Subgroups — C₅×D₃×D₅×C₁₇ #19099804

Order 5100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₇	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×D₁₅	C₂	semidirect
2. C₅²×D₃×C₁₇	C₂	semidirect
3. C₃×C₅×D₅×C₁₇	C₂	semidirect
5. C₃×C₅²×C₁₇	C₂²	semidirect
7. D₃×D₅×C₁₇	C₅	direct (N × H)
10. C₅×D₅×C₁₇	D₃	direct (N × H)
12. C₁₇×D₁₅	C₂×C₅	semidirect
15. C₅×D₃×C₁₇	D₅	direct (N × H)
16. C₅×D₃×C₁₇	C₂×C₅	semidirect
17. C₃×D₅×C₁₇	C₂×C₅	semidirect
18. C₅²×C₁₇	C₂×D₃	semidirect
21. C₅×D₃×D₅	C₁₇	direct (N × H)
23. C₃×C₅×C₁₇	C₂×D₅	semidirect
24. C₃×C₅×C₁₇	C₂²×C₅	semidirect
32. D₅×C₁₇	C₅×D₃	direct (N × H)
33. C₅×D₁₅	C₂×C₁₇	semidirect
34. C₅²×D₃	C₂×C₁₇	semidirect
35. C₃×C₅×D₅	C₂×C₁₇	semidirect
38. D₃×C₁₇	C₅×D₅	direct (N × H)
41. C₅×C₁₇	D₃×D₅	direct (N × H)
42. C₅×C₁₇	C₂×C₅×D₃	semidirect
43. C₃×C₅²	C₂²×C₁₇	semidirect
46. D₃×D₅	C₅×C₁₇	direct (N × H)
47. C₃×C₁₇	C₂×C₅×D₅	semidirect
50. C₅×D₅	D₃×C₁₇	direct (N × H)
55. D₁₅	C₂×C₅×C₁₇	semidirect
56. C₃×D₅	C₂×C₅×C₁₇	semidirect
59. C₅×D₃	D₅×C₁₇	direct (N × H)
60. C₅×D₃	C₂×C₅×C₁₇	semidirect
61. C₅²	C₂×D₃×C₁₇	semidirect
64. C₁₇	C₅×D₃×D₅	direct (N × H)
66. C₃×C₅	C₂×D₅×C₁₇	semidirect
67. C₃×C₅	C₂²×C₅×C₁₇	semidirect
75. D₅	C₅×D₃×C₁₇	direct (N × H)
78. D₃	C₅×D₅×C₁₇	direct (N × H)
80. C₅	D₃×D₅×C₁₇	direct (N × H)
81. C₅	C₂×C₅×D₃×C₁₇	semidirect
83. C₃	C₂×C₅×D₅×C₁₇	semidirect

Subgroups — C5×D3×D5×C17 #19099804

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃×D₅×C₁₇ #19099804