Subgroups — C₅×C₁₁×D₂₅₅ #43242545

Order 28050.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₈₅	—	3	1	no	maximal, Hall
3	C₁₁×D₂₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₁₁×D₅₁	—	5	1	no	maximal
5	C₅²×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁×C₁₇	—	2	2	no	—
7	C₃×C₅×C₁₁×C₁₇	D₅	1	1	yes	characteristic, complemented
8	C₃×C₅×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₂₅₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₁×D₈₅	—	3	1	no	—
11	C₅×C₁₁×D₁₇	—	15	1	no	—
12	C₅×C₁₁×D₁₅	—	17	1	no	maximal, Hall
13	C₃×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×D₅₁	—	5	1	no	Hall
15	C₅×C₁₁×C₁₇	—	2	2	no	—
16	C₅×C₁₁×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented
17	C₅×C₁₁×C₁₇	D₁₅	1	1	yes	characteristic, complemented
18	C₅×D₈₅	—	3	1	no	Hall
19	C₃×C₅²×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×C₁₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
21	C₅×D₅×C₁₁	—	51	1	no	Hall
22	D₂₅₅	C₅×C₁₁	1	1	yes	characteristic, direct product factor
23	C₅×D₅₁	—	5	1	no	—
24	C₅²×C₁₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁×D₁₇	—	15	1	no	Hall
26	C₁₁×D₁₅	—	17	1	no	—
27	C₅×D₃×C₁₁	—	85	1	no	—
28	C₅²×C₁₁	D₅₁	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₁₇	—	2	2	no	—
30	C₃×C₅×C₁₇	D₅×C₁₁	1	1	yes	characteristic, complemented
31	C₃×C₅×C₁₇	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
32	C₁₁×C₁₇	C₅×D₁₅	1	1	yes	characteristic, complemented, Hall
33	D₈₅	—	3	1	no	—
34	C₅×D₁₇	—	15	1	no	—
35	C₃×C₅×C₁₁	—	2	2	no	—
36	C₃×C₅×C₁₁	C₅×D₁₇	1	1	yes	characteristic, complemented
37	C₃×C₅×C₁₁	D₈₅	1	1	yes	characteristic, complemented
38	C₅×D₁₅	—	17	1	no	Hall
39	C₂×C₅×C₁₁	—	255	1	no	—
40	D₅×C₁₁	—	51	1	no	—
41	D₅₁	—	5	1	no	Hall
42	C₅×C₁₇	—	2	2	no	—
43	C₅×C₁₇	C₅×D₃×C₁₁	1	1	yes	characteristic, complemented
44	C₅×C₁₇	C₁₁×D₁₅	1	1	yes	characteristic, complemented
45	C₃×C₅²	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
46	D₃×C₁₁	—	85	1	no	Hall
47	C₅×C₁₁	—	2	2	no	—
48	C₅×C₁₁	C₅×D₅₁	1	1	yes	characteristic, complemented
49	C₅×C₁₁	D₂₅₅	1	1	yes	characteristic, direct product factor
50	C₃×C₁₇	C₅×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
51	C₅×D₅	—	51	1	no	Hall
52	D₁₇	—	15	1	no	Hall
53	C₃×C₁₁	C₅×D₈₅	1	1	yes	characteristic, complemented, Hall
54	D₁₅	—	17	1	no	—
55	C₅×D₃	—	85	1	no	—
56	C₅²	C₁₁×D₅₁	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₁₁	—	255	1	no	Hall
58	C₁₇	C₅×C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₅	—	2	2	no	—
60	C₃×C₅	C₅×C₁₁×D₁₇	1	1	yes	characteristic, complemented
61	C₃×C₅	C₁₁×D₈₅	1	1	yes	characteristic, complemented
62	C₁₁	C₅×D₂₅₅	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₅	—	255	1	no	—
64	D₅	—	51	1	no	—
65	D₃	—	85	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×C₁₁×D₅₁	1	1	yes	characteristic, complemented
68	C₅	C₁₁×D₂₅₅	1	1	yes	characteristic, direct product factor
69	C₃	C₅×C₁₁×D₈₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	255	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₂₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₇	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₇	C₂	semidirect
3. C₁₁×D₂₅₅	C₅	direct (N × H)
5. C₅²×C₁₁×C₁₇	D₃	semidirect
7. C₃×C₅×C₁₁×C₁₇	D₅	semidirect
8. C₃×C₅×C₁₁×C₁₇	C₂×C₅	semidirect
9. C₅×D₂₅₅	C₁₁	direct (N × H)
13. C₃×C₅²×C₁₇	C₂×C₁₁	semidirect
16. C₅×C₁₁×C₁₇	C₅×D₃	semidirect
17. C₅×C₁₁×C₁₇	D₁₅	semidirect
19. C₃×C₅²×C₁₁	D₁₇	semidirect
20. C₃×C₁₁×C₁₇	C₅×D₅	semidirect
22. D₂₅₅	C₅×C₁₁	direct (N × H)
24. C₅²×C₁₇	D₃×C₁₁	semidirect
28. C₅²×C₁₁	D₅₁	semidirect
30. C₃×C₅×C₁₇	D₅×C₁₁	semidirect
31. C₃×C₅×C₁₇	C₂×C₅×C₁₁	semidirect
32. C₁₁×C₁₇	C₅×D₁₅	semidirect
36. C₃×C₅×C₁₁	C₅×D₁₇	semidirect
37. C₃×C₅×C₁₁	D₈₅	semidirect
43. C₅×C₁₇	C₅×D₃×C₁₁	semidirect
44. C₅×C₁₇	C₁₁×D₁₅	semidirect
45. C₃×C₅²	C₁₁×D₁₇	semidirect
48. C₅×C₁₁	C₅×D₅₁	semidirect
49. C₅×C₁₁	D₂₅₅	direct (N × H)
50. C₃×C₁₇	C₅×D₅×C₁₁	semidirect
53. C₃×C₁₁	C₅×D₈₅	semidirect
56. C₅²	C₁₁×D₅₁	semidirect
58. C₁₇	C₅×C₁₁×D₁₅	semidirect
60. C₃×C₅	C₅×C₁₁×D₁₇	semidirect
61. C₃×C₅	C₁₁×D₈₅	semidirect
62. C₁₁	C₅×D₂₅₅	direct (N × H)
67. C₅	C₅×C₁₁×D₅₁	semidirect
68. C₅	C₁₁×D₂₅₅	direct (N × H)
69. C₃	C₅×C₁₁×D₈₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁×C₁₇	2
C₅×C₁₁×D₈₅	3
C₁₁×D₂₅₅	5
C₅×C₁₁×D₅₁	5
C₅×D₂₅₅	11
C₅×C₁₁×D₁₅	17

Subgroups — C5×C11×D255 #43242545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₂₅₅ #43242545