Subgroups — D₅₅⋊D₈₅ #34035267

Order 18700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₅⋊D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₉₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₅⋊D₁₇	—	5	1	no	maximal
6	D₁₁×D₈₅	—	5	1	no	maximal
7	D₉₃₅	D₅	1	1	yes	characteristic, complemented
8	C₁₇×D₅₅	D₅	1	1	yes	characteristic, complemented
9	C₁₁×D₈₅	—	5	1	no	—
10	C₁₁×D₈₅	—	5	1	no	—
11	C₁₁×D₈₅	—	10	2	no	—
12	C₅×D₁₈₇	—	5	1	no	—
13	C₅×C₁₇×D₁₁	—	5	1	no	—
14	D₅×D₈₅	—	11	1	no	maximal, Hall
15	(C₅⋊D₅)⋊D₁₁	—	17	1	no	maximal, Hall
16	C₅×C₁₁×C₁₇	—	2	2	no	—
17	C₅×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
18	C₅×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
19	C₅⋊D₈₅	D₁₁	1	1	yes	characteristic, complemented
20	C₅×D₈₅	—	11	1	no	—
21	C₅×D₅×C₁₇	—	11	1	no	—
22	D₁₁×D₁₇	—	25	1	no	Hall
23	C₁₁×C₅⋊D₅	—	17	1	no	—
24	C₅×D₅₅	—	17	1	no	—
25	C₅×D₅₅	D₁₇	1	1	yes	characteristic, complemented
26	C₅²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
27	D₁₈₇	—	5	1	no	—
28	C₁₁×D₁₇	—	25	1	no	—
29	C₁₇×D₁₁	—	5	1	no	—
30	C₂×D₈₅	—	55	1	no	—
31	D₅×D₁₇	—	55	1	no	—
32	C₅²×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
33	D₅×D₁₁	—	85	1	no	—
34	D₅×D₁₁	—	85	1	no	—
35	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₇	—	55	1	no	—
37	D₈₅	—	5	1	no	—
38	D₈₅	—	5	1	no	—
39	D₈₅	—	10	2	no	—
40	D₈₅	—	11	1	no	—
41	C₅×D₁₇	—	55	1	no	—
42	D₅×C₁₇	—	11	1	no	—
43	D₅₅	—	17	1	no	—
44	D₅₅	D₈₅	1	1	yes	characteristic, complemented
45	C₅×D₁₁	—	5	1	no	—
46	C₅×D₁₁	—	85	1	no	—
47	D₅×C₁₁	—	85	1	no	—
48	D₅×C₁₁	—	85	1	no	—
49	D₅×C₁₁	—	170	2	no	—
50	D₅²	—	187	1	no	Hall
51	C₅×C₁₇	—	2	2	no	—
52	C₅×C₁₇	D₅×D₁₁	1	1	yes	characteristic, complemented
53	C₅×C₁₇	D₅×D₁₁	1	1	yes	characteristic, complemented
54	C₂×D₁₇	—	275	1	no	Hall
55	C₅×C₁₁	—	2	2	no	—
56	C₅×C₁₁	D₅×D₁₇	1	1	yes	characteristic, complemented
57	C₅×C₁₁	C₂×D₈₅	1	1	yes	characteristic, complemented
58	C₅⋊D₅	—	17	1	no	—
59	C₅×D₅	—	11	1	no	—
60	C₅×D₅	—	187	1	no	—
61	C₂×D₁₁	—	425	1	no	Hall
62	C₂×C₁₇	—	55	1	no	—
63	D₁₇	—	25	1	no	—
64	D₁₇	—	55	1	no	—
65	C₅²	D₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₁₁	—	425	1	no	—
67	D₁₁	—	5	1	no	—
68	D₁₁	—	85	1	no	—
69	C₂×D₅	—	935	1	no	—
70	C₂×D₅	—	935	1	no	—
71	C₁₇	(C₅⋊D₅)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
72	C₁₁	D₅×D₈₅	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	55	1	no	—
74	C₂×C₅	—	935	1	no	—
75	D₅	—	11	1	no	—
76	D₅	—	85	1	no	—
77	D₅	—	85	1	no	—
78	D₅	—	170	2	no	—
79	D₅	—	187	1	no	—
80	C₅	—	2	2	no	—
81	C₅	D₁₁×D₈₅	1	1	yes	characteristic, complemented
82	C₅	D₅₅⋊D₁₇	1	1	yes	characteristic, complemented
83	C₂²	—	4675	1	no	Sylow
84	C₂	—	55	1	no	—
85	C₂	—	935	1	no	—
86	C₂	—	425	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₁×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₅⋊D₈₅	C₂	semidirect
2. C₅×D₉₃₅	C₂	semidirect
3. C₅×C₁₇×D₅₅	C₂	semidirect
4. C₅²×C₁₁×C₁₇	C₂²	semidirect
7. D₉₃₅	D₅	semidirect
8. C₁₇×D₅₅	D₅	semidirect
17. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
18. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
19. C₅⋊D₈₅	D₁₁	semidirect
25. C₅×D₅₅	D₁₇	semidirect
26. C₅²×C₁₇	C₂×D₁₁	semidirect
32. C₅²×C₁₁	C₂×D₁₇	semidirect
35. C₁₁×C₁₇	D₅²	semidirect
44. D₅₅	D₈₅	semidirect
52. C₅×C₁₇	D₅×D₁₁	semidirect
53. C₅×C₁₇	D₅×D₁₁	semidirect
56. C₅×C₁₁	D₅×D₁₇	semidirect
57. C₅×C₁₁	C₂×D₈₅	semidirect
65. C₅²	D₁₁×D₁₇	semidirect
71. C₁₇	(C₅⋊D₅)⋊D₁₁	semidirect
72. C₁₁	D₅×D₈₅	semidirect
81. C₅	D₁₁×D₈₅	semidirect
82. C₅	D₅₅⋊D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₅⋊D₈₅	2
C₅×D₉₃₅	2
C₅×C₁₇×D₅₅	2
D₅₅⋊D₁₇	5
D₁₁×D₈₅	5
D₅×D₈₅	11
(C₅⋊D₅)⋊D₁₁	17

Subgroups — D55⋊D85 #34035267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₅⋊D₈₅ #34035267