Subgroups — C₂×C₅×D₃×C₁₇×C₃₁ #44539404

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₁₇×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₁₇×C₃₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₇×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₇×C₃₁	—	3	2	no	—
7	C₂×C₅×C₁₇×C₃₁	D₃	1	1	yes	characteristic, direct product factor
8	D₃×C₁₇×C₃₁	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×C₁₇×C₃₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₁₇×C₃₁	—	3	1	no	Hall
12	C₂×C₅×D₃×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₇×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₇×C₃₁	—	3	2	no	—
15	C₂×C₁₇×C₃₁	C₅×D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₅×D₃×C₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₅×D₃×C₃₁	C₂×C₁₇	1	2	yes	direct product factor
19	C₂²×C₅×C₃₁	—	3	1	no	Hall
20	C₁₇×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅×C₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented
22	C₅×D₃×C₁₇	C₂×C₃₁	1	2	yes	direct product factor
23	C₃×C₅×C₃₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×D₃×C₃₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₅×C₁₇	—	3	1	no	Hall
26	C₂×C₅×C₃₁	—	3	2	no	—
27	C₂×C₅×C₃₁	D₃×C₁₇	1	1	yes	characteristic, direct product factor
28	C₃×C₅×C₁₇	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
29	C₂×D₃×C₁₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₃₁	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
31	D₃×C₃₁	C₂×C₅×C₁₇	1	2	yes	direct product factor
32	C₂×C₅×C₁₇	—	3	2	no	—
33	C₂×C₅×C₁₇	D₃×C₃₁	1	1	yes	characteristic, direct product factor
34	C₅×C₃₁	C₂×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂²×C₃₁	—	3	1	no	Hall
36	C₂×C₃×C₁₇	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
37	D₃×C₁₇	C₂×C₅×C₃₁	1	2	yes	direct product factor
38	C₃×C₃₁	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₁₇	—	3	1	no	Hall
41	C₂×C₃₁	—	3	2	no	—
42	C₂×C₃₁	C₅×D₃×C₁₇	1	1	yes	characteristic, direct product factor
43	C₂×C₅×D₃	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₁₇	C₂²×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
45	C₂×C₁₇	—	3	2	no	—
46	C₂×C₁₇	C₅×D₃×C₃₁	1	1	yes	characteristic, direct product factor
47	C₃₁	C₂×C₅×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃×C₅	C₂×C₁₇×C₃₁	1	1	yes	characteristic, complemented
49	C₅×D₃	C₂×C₁₇×C₃₁	1	2	yes	direct product factor
50	C₂²×C₅	—	3	1	no	Hall
51	C₁₇	C₂×C₅×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	C₂²×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃	C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₅	—	3	2	no	—
55	C₂×C₅	D₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor
56	C₂×C₃	C₂×C₅×C₁₇×C₃₁	1	1	yes	characteristic, complemented
57	D₃	C₂×C₅×C₁₇×C₃₁	1	2	yes	direct product factor
58	C₅	C₂×D₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	3	1	no	Sylow
60	C₃	C₂²×C₅×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	3	2	no	—
62	C₂	C₅×D₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₁₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₁₇×C₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₃₁	C₂	semidirect
4. C₃×C₅×C₁₇×C₃₁	C₂²	semidirect
5. C₂×D₃×C₁₇×C₃₁	C₅	direct (N × H)
7. C₂×C₅×C₁₇×C₃₁	D₃	direct (N × H)
8. D₃×C₁₇×C₃₁	C₂×C₅	direct (N × H)
9. C₂×C₃×C₁₇×C₃₁	C₂×C₅	semidirect
10. C₅×C₁₇×C₃₁	C₂×D₃	direct (N × H)
12. C₂×C₅×D₃×C₃₁	C₁₇	direct (N × H)
13. C₃×C₁₇×C₃₁	C₂²×C₅	semidirect
15. C₂×C₁₇×C₃₁	C₅×D₃	direct (N × H)
16. C₂×C₅×D₃×C₁₇	C₃₁	direct (N × H)
17. C₂×C₃×C₅×C₃₁	C₂×C₁₇	semidirect
18. C₅×D₃×C₃₁	C₂×C₁₇	direct (N × H)
20. C₁₇×C₃₁	C₂×C₅×D₃	direct (N × H)
21. C₂×C₃×C₅×C₁₇	C₂×C₃₁	semidirect
22. C₅×D₃×C₁₇	C₂×C₃₁	direct (N × H)
23. C₃×C₅×C₃₁	C₂²×C₁₇	semidirect
24. C₂×D₃×C₃₁	C₅×C₁₇	direct (N × H)
27. C₂×C₅×C₃₁	D₃×C₁₇	direct (N × H)
28. C₃×C₅×C₁₇	C₂²×C₃₁	semidirect
29. C₂×D₃×C₁₇	C₅×C₃₁	direct (N × H)
30. C₂×C₃×C₃₁	C₂×C₅×C₁₇	semidirect
31. D₃×C₃₁	C₂×C₅×C₁₇	direct (N × H)
33. C₂×C₅×C₁₇	D₃×C₃₁	direct (N × H)
34. C₅×C₃₁	C₂×D₃×C₁₇	direct (N × H)
36. C₂×C₃×C₁₇	C₂×C₅×C₃₁	semidirect
37. D₃×C₁₇	C₂×C₅×C₃₁	direct (N × H)
38. C₃×C₃₁	C₂²×C₅×C₁₇	semidirect
39. C₅×C₁₇	C₂×D₃×C₃₁	direct (N × H)
42. C₂×C₃₁	C₅×D₃×C₁₇	direct (N × H)
43. C₂×C₅×D₃	C₁₇×C₃₁	direct (N × H)
44. C₃×C₁₇	C₂²×C₅×C₃₁	semidirect
46. C₂×C₁₇	C₅×D₃×C₃₁	direct (N × H)
47. C₃₁	C₂×C₅×D₃×C₁₇	direct (N × H)
48. C₂×C₃×C₅	C₂×C₁₇×C₃₁	semidirect
49. C₅×D₃	C₂×C₁₇×C₃₁	direct (N × H)
51. C₁₇	C₂×C₅×D₃×C₃₁	direct (N × H)
52. C₃×C₅	C₂²×C₁₇×C₃₁	semidirect
53. C₂×D₃	C₅×C₁₇×C₃₁	direct (N × H)
55. C₂×C₅	D₃×C₁₇×C₃₁	direct (N × H)
56. C₂×C₃	C₂×C₅×C₁₇×C₃₁	semidirect
57. D₃	C₂×C₅×C₁₇×C₃₁	direct (N × H)
58. C₅	C₂×D₃×C₁₇×C₃₁	direct (N × H)
60. C₃	C₂²×C₅×C₁₇×C₃₁	semidirect
62. C₂	C₅×D₃×C₁₇×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
C₅×D₃×C₁₇×C₃₁	2
C₂×C₃×C₅×C₁₇×C₃₁	2
C₂²×C₅×C₁₇×C₃₁	3
C₂×D₃×C₁₇×C₃₁	5
C₂×C₅×D₃×C₃₁	17
C₂×C₅×D₃×C₁₇	31

Subgroups — C2×C5×D3×C17×C31 #44539404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₁₇×C₃₁ #44539404