Subgroups — C₂×C₅×C₁₇×D₉₁ #44525964

Order 30940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×D₉₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×D₉₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₇×D₁₃	—	7	1	no	maximal, Hall
6	C₁₇×D₉₁	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₇×C₁₃×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
8	C₂×C₅×D₇×C₁₇	—	13	1	no	maximal, Hall
9	C₅×C₁₇×D₁₃	—	7	2	no	—
10	C₂×C₅×C₁₃×C₁₇	D₇	1	1	yes	characteristic, complemented
11	C₂×C₅×D₉₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₁₃×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₇×C₁₇	D₁₃	1	1	yes	characteristic, complemented
14	C₅×D₇×C₁₇	—	13	2	no	—
15	C₅×C₁₃×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented
17	C₅×D₉₁	C₂×C₁₇	1	2	yes	direct product factor
18	C₂×C₁₇×D₁₃	—	7	1	no	Hall
19	C₅×C₇×C₁₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇×C₁₇	—	13	1	no	Hall
21	C₅×C₇×C₁₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃×C₁₇	C₅×D₇	1	1	yes	characteristic, complemented
23	C₁₇×D₁₃	—	7	2	no	—
24	C₂×D₉₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₅×C₁₇	—	91	1	no	Hall
26	C₂×C₅×D₁₃	—	7	1	no	Hall
27	C₂×C₇×C₁₇	C₅×D₁₃	1	1	yes	characteristic, complemented
28	D₇×C₁₇	—	13	2	no	—
29	C₁₃×C₁₇	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₃	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
31	D₉₁	C₂×C₅×C₁₇	1	2	yes	direct product factor
32	C₂×C₅×C₁₇	—	91	2	no	—
33	C₂×C₅×C₁₇	D₉₁	1	1	yes	characteristic, direct product factor
34	C₂×C₅×D₇	—	13	1	no	Hall
35	C₂×C₅×C₁₃	D₇×C₁₇	1	1	yes	characteristic, complemented
36	C₅×D₁₃	—	7	2	no	—
37	C₇×C₁₇	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₃	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×D₉₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅×C₇	C₁₇×D₁₃	1	1	yes	characteristic, complemented
41	C₅×D₇	—	13	2	no	—
42	C₂²×C₁₇	—	91	1	no	Hall
43	C₅×C₁₃	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₁₃	—	7	1	no	Hall
45	C₅×C₇	C₂×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₁₇	—	91	2	no	—
47	C₂×C₁₇	C₅×D₉₁	1	1	yes	characteristic, direct product factor
48	C₂×D₇	—	13	1	no	Hall
49	C₂×C₁₃	C₅×D₇×C₁₇	1	1	yes	characteristic, complemented
50	D₁₃	—	7	2	no	—
51	C₂²×C₅	—	91	1	no	Hall
52	C₁₇	C₂×C₅×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₇	C₅×C₁₇×D₁₃	1	1	yes	characteristic, complemented
54	D₇	—	13	2	no	—
55	C₁₃	C₂×C₅×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	91	2	no	—
57	C₂×C₅	C₁₇×D₉₁	1	1	yes	characteristic, direct product factor
58	C₇	C₂×C₅×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₅	C₂×C₁₇×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	—	91	1	no	Sylow
61	C₂	—	91	2	no	—
62	C₂	C₅×C₁₇×D₉₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇	D₉₁
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃×C₁₇	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×D₉₁	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₃×C₁₇	C₂	semidirect
3. C₅×C₇×C₁₃×C₁₇	C₂²	semidirect
4. C₂×C₁₇×D₉₁	C₅	direct (N × H)
6. C₁₇×D₉₁	C₂×C₅	direct (N × H)
7. C₂×C₇×C₁₃×C₁₇	C₂×C₅	semidirect
10. C₂×C₅×C₁₃×C₁₇	D₇	semidirect
11. C₂×C₅×D₉₁	C₁₇	direct (N × H)
12. C₇×C₁₃×C₁₇	C₂²×C₅	semidirect
13. C₂×C₅×C₇×C₁₇	D₁₃	semidirect
15. C₅×C₁₃×C₁₇	C₂×D₇	semidirect
16. C₂×C₅×C₇×C₁₃	C₂×C₁₇	semidirect
17. C₅×D₉₁	C₂×C₁₇	direct (N × H)
19. C₅×C₇×C₁₇	C₂×D₁₃	semidirect
21. C₅×C₇×C₁₃	C₂²×C₁₇	semidirect
22. C₂×C₁₃×C₁₇	C₅×D₇	semidirect
24. C₂×D₉₁	C₅×C₁₇	direct (N × H)
27. C₂×C₇×C₁₇	C₅×D₁₃	semidirect
29. C₁₃×C₁₇	C₂×C₅×D₇	semidirect
30. C₂×C₇×C₁₃	C₂×C₅×C₁₇	semidirect
31. D₉₁	C₂×C₅×C₁₇	direct (N × H)
33. C₂×C₅×C₁₇	D₉₁	direct (N × H)
35. C₂×C₅×C₁₃	D₇×C₁₇	semidirect
37. C₇×C₁₇	C₂×C₅×D₁₃	semidirect
38. C₇×C₁₃	C₂²×C₅×C₁₇	semidirect
39. C₅×C₁₇	C₂×D₉₁	direct (N × H)
40. C₂×C₅×C₇	C₁₇×D₁₃	semidirect
43. C₅×C₁₃	C₂×D₇×C₁₇	semidirect
45. C₅×C₇	C₂×C₁₇×D₁₃	semidirect
47. C₂×C₁₇	C₅×D₉₁	direct (N × H)
49. C₂×C₁₃	C₅×D₇×C₁₇	semidirect
52. C₁₇	C₂×C₅×D₉₁	direct (N × H)
53. C₂×C₇	C₅×C₁₇×D₁₃	semidirect
55. C₁₃	C₂×C₅×D₇×C₁₇	semidirect
57. C₂×C₅	C₁₇×D₉₁	direct (N × H)
58. C₇	C₂×C₅×C₁₇×D₁₃	semidirect
59. C₅	C₂×C₁₇×D₉₁	direct (N × H)
62. C₂	C₅×C₁₇×D₉₁	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×C₁₇×D₉₁	2
C₂×C₅×C₇×C₁₃×C₁₇	2
C₂×C₁₇×D₉₁	5
C₂×C₅×C₁₇×D₁₃	7
C₂×C₅×D₇×C₁₇	13
C₂×C₅×D₉₁	17

Subgroups — C2×C5×C17×D91 #44525964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₇×D₉₁ #44525964