Subgroups — C₁₃×D₇×D₈₅ #44525944

Order 30940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₅₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₃×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₇×D₁₇	—	5	1	no	maximal, Hall
6	C₂×C₁₃×D₈₅	—	7	1	no	maximal, Hall
7	C₁₃×D₁₁₉	—	5	1	no	—
8	C₁₃×D₇×C₁₇	D₅	1	1	yes	characteristic, complemented
9	C₇×C₁₃×D₁₇	—	5	1	no	—
10	D₇×D₈₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×D₈₅	—	7	1	no	—
12	C₁₃×D₈₅	D₇	1	1	yes	characteristic, direct product factor
13	C₂×C₅×C₁₃×C₁₇	—	7	1	no	—
14	D₅×C₁₃×D₇	—	17	1	no	maximal, Hall
15	C₇×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	D₅₉₅	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₇×D₈₅	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₅×D₇×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₅×C₁₃×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₁₃×D₃₅	—	17	1	no	—
21	C₇×D₅×C₁₃	—	17	1	no	—
22	C₅×C₁₃×D₇	D₁₇	1	1	yes	characteristic, complemented
23	C₂×C₁₃×D₁₇	—	35	1	no	Hall
24	C₅×C₇×C₁₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	D₇×D₁₇	—	5	1	no	Hall
26	C₅×C₇×C₁₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₃×C₁₇	—	7	1	no	—
28	C₁₃×D₁₇	—	5	1	no	—
29	C₁₃×D₁₇	—	35	1	no	—
30	C₂×C₁₃×D₇	—	85	1	no	Hall
31	C₂×D₈₅	—	7	1	no	Hall
32	C₂×D₅×C₁₃	—	119	1	no	Hall
33	D₁₁₉	—	5	1	no	—
34	C₇×D₁₇	—	5	1	no	—
35	D₇×C₁₇	D₅×C₁₃	1	1	yes	characteristic, complemented
36	C₁₃×C₁₇	D₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₃	—	85	1	no	—
38	C₁₃×D₇	—	85	1	no	—
39	C₁₃×D₇	D₈₅	1	1	yes	characteristic, direct product factor
40	C₂×C₅×C₁₇	—	7	1	no	—
41	D₈₅	—	7	1	no	—
42	D₈₅	C₁₃×D₇	1	1	yes	characteristic, direct product factor
43	D₅×D₇	—	17	1	no	Hall
44	C₂×C₅×C₁₃	—	7	1	no	—
45	D₅×C₁₃	—	17	1	no	—
46	D₅×C₁₃	—	119	1	no	—
47	C₇×C₁₇	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
48	C₇×C₁₃	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
50	D₃₅	—	17	1	no	—
51	C₅×D₇	C₁₃×D₁₇	1	1	yes	characteristic, complemented
52	C₇×D₅	—	17	1	no	—
53	C₂×D₁₇	—	35	1	no	Hall
54	C₅×C₁₃	D₇×D₁₇	1	1	yes	characteristic, complemented, Hall
55	C₂²×C₁₃	—	595	1	no	Hall
56	C₅×C₇	C₂×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₇	—	7	1	no	—
58	D₁₇	—	5	1	no	—
59	D₁₇	—	35	1	no	—
60	C₂×D₇	—	85	1	no	Hall
61	C₂×C₁₃	—	7	1	no	—
62	C₂×C₁₃	—	595	1	no	—
63	C₂×C₁₃	—	85	1	no	—
64	C₂×D₅	—	119	1	no	Hall
65	C₁₇	D₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₇	—	85	1	no	—
67	D₇	—	85	1	no	—
68	D₇	C₁₃×D₈₅	1	1	yes	characteristic, direct product factor
69	C₁₃	D₇×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₅	—	7	1	no	—
71	D₅	—	17	1	no	—
72	D₅	—	119	1	no	—
73	C₇	C₂×C₁₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
74	C₅	C₁₃×D₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	595	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	595	1	no	—
78	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₇×D₈₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₂²
LCS	G ▷ C₅×C₇×C₁₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₅₉₅	C₂	semidirect
2. C₇×C₁₃×D₈₅	C₂	semidirect
3. C₅×C₁₃×D₇×C₁₇	C₂	semidirect
4. C₅×C₇×C₁₃×C₁₇	C₂²	semidirect
8. C₁₃×D₇×C₁₇	D₅	semidirect
10. D₇×D₈₅	C₁₃	direct (N × H)
12. C₁₃×D₈₅	D₇	direct (N × H)
15. C₇×C₁₃×C₁₇	C₂×D₅	semidirect
16. D₅₉₅	C₂×C₁₃	semidirect
17. C₇×D₈₅	C₂×C₁₃	semidirect
18. C₅×D₇×C₁₇	C₂×C₁₃	semidirect
19. C₅×C₁₃×C₁₇	C₂×D₇	semidirect
22. C₅×C₁₃×D₇	D₁₇	semidirect
24. C₅×C₇×C₁₇	C₂²×C₁₃	semidirect
26. C₅×C₇×C₁₃	C₂×D₁₇	semidirect
35. D₇×C₁₇	D₅×C₁₃	semidirect
36. C₁₃×C₁₇	D₅×D₇	semidirect
39. C₁₃×D₇	D₈₅	direct (N × H)
42. D₈₅	C₁₃×D₇	direct (N × H)
47. C₇×C₁₇	C₂×D₅×C₁₃	semidirect
48. C₇×C₁₃	C₂×D₈₅	semidirect
49. C₅×C₁₇	C₂×C₁₃×D₇	semidirect
51. C₅×D₇	C₁₃×D₁₇	semidirect
54. C₅×C₁₃	D₇×D₁₇	semidirect
56. C₅×C₇	C₂×C₁₃×D₁₇	semidirect
65. C₁₇	D₅×C₁₃×D₇	semidirect
68. D₇	C₁₃×D₈₅	direct (N × H)
69. C₁₃	D₇×D₈₅	direct (N × H)
73. C₇	C₂×C₁₃×D₈₅	semidirect
74. C₅	C₁₃×D₇×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₅₉₅	2
C₇×C₁₃×D₈₅	2
C₅×C₁₃×D₇×C₁₇	2
C₁₃×D₇×D₁₇	5
C₂×C₁₃×D₈₅	7
D₇×D₈₅	13
D₅×C₁₃×D₇	17

Subgroups — C13×D7×D85 #44525944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₇×D₈₅ #44525944