Subgroups — D₃₅⋊D₁₈₅ #39906014

Order 25900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₂₉₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₅⋊D₁₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₅⋊D₃₇	—	5	1	no	maximal
6	D₇×D₁₈₅	—	5	1	no	maximal
7	D₅×D₁₈₅	—	7	1	no	maximal, Hall
8	D₁₂₉₅	D₅	1	1	yes	characteristic, complemented
9	C₃₇×D₃₅	D₅	1	1	yes	characteristic, complemented
10	C₇×D₁₈₅	—	5	1	no	—
11	C₇×D₁₈₅	—	5	1	no	—
12	C₇×D₁₈₅	—	10	2	no	—
13	C₅×D₂₅₉	—	5	1	no	—
14	C₅×D₇×C₃₇	—	5	1	no	—
15	C₅⋊D₁₈₅	D₇	1	1	yes	characteristic, complemented
16	C₅×D₁₈₅	—	7	1	no	—
17	C₅×D₅×C₃₇	—	7	1	no	—
18	C₅×C₇×C₃₇	—	2	2	no	—
19	C₅×C₇×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented
20	C₅×C₇×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented
21	D₇×D₃₇	—	25	1	no	Hall
22	C₅²×C₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	C₂×D₁₈₅	—	35	1	no	—
24	D₅×D₃₇	—	35	1	no	—
25	(C₅⋊D₅)⋊D₇	—	37	1	no	maximal, Hall
26	D₂₅₉	—	5	1	no	—
27	C₇×D₃₇	—	25	1	no	—
28	D₇×C₃₇	—	5	1	no	—
29	C₂×C₅×C₃₇	—	35	1	no	—
30	D₁₈₅	—	5	1	no	—
31	D₁₈₅	—	5	1	no	—
32	D₁₈₅	—	7	1	no	—
33	D₁₈₅	—	10	2	no	—
34	C₅×D₃₇	—	35	1	no	—
35	D₅×C₃₇	—	7	1	no	—
36	C₇×C₅⋊D₅	—	37	1	no	—
37	C₅×D₃₅	—	37	1	no	—
38	C₅×D₃₅	D₃₇	1	1	yes	characteristic, complemented
39	C₇×C₃₇	D₅²	1	1	yes	characteristic, complemented, Hall
40	C₅×C₃₇	—	2	2	no	—
41	C₅×C₃₇	D₅×D₇	1	1	yes	characteristic, complemented
42	C₅×C₃₇	D₅×D₇	1	1	yes	characteristic, complemented
43	C₅²×C₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₇	—	175	1	no	Hall
45	D₅×D₇	—	185	1	no	—
46	D₅×D₇	—	185	1	no	—
47	D₅²	—	259	1	no	Hall
48	C₂×C₃₇	—	35	1	no	—
49	D₃₇	—	25	1	no	—
50	D₃₇	—	35	1	no	—
51	D₃₅	—	37	1	no	—
52	D₃₅	D₁₈₅	1	1	yes	characteristic, complemented
53	C₅×D₇	—	5	1	no	—
54	C₅×D₇	—	185	1	no	—
55	C₇×D₅	—	370	2	no	—
56	C₇×D₅	—	185	1	no	—
57	C₇×D₅	—	185	1	no	—
58	C₅⋊D₅	—	37	1	no	—
59	C₅×D₅	—	259	1	no	—
60	C₅×D₅	—	7	1	no	—
61	C₃₇	(C₅⋊D₅)⋊D₇	1	1	yes	characteristic, complemented, Sylow
62	C₅×C₇	—	2	2	no	—
63	C₅×C₇	D₅×D₃₇	1	1	yes	characteristic, complemented
64	C₅×C₇	C₂×D₁₈₅	1	1	yes	characteristic, complemented
65	C₂×D₇	—	925	1	no	Hall
66	C₅²	D₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
67	C₂×D₅	—	1295	1	no	—
68	C₂×D₅	—	1295	1	no	—
69	C₂×C₇	—	925	1	no	—
70	D₇	—	5	1	no	—
71	D₇	—	185	1	no	—
72	C₂×C₅	—	1295	1	no	—
73	C₂×C₅	—	35	1	no	—
74	D₅	—	259	1	no	—
75	D₅	—	7	1	no	—
76	D₅	—	370	2	no	—
77	D₅	—	185	1	no	—
78	D₅	—	185	1	no	—
79	C₇	D₅×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
80	C₅	—	2	2	no	—
81	C₅	D₇×D₁₈₅	1	1	yes	characteristic, complemented
82	C₅	D₃₅⋊D₃₇	1	1	yes	characteristic, complemented
83	C₂²	—	6475	1	no	Sylow
84	C₂	—	1295	1	no	—
85	C₂	—	35	1	no	—
86	C₂	—	925	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₃₇	C₂²
LCS	G ▷ C₅²×C₇×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×D₃₅	C₂	semidirect
2. C₅×D₁₂₉₅	C₂	semidirect
3. C₇×C₅⋊D₁₈₅	C₂	semidirect
4. C₅²×C₇×C₃₇	C₂²	semidirect
8. D₁₂₉₅	D₅	semidirect
9. C₃₇×D₃₅	D₅	semidirect
15. C₅⋊D₁₈₅	D₇	semidirect
19. C₅×C₇×C₃₇	C₂×D₅	semidirect
20. C₅×C₇×C₃₇	C₂×D₅	semidirect
22. C₅²×C₃₇	C₂×D₇	semidirect
38. C₅×D₃₅	D₃₇	semidirect
39. C₇×C₃₇	D₅²	semidirect
41. C₅×C₃₇	D₅×D₇	semidirect
42. C₅×C₃₇	D₅×D₇	semidirect
43. C₅²×C₇	C₂×D₃₇	semidirect
52. D₃₅	D₁₈₅	semidirect
61. C₃₇	(C₅⋊D₅)⋊D₇	semidirect
63. C₅×C₇	D₅×D₃₇	semidirect
64. C₅×C₇	C₂×D₁₈₅	semidirect
66. C₅²	D₇×D₃₇	semidirect
79. C₇	D₅×D₁₈₅	semidirect
81. C₅	D₇×D₁₈₅	semidirect
82. C₅	D₃₅⋊D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₇×D₃₅	2
C₅×D₁₂₉₅	2
C₇×C₅⋊D₁₈₅	2
D₃₅⋊D₃₇	5
D₇×D₁₈₅	5
D₅×D₁₈₅	7
(C₅⋊D₅)⋊D₇	37

Subgroups — D35⋊D185 #39906014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅⋊D₁₈₅ #39906014