Subgroups — C₂×D₅×C₁₇×C₃₁⋊C₃ #44539331

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₇×C₃₁⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₇×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₇×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₁₇×C₃₁⋊C₃	—	5	1	no	maximal, Hall
6	D₅×C₁₇×C₃₁	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₁₇×C₃₁⋊C₃	—	5	2	no	—
9	C₂×C₁₇×C₃₁⋊C₃	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₁₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₁₇×C₃₁	—	5	1	no	Hall
12	C₂×D₅×C₃₁⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₇×C₃₁⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₇×C₃₁	—	5	2	no	—
15	C₂×C₁₇×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
16	C₂×C₃×D₅×C₁₇	—	31	1	no	maximal, Hall
17	C₂×C₅×C₃₁⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented
18	D₅×C₃₁⋊C₃	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×D₅×C₃₁	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₁₇×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅×C₁₇	—	31	1	no	—
22	C₃×D₅×C₁₇	—	31	2	no	—
23	C₅×C₃₁⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₃₁⋊C₃	—	5	1	no	Hall
25	C₂×D₅×C₁₇	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
27	D₅×C₃₁	C₂×C₃×C₁₇	1	2	yes	complemented
28	C₃×C₅×C₁₇	—	31	1	no	Hall
29	C₂²×C₃×C₁₇	—	155	1	no	Hall
30	C₂×C₃₁⋊C₃	—	5	2	no	—
31	C₂×C₃₁⋊C₃	D₅×C₁₇	1	1	yes	characteristic, direct product factor
32	C₂×C₅×C₁₇	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
33	D₅×C₁₇	C₂×C₃₁⋊C₃	1	2	yes	direct product factor
34	C₅×C₃₁	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃₁	—	5	1	no	Hall
36	C₂×C₃×C₁₇	—	31	1	no	—
37	C₂×C₃×C₁₇	—	155	2	no	—
38	C₃₁⋊C₃	C₂×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₅×C₁₇	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₁₇	—	5	1	no	Hall
41	C₂×C₃₁	—	5	2	no	—
42	C₂×C₃₁	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented
43	C₂×C₃×D₅	—	31	1	no	Hall
44	C₃×C₁₇	—	31	1	no	Hall
45	C₂×C₁₇	—	5	2	no	—
46	C₂×C₁₇	D₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
47	C₃₁	C₂×C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	31	1	no	—
49	C₃×D₅	—	31	2	no	—
50	C₂×D₅	C₁₇×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
51	C₁₇	C₂×D₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	—	31	1	no	Hall
53	C₂²×C₃	—	155	1	no	Hall
54	C₂×C₅	C₂×C₁₇×C₃₁⋊C₃	1	1	yes	characteristic, complemented
55	D₅	C₂×C₁₇×C₃₁⋊C₃	1	2	yes	direct product factor
56	C₂×C₃	—	31	1	no	—
57	C₂×C₃	—	155	2	no	—
58	C₅	C₂²×C₁₇×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	—	31	1	no	Sylow
61	C₂	—	5	2	no	—
62	C₂	D₅×C₁₇×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₅×C₃₁⋊C₃
commutator, cosocle, hypocenter	C₅×C₃₁	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. D₅×C₁₇×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₁₇×C₃₁⋊C₃	C₂	semidirect
3. C₂×D₅×C₁₇×C₃₁	C₃	semidirect
4. C₅×C₁₇×C₃₁⋊C₃	C₂²	semidirect
6. D₅×C₁₇×C₃₁	C₂×C₃	semidirect
7. C₂×C₅×C₁₇×C₃₁	C₂×C₃	semidirect
9. C₂×C₁₇×C₃₁⋊C₃	D₅	direct (N × H)
10. C₅×C₁₇×C₃₁	C₂²×C₃	semidirect
12. C₂×D₅×C₃₁⋊C₃	C₁₇	direct (N × H)
13. C₁₇×C₃₁⋊C₃	C₂×D₅	direct (N × H)
15. C₂×C₁₇×C₃₁	C₃×D₅	semidirect
17. C₂×C₅×C₃₁⋊C₃	C₂×C₁₇	semidirect
18. D₅×C₃₁⋊C₃	C₂×C₁₇	direct (N × H)
19. C₂×D₅×C₃₁	C₃×C₁₇	semidirect
20. C₁₇×C₃₁	C₂×C₃×D₅	semidirect
23. C₅×C₃₁⋊C₃	C₂²×C₁₇	semidirect
25. C₂×D₅×C₁₇	C₃₁⋊C₃	direct (N × H)
26. C₂×C₅×C₃₁	C₂×C₃×C₁₇	semidirect
27. D₅×C₃₁	C₂×C₃×C₁₇	semidirect
31. C₂×C₃₁⋊C₃	D₅×C₁₇	direct (N × H)
32. C₂×C₅×C₁₇	C₂×C₃₁⋊C₃	semidirect
33. D₅×C₁₇	C₂×C₃₁⋊C₃	direct (N × H)
34. C₅×C₃₁	C₂²×C₃×C₁₇	semidirect
38. C₃₁⋊C₃	C₂×D₅×C₁₇	direct (N × H)
39. C₅×C₁₇	C₂²×C₃₁⋊C₃	semidirect
42. C₂×C₃₁	C₃×D₅×C₁₇	semidirect
46. C₂×C₁₇	D₅×C₃₁⋊C₃	direct (N × H)
47. C₃₁	C₂×C₃×D₅×C₁₇	semidirect
50. C₂×D₅	C₁₇×C₃₁⋊C₃	direct (N × H)
51. C₁₇	C₂×D₅×C₃₁⋊C₃	direct (N × H)
54. C₂×C₅	C₂×C₁₇×C₃₁⋊C₃	semidirect
55. D₅	C₂×C₁₇×C₃₁⋊C₃	direct (N × H)
58. C₅	C₂²×C₁₇×C₃₁⋊C₃	semidirect
62. C₂	D₅×C₁₇×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
D₅×C₁₇×C₃₁⋊C₃	2
C₂×C₅×C₁₇×C₃₁⋊C₃	2
C₂×D₅×C₁₇×C₃₁	3
C₂²×C₁₇×C₃₁⋊C₃	5
C₂×D₅×C₃₁⋊C₃	17
C₂×C₃×D₅×C₁₇	31

Subgroups — C2×D5×C17×C31⋊C3 #44539331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₁₇×C₃₁⋊C₃ #44539331