Subgroups — C₂×C₅×D₂₅₅ #19099843

Order 5100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₈₅	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₂₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×D₅₁	—	5	1	no	maximal
7	C₂×C₅²×C₁₇	D₃	1	1	yes	characteristic, complemented
8	C₅×D₈₅	—	3	2	no	—
9	C₂×C₃×C₅×C₁₇	—	2	2	no	—
10	C₂×C₃×C₅×C₁₇	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
12	D₂₅₅	C₂×C₅	1	2	yes	direct product factor
13	C₅×D₅₁	—	5	2	no	—
14	C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₈₅	—	3	1	no	—
16	C₂×C₅×D₁₇	—	15	1	no	—
17	C₂×C₅×D₁₅	—	17	1	no	maximal, Hall
18	C₃×C₅×C₁₇	—	2	2	no	—
19	C₃×C₅×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
20	C₃×C₅×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented
21	C₂×D₅₁	—	5	1	no	Hall
22	C₂×C₅×C₁₇	—	2	2	no	—
23	C₂×C₅×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented
24	C₂×C₅×C₁₇	D₁₅	1	1	yes	characteristic, complemented
25	D₈₅	—	3	2	no	—
26	C₅×D₁₇	—	15	2	no	—
27	C₂×C₃×C₅²	D₁₇	1	1	yes	characteristic, complemented
28	C₅×D₁₅	—	17	2	no	—
29	C₂×C₃×C₁₇	C₅×D₅	1	1	yes	characteristic, complemented
30	D₅₁	—	5	2	no	—
31	C₂×C₅×D₅	—	51	1	no	Hall
32	C₅×C₁₇	—	2	2	no	—
33	C₅×C₁₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented
34	C₅×C₁₇	C₂×D₁₅	1	1	yes	characteristic, complemented
35	C₃×C₅²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₇	—	15	1	no	Hall
37	C₂×D₁₅	—	17	1	no	—
38	C₂×C₅×D₃	—	85	1	no	—
39	C₃×C₁₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅²	D₅₁	1	1	yes	characteristic, complemented
41	C₅×D₅	—	51	2	no	—
42	C₂×C₁₇	C₅×D₁₅	1	1	yes	characteristic, complemented
43	D₁₇	—	15	2	no	—
44	C₂×C₃×C₅	—	2	2	no	—
45	C₂×C₃×C₅	C₅×D₁₇	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅	D₈₅	1	1	yes	characteristic, complemented
47	D₁₅	—	17	2	no	—
48	C₅×D₃	—	85	2	no	—
49	C₅²	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₅	—	255	1	no	—
51	C₂×D₅	—	51	1	no	—
52	C₁₇	C₂×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented
55	C₃×C₅	C₂×D₈₅	1	1	yes	characteristic, complemented
56	C₂×D₃	—	85	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	255	2	no	—
59	C₂×C₅	C₅×D₅₁	1	1	yes	characteristic, complemented
60	C₂×C₅	D₂₅₅	1	1	yes	characteristic, direct product factor
61	D₅	—	51	2	no	—
62	C₂×C₃	C₅×D₈₅	1	1	yes	characteristic, complemented
63	D₃	—	85	2	no	—
64	C₅	—	2	2	no	—
65	C₅	C₂×C₅×D₅₁	1	1	yes	characteristic, complemented
66	C₅	C₂×D₂₅₅	1	1	yes	characteristic, direct product factor
67	C₂²	—	255	1	no	Sylow
68	C₃	C₂×C₅×D₈₅	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	255	2	no	—
70	C₂	C₅×D₂₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₅₅
commutator, hypocenter	C₃×C₅×C₁₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₇	C₂
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₂₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₇	C₂	semidirect
4. C₃×C₅²×C₁₇	C₂²	semidirect
5. C₂×D₂₅₅	C₅	direct (N × H)
7. C₂×C₅²×C₁₇	D₃	semidirect
10. C₂×C₃×C₅×C₁₇	D₅	semidirect
11. C₂×C₃×C₅×C₁₇	C₂×C₅	semidirect
12. D₂₅₅	C₂×C₅	direct (N × H)
14. C₅²×C₁₇	C₂×D₃	semidirect
19. C₃×C₅×C₁₇	C₂×D₅	semidirect
20. C₃×C₅×C₁₇	C₂²×C₅	semidirect
23. C₂×C₅×C₁₇	C₅×D₃	semidirect
24. C₂×C₅×C₁₇	D₁₅	semidirect
27. C₂×C₃×C₅²	D₁₇	semidirect
29. C₂×C₃×C₁₇	C₅×D₅	semidirect
33. C₅×C₁₇	C₂×C₅×D₃	semidirect
34. C₅×C₁₇	C₂×D₁₅	semidirect
35. C₃×C₅²	C₂×D₁₇	semidirect
39. C₃×C₁₇	C₂×C₅×D₅	semidirect
40. C₂×C₅²	D₅₁	semidirect
42. C₂×C₁₇	C₅×D₁₅	semidirect
45. C₂×C₃×C₅	C₅×D₁₇	semidirect
46. C₂×C₃×C₅	D₈₅	semidirect
49. C₅²	C₂×D₅₁	semidirect
52. C₁₇	C₂×C₅×D₁₅	semidirect
54. C₃×C₅	C₂×C₅×D₁₇	semidirect
55. C₃×C₅	C₂×D₈₅	semidirect
59. C₂×C₅	C₅×D₅₁	semidirect
60. C₂×C₅	D₂₅₅	direct (N × H)
62. C₂×C₃	C₅×D₈₅	semidirect
65. C₅	C₂×C₅×D₅₁	semidirect
66. C₅	C₂×D₂₅₅	direct (N × H)
68. C₃	C₂×C₅×D₈₅	semidirect
70. C₂	C₅×D₂₅₅	direct (N × H)

Subgroups — C2×C5×D255 #19099843

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₂₅₅ #19099843