Subgroups — C₃×C₅×C₁₇×D₂₁ #24924240

Order 10710.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₇×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₇×C₁₇	—	3	1	no	maximal
4	C₃×C₁₇×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₁₇	—	2	1	no	—
6	C₃×C₅×C₇×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₅×D₃×C₁₇	—	7	1	no	maximal, Hall
9	C₅×D₇×C₁₇	—	3	1	no	Hall
10	C₃²×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₅×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₂₁	C₃×C₅	1	1	yes	characteristic, direct product factor
13	C₃×D₇×C₁₇	—	3	1	no	—
14	C₃×C₅×D₂₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₇×C₁₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₇	—	21	1	no	—
17	C₅×D₃×C₁₇	—	7	1	no	—
18	C₃×C₇×C₁₇	—	2	1	no	—
19	C₃×C₇×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₃²×C₅×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
22	C₃×D₃×C₁₇	—	7	1	no	Hall
23	C₃×C₅×C₁₇	—	2	1	no	—
24	C₃×C₅×C₁₇	C₃×D₇	1	1	yes	characteristic, complemented
25	C₃×C₅×C₁₇	D₂₁	1	1	yes	characteristic, direct product factor
26	D₇×C₁₇	—	3	1	no	Hall
27	C₅×D₂₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor
28	C₃×C₅×D₇	—	3	1	no	—
29	C₂×C₅×C₁₇	—	21	1	no	Hall
30	C₃²×C₁₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
31	C₃×D₂₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
32	C₇×C₁₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₇	—	2	1	no	—
34	C₃×C₅×C₇	D₃×C₁₇	1	1	yes	characteristic, complemented
35	C₃×C₅×C₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
36	C₂×C₃×C₁₇	—	21	1	no	—
37	D₃×C₁₇	—	7	1	no	—
38	C₃×C₅×D₃	—	7	1	no	Hall
39	C₅×C₁₇	C₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
40	C₅×D₇	—	3	1	no	Hall
41	C₃²×C₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₇	—	2	1	no	—
43	C₃×C₁₇	C₃×C₅×D₇	1	1	yes	characteristic, complemented
44	C₃×C₁₇	C₅×D₂₁	1	1	yes	characteristic, direct product factor
45	C₃²×C₅	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
46	D₂₁	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor
47	C₃×D₇	—	3	1	no	—
48	C₅×C₇	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₁₇	—	21	1	no	Hall
50	C₂×C₃×C₅	—	21	1	no	—
51	C₅×D₃	—	7	1	no	—
52	C₃×C₇	—	2	1	no	—
53	C₃×C₇	C₅×D₃×C₁₇	1	1	yes	characteristic, complemented
54	C₃×C₇	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
55	C₃×D₃	—	7	1	no	Hall
56	C₁₇	C₃×C₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
57	C₃×C₅	—	2	1	no	—
58	C₃×C₅	C₃×D₇×C₁₇	1	1	yes	characteristic, complemented
59	C₃×C₅	C₁₇×D₂₁	1	1	yes	characteristic, direct product factor
60	D₇	—	3	1	no	Hall
61	C₂×C₅	—	21	1	no	Hall
62	C₃²	C₅×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
63	C₇	C₃×C₅×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	21	1	no	—
65	D₃	—	7	1	no	—
66	C₅	C₃×C₁₇×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₅×D₇×C₁₇	1	1	yes	characteristic, complemented
69	C₃	C₅×C₁₇×D₂₁	1	1	yes	characteristic, direct product factor
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₇	C₂	semidirect
2. C₅×C₁₇×D₂₁	C₃	direct (N × H)
4. C₃×C₁₇×D₂₁	C₅	direct (N × H)
6. C₃×C₅×C₇×C₁₇	D₃	semidirect
7. C₃×C₅×C₇×C₁₇	C₂×C₃	semidirect
10. C₃²×C₇×C₁₇	C₂×C₅	semidirect
11. C₃²×C₅×C₁₇	D₇	semidirect
12. C₁₇×D₂₁	C₃×C₅	direct (N × H)
14. C₃×C₅×D₂₁	C₁₇	direct (N × H)
15. C₅×C₇×C₁₇	C₃×D₃	semidirect
19. C₃×C₇×C₁₇	C₅×D₃	semidirect
20. C₃×C₇×C₁₇	C₂×C₃×C₅	semidirect
21. C₃²×C₅×C₇	C₂×C₁₇	semidirect
24. C₃×C₅×C₁₇	C₃×D₇	semidirect
25. C₃×C₅×C₁₇	D₂₁	direct (N × H)
27. C₅×D₂₁	C₃×C₁₇	direct (N × H)
30. C₃²×C₁₇	C₅×D₇	semidirect
31. C₃×D₂₁	C₅×C₁₇	direct (N × H)
32. C₇×C₁₇	C₃×C₅×D₃	semidirect
34. C₃×C₅×C₇	D₃×C₁₇	semidirect
35. C₃×C₅×C₇	C₂×C₃×C₁₇	semidirect
39. C₅×C₁₇	C₃×D₂₁	direct (N × H)
41. C₃²×C₇	C₂×C₅×C₁₇	semidirect
43. C₃×C₁₇	C₃×C₅×D₇	semidirect
44. C₃×C₁₇	C₅×D₂₁	direct (N × H)
45. C₃²×C₅	D₇×C₁₇	semidirect
46. D₂₁	C₃×C₅×C₁₇	direct (N × H)
48. C₅×C₇	C₃×D₃×C₁₇	semidirect
53. C₃×C₇	C₅×D₃×C₁₇	semidirect
54. C₃×C₇	C₂×C₃×C₅×C₁₇	semidirect
56. C₁₇	C₃×C₅×D₂₁	direct (N × H)
58. C₃×C₅	C₃×D₇×C₁₇	semidirect
59. C₃×C₅	C₁₇×D₂₁	direct (N × H)
62. C₃²	C₅×D₇×C₁₇	semidirect
63. C₇	C₃×C₅×D₃×C₁₇	semidirect
66. C₅	C₃×C₁₇×D₂₁	direct (N × H)
68. C₃	C₃×C₅×D₇×C₁₇	semidirect
69. C₃	C₅×C₁₇×D₂₁	direct (N × H)

Subgroups — C3×C5×C17×D21 #24924240

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×C₁₇×D₂₁ #24924240