×C₅	1	1	yes	characteristic, complemented
11	C₃×D₂₈₁	—	3	1	no	—
12	C₂₈₁⋊C₅	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₂₈₁	—	2	1	no	—
14	C₃×C₂₈₁	C₅×D₃	1	1	yes	characteristic, complemented
15	C₃×C₂₈₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	D₂₈₁	—	3	1	no	Hall
17	C₂₈₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×D₃	—	281	1	no	maximal, Hall
19	C₃²×C₅	—	281	1	no	Hall
20	C₂×C₃×C₅	—	843	1	no	—
21	C₅×D₃	—	281	1	no	—
22	C₃×D₃	—	1405	1	no	Hall
23	C₃×C₅	—	281	1	no	—
24	C₃×C₅	—	281	1	no	—
25	C₃×C₅	—	562	1	no	—
26	C₂×C₅	—	843	1	no	Hall
27	C₃²	D₂₈₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	4215	1	no	—
29	D₃	—	1405	1	no	—
30	C₅	—	281	1	no	Sylow
31	C₃	—	2	1	no	—
32	C₃	C₃×D₂₈₁⋊C₅	1	1	yes	characteristic, complemented
33	C₃	C₃⋊(D₂₈₁⋊C₅)	1	1	yes	characteristic, direct product factor
34	C₂	—	4215	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(D₂₈₁⋊C₅)
commutator, cosocle, hypocenter	C₃×C₂₈₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₂₈₁	C₂×C₅
LCS	G ▷ C₃×C₂₈₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₈₁⋊C₅	C₂	semidirect
2. C₃⋊(D₂₈₁⋊C₅)	C₃	direct (N × H)
4. C₃×D₈₄₃	C₅	semidirect
6. C₃×C₂₈₁⋊C₅	D₃	semidirect
7. C₃×C₂₈₁⋊C₅	C₂×C₃	semidirect
9. C₃²×C₂₈₁	C₂×C₅	semidirect
10. D₈₄₃	C₃×C₅	semidirect
12. C₂₈₁⋊C₅	C₃×D₃	semidirect
14. C₃×C₂₈₁	C₅×D₃	semidirect
15. C₃×C₂₈₁	C₂×C₃×C₅	semidirect
17. C₂₈₁	C₃×C₅×D₃	semidirect
27. C₃²	D₂₈₁⋊C₅	semidirect
32. C₃	C₃×D₂₈₁⋊C₅	semidirect
33. C₃	C₃⋊(D₂₈₁⋊C₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₈₁⋊C₅	2
C₃⋊(D₂₈₁⋊C₅)	3
C₃×D₂₈₁⋊C₅	3
C₃×D₈₄₃	5
C₃×C₅×D₃	281

Subgroups — C3×C3⋊(D281⋊C5) #38760613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(D₂₈₁⋊C₅) #38760613