Subgroups — C₂×C₃×C₅×C₁₇×D₃₁ #44539397

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×D₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₇×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇×D₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₇×D₃₁	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₁₇×D₃₁	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×C₁₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×D₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×D₃₁	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	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	C₁₇×D₃₁	C₂×C₃×C₅	1	2	yes	direct product factor
16	C₂²×C₃×C₅×C₁₇	—	31	1	no	maximal, Hall
17	C₂×C₃×C₅×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₃×C₅×D₃₁	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×C₅×D₃₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₁₇×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅×C₁₇	—	31	2	no	—
22	C₂×C₃×C₅×C₁₇	D₃₁	1	1	yes	characteristic, direct product factor
23	C₃×C₅×C₃₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₃₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₅×C₁₇	—	31	1	no	Hall
26	C₂×C₅×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
27	C₅×D₃₁	C₂×C₃×C₁₇	1	2	yes	direct product factor
28	C₃×C₅×C₁₇	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃×C₁₇	—	31	1	no	Hall
30	C₂×C₃×C₃₁	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
31	C₃×D₃₁	C₂×C₅×C₁₇	1	2	yes	direct product factor
32	C₂×C₅×C₁₇	—	31	2	no	—
33	C₂×C₅×C₁₇	C₃×D₃₁	1	1	yes	characteristic, direct product factor
34	C₅×C₃₁	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₁₇	—	31	2	no	—
37	C₂×C₃×C₁₇	C₅×D₃₁	1	1	yes	characteristic, direct product factor
38	C₃×C₃₁	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×C₃×D₃₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₁₇	—	31	1	no	Hall
41	C₂×C₃₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
42	D₃₁	C₂×C₃×C₅×C₁₇	1	2	yes	direct product factor
43	C₂²×C₃×C₅	—	31	1	no	Hall
44	C₃×C₁₇	C₂×C₅×D₃₁	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₁₇	—	31	2	no	—
46	C₂×C₁₇	C₃×C₅×D₃₁	1	1	yes	characteristic, direct product factor
47	C₃₁	C₂²×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	31	2	no	—
49	C₂×C₃×C₅	C₁₇×D₃₁	1	1	yes	characteristic, direct product factor
50	C₂²×C₅	—	31	1	no	Hall
51	C₁₇	C₂×C₃×C₅×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	C₂×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor, Hall
53	C₂²×C₃	—	31	1	no	Hall
54	C₂×C₅	—	31	2	no	—
55	C₂×C₅	C₃×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor
56	C₂×C₃	—	31	2	no	—
57	C₂×C₃	C₅×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	31	1	no	Sylow
60	C₃	C₂×C₅×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	31	2	no	—
62	C₂	C₃×C₅×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂²×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×D₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₃₁	C₂	semidirect
3. C₂×C₅×C₁₇×D₃₁	C₃	direct (N × H)
4. C₃×C₅×C₁₇×C₃₁	C₂²	semidirect
5. C₂×C₃×C₁₇×D₃₁	C₅	direct (N × H)
6. C₅×C₁₇×D₃₁	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₇×C₃₁	C₂×C₃	semidirect
8. C₃×C₁₇×D₃₁	C₂×C₅	direct (N × H)
9. C₂×C₃×C₁₇×C₃₁	C₂×C₅	semidirect
10. C₅×C₁₇×C₃₁	C₂²×C₃	semidirect
11. C₂×C₁₇×D₃₁	C₃×C₅	direct (N × H)
12. C₂×C₃×C₅×D₃₁	C₁₇	direct (N × H)
13. C₃×C₁₇×C₃₁	C₂²×C₅	semidirect
14. C₂×C₁₇×C₃₁	C₂×C₃×C₅	semidirect
15. C₁₇×D₃₁	C₂×C₃×C₅	direct (N × H)
17. C₂×C₃×C₅×C₃₁	C₂×C₁₇	semidirect
18. C₃×C₅×D₃₁	C₂×C₁₇	direct (N × H)
19. C₂×C₅×D₃₁	C₃×C₁₇	direct (N × H)
20. C₁₇×C₃₁	C₂²×C₃×C₅	semidirect
22. C₂×C₃×C₅×C₁₇	D₃₁	direct (N × H)
23. C₃×C₅×C₃₁	C₂²×C₁₇	semidirect
24. C₂×C₃×D₃₁	C₅×C₁₇	direct (N × H)
26. C₂×C₅×C₃₁	C₂×C₃×C₁₇	semidirect
27. C₅×D₃₁	C₂×C₃×C₁₇	direct (N × H)
28. C₃×C₅×C₁₇	C₂×D₃₁	direct (N × H)
30. C₂×C₃×C₃₁	C₂×C₅×C₁₇	semidirect
31. C₃×D₃₁	C₂×C₅×C₁₇	direct (N × H)
33. C₂×C₅×C₁₇	C₃×D₃₁	direct (N × H)
34. C₅×C₃₁	C₂²×C₃×C₁₇	semidirect
35. C₂×D₃₁	C₃×C₅×C₁₇	direct (N × H)
37. C₂×C₃×C₁₇	C₅×D₃₁	direct (N × H)
38. C₃×C₃₁	C₂²×C₅×C₁₇	semidirect
39. C₅×C₁₇	C₂×C₃×D₃₁	direct (N × H)
41. C₂×C₃₁	C₂×C₃×C₅×C₁₇	semidirect
42. D₃₁	C₂×C₃×C₅×C₁₇	direct (N × H)
44. C₃×C₁₇	C₂×C₅×D₃₁	direct (N × H)
46. C₂×C₁₇	C₃×C₅×D₃₁	direct (N × H)
47. C₃₁	C₂²×C₃×C₅×C₁₇	semidirect
49. C₂×C₃×C₅	C₁₇×D₃₁	direct (N × H)
51. C₁₇	C₂×C₃×C₅×D₃₁	direct (N × H)
52. C₃×C₅	C₂×C₁₇×D₃₁	direct (N × H)
55. C₂×C₅	C₃×C₁₇×D₃₁	direct (N × H)
57. C₂×C₃	C₅×C₁₇×D₃₁	direct (N × H)
58. C₅	C₂×C₃×C₁₇×D₃₁	direct (N × H)
60. C₃	C₂×C₅×C₁₇×D₃₁	direct (N × H)
62. C₂	C₃×C₅×C₁₇×D₃₁	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×C₁₇×D₃₁	2
C₂×C₃×C₅×C₁₇×C₃₁	2
C₂×C₅×C₁₇×D₃₁	3
C₂×C₃×C₁₇×D₃₁	5
C₂×C₃×C₅×D₃₁	17
C₂²×C₃×C₅×C₁₇	31

Subgroups — C2×C3×C5×C17×D31 #44539397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₇×D₃₁ #44539397