Subgroups — C₁₇×D₁₃×D₃₅ #44525939

Order 30940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₄₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₁₇×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×C₁₇×D₁₃	—	5	1	no	maximal, Hall
6	D₅×C₁₇×D₁₃	—	7	1	no	maximal, Hall
7	C₁₇×D₉₁	—	5	1	no	—
8	C₁₃×D₇×C₁₇	—	5	1	no	—
9	C₇×C₁₇×D₁₃	D₅	1	1	yes	characteristic, complemented
10	C₂×C₁₇×D₃₅	—	13	1	no	maximal, Hall
11	C₁₇×D₆₅	—	7	1	no	—
12	D₅×C₁₃×C₁₇	—	7	1	no	—
13	C₅×C₁₇×D₁₃	D₇	1	1	yes	characteristic, complemented
14	D₁₃×D₃₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₇×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇×C₁₇	—	13	1	no	—
17	C₁₇×D₃₅	—	13	1	no	—
18	C₁₇×D₃₅	D₁₃	1	1	yes	characteristic, direct product factor
19	C₅×C₁₃×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₄₅₅	C₂×C₁₇	1	1	yes	characteristic, complemented
21	C₁₃×D₃₅	C₂×C₁₇	1	1	yes	characteristic, complemented
22	C₅×C₇×D₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented
23	C₂×C₁₇×D₁₃	—	35	1	no	Hall
24	C₅×C₇×C₁₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇×C₁₇	—	65	1	no	Hall
26	C₅×C₇×C₁₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₃×C₁₇	—	35	1	no	—
28	C₁₇×D₁₃	—	35	1	no	—
29	C₁₇×D₁₃	D₃₅	1	1	yes	characteristic, direct product factor
30	D₇×D₁₃	—	5	1	no	Hall
31	C₂×D₅×C₁₇	—	91	1	no	Hall
32	D₅×D₁₃	—	7	1	no	Hall
33	C₂×C₇×C₁₇	—	13	1	no	—
34	D₇×C₁₇	—	5	1	no	—
35	D₇×C₁₇	—	65	1	no	—
36	C₁₃×C₁₇	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
37	D₉₁	—	5	1	no	—
38	C₇×D₁₃	D₅×C₁₇	1	1	yes	characteristic, complemented
39	C₁₃×D₇	—	5	1	no	—
40	C₂×C₅×C₁₇	—	13	1	no	—
41	D₅×C₁₇	—	7	1	no	—
42	D₅×C₁₇	—	91	1	no	—
43	C₂×D₃₅	—	13	1	no	Hall
44	D₆₅	—	7	1	no	—
45	C₅×D₁₃	D₇×C₁₇	1	1	yes	characteristic, complemented
46	D₅×C₁₃	—	7	1	no	—
47	C₇×C₁₇	D₅×D₁₃	1	1	yes	characteristic, complemented, Hall
48	C₇×C₁₃	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₅×C₇	—	13	1	no	—
51	D₃₅	—	13	1	no	—
52	D₃₅	C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
53	C₂²×C₁₇	—	455	1	no	Hall
54	C₅×C₁₃	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
55	C₂×D₁₃	—	35	1	no	Hall
56	C₅×C₇	C₂×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₇	—	13	1	no	—
58	C₂×C₁₇	—	35	1	no	—
59	C₂×C₁₇	—	455	1	no	—
60	C₂×D₇	—	65	1	no	Hall
61	C₂×C₁₃	—	35	1	no	—
62	D₁₃	—	35	1	no	—
63	D₁₃	C₁₇×D₃₅	1	1	yes	characteristic, direct product factor
64	C₂×D₅	—	91	1	no	Hall
65	C₁₇	D₁₃×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₇	—	13	1	no	—
67	D₇	—	5	1	no	—
68	D₇	—	65	1	no	—
69	C₁₃	C₂×C₁₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	—	13	1	no	—
71	D₅	—	7	1	no	—
72	D₅	—	91	1	no	—
73	C₇	D₅×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
74	C₅	D₇×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	455	1	no	Sylow
76	C₂	—	13	1	no	—
77	C₂	—	35	1	no	—
78	C₂	—	455	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₁₃×D₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₃	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₂²
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₄₅₅	C₂	semidirect
2. C₁₃×C₁₇×D₃₅	C₂	semidirect
3. C₅×C₇×C₁₇×D₁₃	C₂	semidirect
4. C₅×C₇×C₁₃×C₁₇	C₂²	semidirect
9. C₇×C₁₇×D₁₃	D₅	semidirect
13. C₅×C₁₇×D₁₃	D₇	semidirect
14. D₁₃×D₃₅	C₁₇	direct (N × H)
15. C₇×C₁₃×C₁₇	C₂×D₅	semidirect
18. C₁₇×D₃₅	D₁₃	direct (N × H)
19. C₅×C₁₃×C₁₇	C₂×D₇	semidirect
20. D₄₅₅	C₂×C₁₇	semidirect
21. C₁₃×D₃₅	C₂×C₁₇	semidirect
22. C₅×C₇×D₁₃	C₂×C₁₇	semidirect
24. C₅×C₇×C₁₇	C₂×D₁₃	semidirect
26. C₅×C₇×C₁₃	C₂²×C₁₇	semidirect
29. C₁₇×D₁₃	D₃₅	direct (N × H)
36. C₁₃×C₁₇	C₂×D₃₅	semidirect
38. C₇×D₁₃	D₅×C₁₇	semidirect
45. C₅×D₁₃	D₇×C₁₇	semidirect
47. C₇×C₁₇	D₅×D₁₃	semidirect
48. C₇×C₁₃	C₂×D₅×C₁₇	semidirect
49. C₅×C₁₇	D₇×D₁₃	semidirect
52. D₃₅	C₁₇×D₁₃	direct (N × H)
54. C₅×C₁₃	C₂×D₇×C₁₇	semidirect
56. C₅×C₇	C₂×C₁₇×D₁₃	semidirect
63. D₁₃	C₁₇×D₃₅	direct (N × H)
65. C₁₇	D₁₃×D₃₅	direct (N × H)
69. C₁₃	C₂×C₁₇×D₃₅	semidirect
73. C₇	D₅×C₁₇×D₁₃	semidirect
74. C₅	D₇×C₁₇×D₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₇×D₄₅₅	2
C₁₃×C₁₇×D₃₅	2
C₅×C₇×C₁₇×D₁₃	2
D₇×C₁₇×D₁₃	5
D₅×C₁₇×D₁₃	7
C₂×C₁₇×D₃₅	13
D₁₃×D₃₅	17

Subgroups — C17×D13×D35 #44525939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₁₃×D₃₅ #44525939