Subgroups — C₃×C₃₁×D₁₄₅ #41004191

Order 26970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₄₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₁×D₂₉	—	5	1	no	maximal, Hall
4	C₅×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₂₉	—	5	1	no	Hall
7	C₃×D₅×C₃₁	—	29	1	no	maximal, Hall
8	C₂₉×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₄₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×C₃₁	D₂₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₂₉	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
12	D₅×C₃₁	—	29	1	no	Hall
13	D₁₄₅	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₃₁	—	145	1	no	Hall
15	C₃×D₂₉	—	5	1	no	Hall
16	C₅×C₃₁	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
17	C₅×C₂₉	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
18	C₃×C₃₁	D₁₄₅	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	—	145	1	no	Hall
21	D₂₉	—	5	1	no	Hall
22	C₃₁	C₃×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×D₅	—	29	1	no	Hall
24	C₂₉	C₃×D₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	C₃₁×D₂₉	1	1	yes	characteristic, complemented, Hall
26	D₅	—	29	1	no	Hall
27	C₂×C₃	—	145	1	no	Hall
28	C₅	C₃×C₃₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₃₁×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	145	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₄₅
commutator, cosocle, hypocenter	C₅×C₂₉	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₉×C₃₁	C₂
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₉×C₃₁	C₂	semidirect
2. C₃₁×D₁₄₅	C₃	direct (N × H)
4. C₅×C₂₉×C₃₁	C₂×C₃	semidirect
5. C₃×C₂₉×C₃₁	D₅	semidirect
8. C₂₉×C₃₁	C₃×D₅	semidirect
9. C₃×D₁₄₅	C₃₁	direct (N × H)
10. C₃×C₅×C₃₁	D₂₉	semidirect
11. C₃×C₅×C₂₉	C₂×C₃₁	semidirect
13. D₁₄₅	C₃×C₃₁	direct (N × H)
16. C₅×C₃₁	C₃×D₂₉	semidirect
17. C₅×C₂₉	C₂×C₃×C₃₁	semidirect
18. C₃×C₃₁	D₁₄₅	direct (N × H)
19. C₃×C₂₉	D₅×C₃₁	semidirect
22. C₃₁	C₃×D₁₄₅	direct (N × H)
24. C₂₉	C₃×D₅×C₃₁	semidirect
25. C₃×C₅	C₃₁×D₂₉	semidirect
28. C₅	C₃×C₃₁×D₂₉	semidirect
29. C₃	C₃₁×D₁₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂₉×C₃₁	2
C₃₁×D₁₄₅	3
C₃×C₃₁×D₂₉	5
C₃×D₅×C₃₁	29
C₃×D₁₄₅	31

Subgroups — C3×C31×D145 #41004191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₁×D₁₄₅ #41004191