Subgroups — D₅×D₂₅₅ #19099826

Order 5100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₈₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₈₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₂₅₅	—	5	1	no	maximal
7	D₅×D₅₁	—	5	1	no	maximal
8	C₅⋊D₈₅	—	3	1	no	—
9	C₅×D₈₅	—	3	1	no	—
10	C₅×D₅×C₁₇	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₁₇	—	5	1	no	—
12	D₂₅₅	—	5	1	no	—
13	D₂₅₅	—	5	1	no	—
14	D₂₅₅	—	10	2	no	—
15	D₂₅₅	D₅	1	1	yes	characteristic, direct product factor
16	C₅×D₅₁	—	5	1	no	—
17	C₃×D₅×C₁₇	D₅	1	1	yes	characteristic, complemented
18	C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₈₅	—	15	1	no	—
20	D₅×D₁₇	—	15	1	no	—
21	D₅×D₁₅	—	17	1	no	maximal, Hall
22	C₃×C₅×C₁₇	—	2	2	no	—
23	C₃×C₅×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
25	C₂×D₅₁	—	25	1	no	Hall
26	C₂×C₅×C₁₇	—	5	1	no	—
27	D₈₅	—	3	1	no	—
28	D₈₅	—	15	1	no	—
29	D₈₅	—	15	1	no	—
30	D₈₅	—	30	2	no	—
31	C₅×D₁₇	—	15	1	no	—
32	D₅×C₁₇	D₁₅	1	1	yes	characteristic, complemented
33	C₃⋊(C₅⋊D₅)	—	17	1	no	—
34	C₅×D₁₅	—	17	1	no	—
35	C₃×C₅×D₅	D₁₇	1	1	yes	characteristic, complemented
36	C₂×C₃×C₁₇	—	5	1	no	—
37	D₅₁	—	5	1	no	—
38	D₅₁	—	25	1	no	—
39	D₅²	—	51	1	no	Hall
40	C₅×C₁₇	—	2	2	no	—
41	C₅×C₁₇	D₃×D₅	1	1	yes	characteristic, complemented
42	C₅×C₁₇	C₂×D₁₅	1	1	yes	characteristic, complemented
43	C₃×C₅²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₁₇	—	75	1	no	Hall
45	C₂×D₁₅	—	85	1	no	—
46	D₃×D₅	—	85	1	no	—
47	C₃×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
48	C₅⋊D₅	—	51	1	no	—
49	C₅×D₅	—	51	1	no	—
50	C₅×D₅	D₅₁	1	1	yes	characteristic, complemented
51	C₂×C₁₇	—	5	1	no	—
52	D₁₇	—	15	1	no	—
53	D₁₇	—	75	1	no	—
54	C₂×C₃×C₅	—	5	1	no	—
55	D₁₅	—	17	1	no	—
56	D₁₅	—	85	1	no	—
57	D₁₅	—	85	1	no	—
58	D₁₅	—	170	2	no	—
59	C₃×D₅	D₈₅	1	1	yes	characteristic, complemented
60	C₅×D₃	—	85	1	no	—
61	C₅²	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
62	C₂×D₅	—	255	1	no	—
63	C₂×D₅	—	255	1	no	—
64	C₁₇	D₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₁₇	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₈₅	1	1	yes	characteristic, complemented
68	C₂×D₃	—	425	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	255	1	no	—
71	D₅	—	51	1	no	—
72	D₅	—	510	2	no	—
73	D₅	—	255	1	no	—
74	D₅	—	255	1	no	—
75	D₅	D₂₅₅	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	5	1	no	—
77	D₃	—	85	1	no	—
78	D₃	—	425	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₅×D₅₁	1	1	yes	characteristic, complemented
81	C₅	C₂×D₂₅₅	1	1	yes	characteristic, complemented
82	C₂²	—	1275	1	no	Sylow
83	C₃	D₅×D₈₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	1275	1	no	—
86	C₂	—	255	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₈₅)	C₂	semidirect
2. C₅×D₂₅₅	C₂	semidirect
3. C₃×C₅×D₅×C₁₇	C₂	semidirect
5. C₃×C₅²×C₁₇	C₂²	semidirect
10. C₅×D₅×C₁₇	D₃	semidirect
15. D₂₅₅	D₅	direct (N × H)
17. C₃×D₅×C₁₇	D₅	semidirect
18. C₅²×C₁₇	C₂×D₃	semidirect
23. C₃×C₅×C₁₇	C₂×D₅	semidirect
24. C₃×C₅×C₁₇	C₂×D₅	semidirect
32. D₅×C₁₇	D₁₅	semidirect
35. C₃×C₅×D₅	D₁₇	semidirect
41. C₅×C₁₇	D₃×D₅	semidirect
42. C₅×C₁₇	C₂×D₁₅	semidirect
43. C₃×C₅²	C₂×D₁₇	semidirect
47. C₃×C₁₇	D₅²	semidirect
50. C₅×D₅	D₅₁	semidirect
59. C₃×D₅	D₈₅	semidirect
61. C₅²	C₂×D₅₁	semidirect
64. C₁₇	D₅×D₁₅	semidirect
66. C₃×C₅	D₅×D₁₇	semidirect
67. C₃×C₅	C₂×D₈₅	semidirect
75. D₅	D₂₅₅	direct (N × H)
80. C₅	D₅×D₅₁	semidirect
81. C₅	C₂×D₂₅₅	semidirect
83. C₃	D₅×D₈₅	semidirect

Subgroups — D5×D255 #19099826

Conjugacy classes of subgroups

Complements

Subgroups — D₅×D₂₅₅ #19099826