Subgroups — D₈₅⋊D₃₅ #26045455

Order 11900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅⋊D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅₉₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₅⋊D₁₇	—	5	1	no	maximal
6	D₁₇×D₃₅	—	5	1	no	maximal
7	(C₅⋊D₅)⋊D₁₇	—	7	1	no	maximal, Hall
8	D₅₉₅	D₅	1	1	yes	characteristic, complemented
9	C₁₇×D₃₅	—	5	1	no	—
10	C₁₇×D₃₅	—	5	1	no	—
11	C₁₇×D₃₅	—	10	2	no	—
12	C₇×D₈₅	D₅	1	1	yes	characteristic, complemented
13	C₅×D₁₁₉	—	5	1	no	—
14	C₅×C₇×D₁₇	—	5	1	no	—
15	C₁₇×C₅⋊D₅	—	7	1	no	—
16	C₅×D₈₅	—	7	1	no	—
17	C₅×D₈₅	D₇	1	1	yes	characteristic, complemented
18	D₅×D₃₅	—	17	1	no	maximal, Hall
19	C₅×C₇×C₁₇	—	2	2	no	—
20	C₅×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
21	C₅×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
22	D₇×D₁₇	—	25	1	no	Hall
23	C₅²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₅⋊D₃₅	D₁₇	1	1	yes	characteristic, complemented
25	C₅×D₃₅	—	17	1	no	—
26	C₅×C₇×D₅	—	17	1	no	—
27	D₅×D₁₇	—	35	1	no	—
28	D₅×D₁₇	—	35	1	no	—
29	D₁₁₉	—	5	1	no	—
30	C₇×D₁₇	—	5	1	no	—
31	D₇×C₁₇	—	25	1	no	—
32	C₅²×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
33	D₈₅	—	7	1	no	—
34	D₈₅	D₃₅	1	1	yes	characteristic, complemented
35	C₅×D₁₇	—	5	1	no	—
36	C₅×D₁₇	—	35	1	no	—
37	D₅×C₁₇	—	35	1	no	—
38	D₅×C₁₇	—	35	1	no	—
39	D₅×C₁₇	—	70	2	no	—
40	C₂×D₃₅	—	85	1	no	—
41	D₅×D₇	—	85	1	no	—
42	C₇×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
43	D₅²	—	119	1	no	Hall
44	C₅×C₁₇	—	2	2	no	—
45	C₅×C₁₇	D₅×D₇	1	1	yes	characteristic, complemented
46	C₅×C₁₇	C₂×D₃₅	1	1	yes	characteristic, complemented
47	C₂×C₅×C₇	—	85	1	no	—
48	D₃₅	—	5	1	no	—
49	D₃₅	—	5	1	no	—
50	D₃₅	—	10	2	no	—
51	D₃₅	—	17	1	no	—
52	C₅×D₇	—	85	1	no	—
53	C₇×D₅	—	17	1	no	—
54	C₂×D₁₇	—	175	1	no	Hall
55	C₅⋊D₅	—	7	1	no	—
56	C₅×D₅	—	17	1	no	—
57	C₅×D₅	—	119	1	no	—
58	C₅×C₇	—	2	2	no	—
59	C₅×C₇	D₅×D₁₇	1	1	yes	characteristic, complemented
60	C₅×C₇	D₅×D₁₇	1	1	yes	characteristic, complemented
61	C₂×C₁₇	—	175	1	no	—
62	D₁₇	—	5	1	no	—
63	D₁₇	—	35	1	no	—
64	C₂×D₇	—	425	1	no	Hall
65	C₅²	D₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₅	—	595	1	no	—
67	C₂×D₅	—	595	1	no	—
68	C₁₇	D₅×D₃₅	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₇	—	85	1	no	—
70	D₇	—	25	1	no	—
71	D₇	—	85	1	no	—
72	C₂×C₅	—	595	1	no	—
73	C₂×C₅	—	85	1	no	—
74	D₅	—	17	1	no	—
75	D₅	—	35	1	no	—
76	D₅	—	35	1	no	—
77	D₅	—	70	2	no	—
78	D₅	—	119	1	no	—
79	C₇	(C₅⋊D₅)⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
80	C₅	—	2	2	no	—
81	C₅	D₁₇×D₃₅	1	1	yes	characteristic, complemented
82	C₅	D₃₅⋊D₁₇	1	1	yes	characteristic, complemented
83	C₂²	—	2975	1	no	Sylow
84	C₂	—	595	1	no	—
85	C₂	—	85	1	no	—
86	C₂	—	175	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₅²×C₇×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅⋊D₃₅	C₂	semidirect
2. C₅×D₅₉₅	C₂	semidirect
3. C₅×C₇×D₈₅	C₂	semidirect
4. C₅²×C₇×C₁₇	C₂²	semidirect
8. D₅₉₅	D₅	semidirect
12. C₇×D₈₅	D₅	semidirect
17. C₅×D₈₅	D₇	semidirect
20. C₅×C₇×C₁₇	C₂×D₅	semidirect
21. C₅×C₇×C₁₇	C₂×D₅	semidirect
23. C₅²×C₁₇	C₂×D₇	semidirect
24. C₅⋊D₃₅	D₁₇	semidirect
32. C₅²×C₇	C₂×D₁₇	semidirect
34. D₈₅	D₃₅	semidirect
42. C₇×C₁₇	D₅²	semidirect
45. C₅×C₁₇	D₅×D₇	semidirect
46. C₅×C₁₇	C₂×D₃₅	semidirect
59. C₅×C₇	D₅×D₁₇	semidirect
60. C₅×C₇	D₅×D₁₇	semidirect
65. C₅²	D₇×D₁₇	semidirect
68. C₁₇	D₅×D₃₅	semidirect
79. C₇	(C₅⋊D₅)⋊D₁₇	semidirect
81. C₅	D₁₇×D₃₅	semidirect
82. C₅	D₃₅⋊D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₅⋊D₃₅	2
C₅×D₅₉₅	2
C₅×C₇×D₈₅	2
D₃₅⋊D₁₇	5
D₁₇×D₃₅	5
(C₅⋊D₅)⋊D₁₇	7
D₅×D₃₅	17

Subgroups — D85⋊D35 #26045455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈₅⋊D₃₅ #26045455