Subgroups — C₃²×C₅×D₇×C₃₁ #34086310

Order 19530.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₇×C₃₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₇×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₃₁	C₂×C₃	1	4	yes	complemented
5	C₂×C₃²×C₅×C₃₁	—	7	1	no	maximal, Hall
6	C₅×D₇×C₃₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₃₁	D₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₇×C₃₁	C₃×C₅	1	4	yes	direct product factor
10	C₅×C₇×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₃₁	—	7	4	no	—
12	C₃×C₇×C₃₁	C₂×C₃×C₅	1	4	yes	complemented
13	C₃²×C₅×D₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃²×C₃₁	—	7	1	no	Hall
15	C₃×C₅×C₃₁	C₃×D₇	1	4	yes	direct product factor
16	D₇×C₃₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₃²×C₅×C₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₃₁	—	7	1	no	Hall
19	C₃²×C₃₁	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
20	C₇×C₃₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×D₇	C₃×C₃₁	1	4	yes	direct product factor
22	C₂×C₃×C₃₁	—	7	4	no	—
23	C₅×C₃₁	C₃²×D₇	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×D₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅×C₇	C₂×C₃×C₃₁	1	4	yes	complemented
26	C₃×C₃₁	C₃×C₅×D₇	1	4	yes	direct product factor
27	C₂×C₃²×C₅	—	7	1	no	Hall
28	C₅×D₇	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
29	C₃²×C₇	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₁	—	7	1	no	Hall
31	C₃²×C₅	D₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
32	C₃×D₇	C₃×C₅×C₃₁	1	4	yes	direct product factor
33	C₅×C₇	C₂×C₃²×C₃₁	1	1	yes	characteristic, complemented, Hall
34	C₃₁	C₃²×C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₅	—	7	4	no	—
36	C₃×C₇	C₂×C₃×C₅×C₃₁	1	4	yes	complemented
37	C₂×C₃²	—	7	1	no	Hall
38	C₃×C₅	C₃×D₇×C₃₁	1	4	yes	direct product factor
39	D₇	C₃²×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	—	7	1	no	Hall
41	C₃²	C₅×D₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₃²×C₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	4	no	—
44	C₅	C₃²×D₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×D₇×C₃₁	1	4	yes	direct product factor
46	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅×C₃₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₅×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₃₁	C₂	semidirect
2. C₃×C₅×D₇×C₃₁	C₃	direct (N × H)
3. C₃²×D₇×C₃₁	C₅	direct (N × H)
4. C₃×C₅×C₇×C₃₁	C₂×C₃	semidirect
6. C₅×D₇×C₃₁	C₃²	direct (N × H)
7. C₃²×C₇×C₃₁	C₂×C₅	semidirect
8. C₃²×C₅×C₃₁	D₇	direct (N × H)
9. C₃×D₇×C₃₁	C₃×C₅	direct (N × H)
10. C₅×C₇×C₃₁	C₂×C₃²	semidirect
12. C₃×C₇×C₃₁	C₂×C₃×C₅	semidirect
13. C₃²×C₅×D₇	C₃₁	direct (N × H)
15. C₃×C₅×C₃₁	C₃×D₇	direct (N × H)
16. D₇×C₃₁	C₃²×C₅	direct (N × H)
17. C₃²×C₅×C₇	C₂×C₃₁	semidirect
19. C₃²×C₃₁	C₅×D₇	direct (N × H)
20. C₇×C₃₁	C₂×C₃²×C₅	semidirect
21. C₃×C₅×D₇	C₃×C₃₁	direct (N × H)
23. C₅×C₃₁	C₃²×D₇	direct (N × H)
24. C₃²×D₇	C₅×C₃₁	direct (N × H)
25. C₃×C₅×C₇	C₂×C₃×C₃₁	semidirect
26. C₃×C₃₁	C₃×C₅×D₇	direct (N × H)
28. C₅×D₇	C₃²×C₃₁	direct (N × H)
29. C₃²×C₇	C₂×C₅×C₃₁	semidirect
31. C₃²×C₅	D₇×C₃₁	direct (N × H)
32. C₃×D₇	C₃×C₅×C₃₁	direct (N × H)
33. C₅×C₇	C₂×C₃²×C₃₁	semidirect
34. C₃₁	C₃²×C₅×D₇	direct (N × H)
36. C₃×C₇	C₂×C₃×C₅×C₃₁	semidirect
38. C₃×C₅	C₃×D₇×C₃₁	direct (N × H)
39. D₇	C₃²×C₅×C₃₁	direct (N × H)
41. C₃²	C₅×D₇×C₃₁	direct (N × H)
42. C₇	C₂×C₃²×C₅×C₃₁	semidirect
44. C₅	C₃²×D₇×C₃₁	direct (N × H)
45. C₃	C₃×C₅×D₇×C₃₁	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×C₅×C₇×C₃₁	2
C₃×C₅×D₇×C₃₁	3
C₃²×D₇×C₃₁	5
C₂×C₃²×C₅×C₃₁	7
C₃²×C₅×D₇	31

Subgroups — C32×C5×D7×C31 #34086310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×D₇×C₃₁ #34086310