Subgroups — C₅×D₂₉×C₃₁⋊C₃ #41004209

Order 26970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₃₁×D₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₂₉×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂₉×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₂₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₃₁⋊C₃	—	29	1	no	maximal, Hall
8	C₂₉×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₂₉	—	31	1	no	maximal, Hall
10	C₅×C₃₁⋊C₃	D₂₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₂₉	—	31	1	no	Hall
12	C₂×C₅×C₃₁	—	29	1	no	Hall
13	C₅×D₂₉	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₁⋊C₃	—	29	1	no	Hall
15	C₃×D₂₉	—	31	1	no	Hall
16	C₅×C₃₁	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
17	C₅×C₂₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₃₁⋊C₃	C₅×D₂₉	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	—	31	1	no	Hall
20	C₂×C₃₁	—	29	1	no	Hall
21	D₂₉	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃₁	C₃×C₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×C₅	—	899	1	no	Hall
24	C₂₉	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	—	31	1	no	Hall
26	C₂×C₅	—	29	1	no	Hall
27	C₂×C₃	—	899	1	no	Hall
28	C₅	D₂₉×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	31	1	no	Sylow
30	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₉×C₃₁⋊C₃
commutator, cosocle, hypocenter	C₂₉×C₃₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₂₉×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×C₃₁⋊C₃	C₂	semidirect
2. C₅×C₃₁×D₂₉	C₃	semidirect
3. D₂₉×C₃₁⋊C₃	C₅	direct (N × H)
4. C₅×C₂₉×C₃₁	C₂×C₃	semidirect
5. C₂₉×C₃₁⋊C₃	C₂×C₅	semidirect
6. C₃₁×D₂₉	C₃×C₅	semidirect
8. C₂₉×C₃₁	C₂×C₃×C₅	semidirect
10. C₅×C₃₁⋊C₃	D₂₉	direct (N × H)
13. C₅×D₂₉	C₃₁⋊C₃	direct (N × H)
16. C₅×C₃₁	C₃×D₂₉	semidirect
17. C₅×C₂₉	C₂×C₃₁⋊C₃	semidirect
18. C₃₁⋊C₃	C₅×D₂₉	direct (N × H)
21. D₂₉	C₅×C₃₁⋊C₃	direct (N × H)
22. C₃₁	C₃×C₅×D₂₉	semidirect
24. C₂₉	C₂×C₅×C₃₁⋊C₃	semidirect
28. C₅	D₂₉×C₃₁⋊C₃	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×C₂₉×C₃₁⋊C₃	2
C₅×C₃₁×D₂₉	3
D₂₉×C₃₁⋊C₃	5
C₂×C₅×C₃₁⋊C₃	29
C₃×C₅×D₂₉	31

Subgroups — C5×D29×C31⋊C3 #41004209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₂₉×C₃₁⋊C₃ #41004209