Subgroups — C₂×C₃×C₅×D₅×C₁₇ #19099836

Order 5100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₇	D₅
commutator, hypocenter	C₅	C₂²×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅×C₁₇	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₇	C₂	semidirect
3. C₂×C₅×D₅×C₁₇	C₃	direct (N × H)
4. C₃×C₅²×C₁₇	C₂²	semidirect
6. C₂×C₃×D₅×C₁₇	C₅	direct (N × H)
7. C₂×C₅²×C₁₇	C₂×C₃	semidirect
8. C₅×D₅×C₁₇	C₂×C₃	direct (N × H)
11. C₂×C₃×C₅×C₁₇	D₅	direct (N × H)
12. C₂×C₃×C₅×C₁₇	C₂×C₅	semidirect
13. C₃×D₅×C₁₇	C₂×C₅	direct (N × H)
14. C₅²×C₁₇	C₂²×C₃	semidirect
16. C₂×D₅×C₁₇	C₃×C₅	direct (N × H)
17. C₂×C₃×C₅×D₅	C₁₇	direct (N × H)
19. C₃×C₅×C₁₇	C₂×D₅	direct (N × H)
20. C₃×C₅×C₁₇	C₂²×C₅	semidirect
24. C₂×C₅×C₁₇	C₃×D₅	direct (N × H)
25. C₂×C₅×C₁₇	C₂×C₃×C₅	semidirect
26. D₅×C₁₇	C₂×C₃×C₅	direct (N × H)
27. C₂×C₃×C₅²	C₂×C₁₇	semidirect
28. C₃×C₅×D₅	C₂×C₁₇	direct (N × H)
30. C₂×C₃×C₁₇	C₅×D₅	direct (N × H)
31. C₂×C₅×D₅	C₃×C₁₇	direct (N × H)
33. C₅×C₁₇	C₂×C₃×D₅	direct (N × H)
34. C₅×C₁₇	C₂²×C₃×C₅	semidirect
35. C₃×C₅²	C₂²×C₁₇	semidirect
38. C₂×C₃×D₅	C₅×C₁₇	direct (N × H)
39. C₃×C₁₇	C₂×C₅×D₅	direct (N × H)
40. C₂×C₅²	C₂×C₃×C₁₇	semidirect
41. C₅×D₅	C₂×C₃×C₁₇	direct (N × H)
43. C₂×C₁₇	C₃×C₅×D₅	direct (N × H)
46. C₂×C₃×C₅	D₅×C₁₇	direct (N × H)
47. C₂×C₃×C₅	C₂×C₅×C₁₇	semidirect
48. C₃×D₅	C₂×C₅×C₁₇	direct (N × H)
49. C₅²	C₂²×C₃×C₁₇	semidirect
51. C₂×D₅	C₃×C₅×C₁₇	direct (N × H)
52. C₁₇	C₂×C₃×C₅×D₅	direct (N × H)
54. C₃×C₅	C₂×D₅×C₁₇	direct (N × H)
55. C₃×C₅	C₂²×C₅×C₁₇	semidirect
59. C₂×C₅	C₃×D₅×C₁₇	direct (N × H)
60. C₂×C₅	C₂×C₃×C₅×C₁₇	semidirect
61. D₅	C₂×C₃×C₅×C₁₇	direct (N × H)
63. C₂×C₃	C₅×D₅×C₁₇	direct (N × H)
65. C₅	C₂×C₃×D₅×C₁₇	direct (N × H)
66. C₅	C₂²×C₃×C₅×C₁₇	semidirect
68. C₃	C₂×C₅×D₅×C₁₇	direct (N × H)
70. C₂	C₃×C₅×D₅×C₁₇	direct (N × H)

Subgroups — C2×C3×C5×D5×C17 #19099836

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×D₅×C₁₇ #19099836