Subgroups — D₅×C₁₁×D₈₅ #34035260

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×C₁₁×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×D₈₅	—	5	1	no	maximal
6	D₅×C₁₁×D₁₇	—	5	1	no	maximal
7	C₂×C₅×C₁₁×C₁₇	—	5	1	no	—
8	C₁₁×D₈₅	—	5	1	no	—
9	C₁₁×D₈₅	—	5	1	no	—
10	C₁₁×D₈₅	—	10	2	no	—
11	C₁₁×D₈₅	D₅	1	1	yes	characteristic, direct product factor
12	D₅×C₁₁×C₁₇	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₁×D₁₇	—	5	1	no	—
14	D₅×D₈₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	D₅²×C₁₁	—	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	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₅×D₈₅	C₂×C₁₁	1	1	yes	characteristic, complemented
21	C₅×D₅×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented
22	C₂×C₁₁×D₁₇	—	25	1	no	Hall
23	C₁₁×C₅⋊D₅	—	17	1	no	—
24	C₅×D₅×C₁₁	—	17	1	no	—
25	C₅×D₅×C₁₁	D₁₇	1	1	yes	characteristic, complemented
26	C₅²×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₁×C₁₇	—	5	1	no	—
28	C₁₁×D₁₇	—	5	1	no	—
29	C₁₁×D₁₇	—	25	1	no	—
30	C₂×D₈₅	—	5	1	no	—
31	D₅×D₁₇	—	5	1	no	—
32	C₅²×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×D₅×C₁₁	—	85	1	no	—
34	C₂×D₅×C₁₁	—	85	1	no	—
35	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₇	—	5	1	no	—
37	D₈₅	—	5	1	no	—
38	D₈₅	—	5	1	no	—
39	D₈₅	—	10	2	no	—
40	D₈₅	D₅×C₁₁	1	1	yes	characteristic, direct product factor
41	C₅×D₁₇	—	5	1	no	—
42	D₅×C₁₇	D₅×C₁₁	1	1	yes	characteristic, complemented
43	C₂×C₅×C₁₁	—	5	1	no	—
44	C₂×C₅×C₁₁	—	85	1	no	—
45	D₅×C₁₁	—	17	1	no	—
46	D₅×C₁₁	—	85	1	no	—
47	D₅×C₁₁	—	85	1	no	—
48	D₅×C₁₁	—	170	2	no	—
49	D₅×C₁₁	D₈₅	1	1	yes	characteristic, direct product factor
50	D₅²	—	17	1	no	Hall
51	C₅×C₁₇	—	2	2	no	—
52	C₅×C₁₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
53	C₅×C₁₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
54	C₂×D₁₇	—	25	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	—	17	1	no	—
60	C₅×D₅	C₁₁×D₁₇	1	1	yes	characteristic, complemented
61	C₂²×C₁₁	—	425	1	no	Hall
62	C₂×C₁₇	—	5	1	no	—
63	D₁₇	—	5	1	no	—
64	D₁₇	—	25	1	no	—
65	C₅²	C₂×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₁₁	—	5	1	no	—
67	C₂×C₁₁	—	85	1	no	—
68	C₂×C₁₁	—	425	1	no	—
69	C₂×D₅	—	85	1	no	—
70	C₂×D₅	—	85	1	no	—
71	C₁₇	D₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
72	C₁₁	D₅×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₅	—	5	1	no	—
74	C₂×C₅	—	85	1	no	—
75	D₅	—	17	1	no	—
76	D₅	—	85	1	no	—
77	D₅	—	85	1	no	—
78	D₅	—	170	2	no	—
79	D₅	C₁₁×D₈₅	1	1	yes	characteristic, direct product factor
80	C₅	—	2	2	no	—
81	C₅	D₅×C₁₁×D₁₇	1	1	yes	characteristic, complemented
82	C₅	C₂×C₁₁×D₈₅	1	1	yes	characteristic, complemented
83	C₂²	—	425	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	85	1	no	—
86	C₂	—	425	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₅×D₈₅
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₅⋊D₈₅	C₂	semidirect
2. C₅×C₁₁×D₈₅	C₂	semidirect
3. C₅×D₅×C₁₁×C₁₇	C₂	semidirect
4. C₅²×C₁₁×C₁₇	C₂²	semidirect
11. C₁₁×D₈₅	D₅	direct (N × H)
12. D₅×C₁₁×C₁₇	D₅	semidirect
14. D₅×D₈₅	C₁₁	direct (N × H)
17. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
18. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
19. C₅⋊D₈₅	C₂×C₁₁	semidirect
20. C₅×D₈₅	C₂×C₁₁	semidirect
21. C₅×D₅×C₁₇	C₂×C₁₁	semidirect
25. C₅×D₅×C₁₁	D₁₇	semidirect
26. C₅²×C₁₇	C₂²×C₁₁	semidirect
32. C₅²×C₁₁	C₂×D₁₇	semidirect
35. C₁₁×C₁₇	D₅²	semidirect
40. D₈₅	D₅×C₁₁	direct (N × H)
42. D₅×C₁₇	D₅×C₁₁	semidirect
49. D₅×C₁₁	D₈₅	direct (N × H)
52. C₅×C₁₇	C₂×D₅×C₁₁	semidirect
53. C₅×C₁₇	C₂×D₅×C₁₁	semidirect
56. C₅×C₁₁	D₅×D₁₇	semidirect
57. C₅×C₁₁	C₂×D₈₅	semidirect
60. C₅×D₅	C₁₁×D₁₇	semidirect
65. C₅²	C₂×C₁₁×D₁₇	semidirect
71. C₁₇	D₅²×C₁₁	semidirect
72. C₁₁	D₅×D₈₅	direct (N × H)
79. D₅	C₁₁×D₈₅	direct (N × H)
81. C₅	D₅×C₁₁×D₁₇	semidirect
82. C₅	C₂×C₁₁×D₈₅	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×C₁₁×D₈₅	2
C₅×D₅×C₁₁×C₁₇	2
C₂×C₁₁×D₈₅	5
D₅×C₁₁×D₁₇	5
D₅×D₈₅	11
D₅²×C₁₁	17

Subgroups — D5×C11×D85 #34035260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×D₈₅ #34035260