Subgroups — C₃²×C₅×C₇×D₁₇ #24924249

Order 10710.

96 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	C₃×C₅×C₇×D₁₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×D₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	C₂×C₃	1	4	yes	complemented
5	C₃²×C₅×D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×D₁₇	C₃×C₅	1	4	yes	direct product factor
10	C₂×C₃²×C₅×C₇	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₁₇	C₃×C₇	1	4	yes	direct product factor
13	C₃×C₇×C₁₇	C₂×C₃×C₅	1	4	yes	complemented
14	C₃²×C₅×C₇	D₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃²×D₁₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅×C₁₇	C₂×C₃×C₇	1	4	yes	complemented
17	C₇×D₁₇	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₅×C₇	—	17	4	no	—
19	C₅×D₁₇	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₃²×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃²×C₇	—	17	1	no	Hall
22	C₇×C₁₇	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	C₃×D₁₇	1	4	yes	direct product factor
24	C₃×D₁₇	C₃×C₅×C₇	1	4	yes	direct product factor
25	C₂×C₃²×C₅	—	17	1	no	Hall
26	C₅×C₁₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₇	—	17	1	no	Hall
28	C₃²×C₇	C₅×D₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₁₇	C₂×C₃×C₅×C₇	1	4	yes	complemented
30	C₃²×C₅	C₇×D₁₇	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₇	—	17	4	no	—
32	C₅×C₇	C₃²×D₁₇	1	1	yes	characteristic, direct product factor, Hall
33	D₁₇	C₃²×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅	—	17	4	no	—
35	C₃×C₇	C₃×C₅×D₁₇	1	4	yes	direct product factor
36	C₂×C₃²	—	17	1	no	Hall
37	C₁₇	C₂×C₃²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	C₃×C₇×D₁₇	1	4	yes	direct product factor
39	C₂×C₇	—	17	1	no	Hall
40	C₂×C₅	—	17	1	no	Hall
41	C₃²	C₅×C₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃²×C₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	17	4	no	—
44	C₅	C₃²×C₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×C₇×D₁₇	1	4	yes	direct product factor
46	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅×C₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃²×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₇	C₂	semidirect
2. C₃×C₅×C₇×D₁₇	C₃	direct (N × H)
3. C₃²×C₇×D₁₇	C₅	direct (N × H)
4. C₃×C₅×C₇×C₁₇	C₂×C₃	semidirect
5. C₃²×C₅×D₁₇	C₇	direct (N × H)
6. C₅×C₇×D₁₇	C₃²	direct (N × H)
7. C₃²×C₇×C₁₇	C₂×C₅	semidirect
8. C₃²×C₅×C₁₇	C₂×C₇	semidirect
9. C₃×C₇×D₁₇	C₃×C₅	direct (N × H)
11. C₅×C₇×C₁₇	C₂×C₃²	semidirect
12. C₃×C₅×D₁₇	C₃×C₇	direct (N × H)
13. C₃×C₇×C₁₇	C₂×C₃×C₅	semidirect
14. C₃²×C₅×C₇	D₁₇	direct (N × H)
15. C₃²×D₁₇	C₅×C₇	direct (N × H)
16. C₃×C₅×C₁₇	C₂×C₃×C₇	semidirect
17. C₇×D₁₇	C₃²×C₅	direct (N × H)
19. C₅×D₁₇	C₃²×C₇	direct (N × H)
20. C₃²×C₁₇	C₂×C₅×C₇	semidirect
22. C₇×C₁₇	C₂×C₃²×C₅	semidirect
23. C₃×C₅×C₇	C₃×D₁₇	direct (N × H)
24. C₃×D₁₇	C₃×C₅×C₇	direct (N × H)
26. C₅×C₁₇	C₂×C₃²×C₇	semidirect
28. C₃²×C₇	C₅×D₁₇	direct (N × H)
29. C₃×C₁₇	C₂×C₃×C₅×C₇	semidirect
30. C₃²×C₅	C₇×D₁₇	direct (N × H)
32. C₅×C₇	C₃²×D₁₇	direct (N × H)
33. D₁₇	C₃²×C₅×C₇	direct (N × H)
35. C₃×C₇	C₃×C₅×D₁₇	direct (N × H)
37. C₁₇	C₂×C₃²×C₅×C₇	semidirect
38. C₃×C₅	C₃×C₇×D₁₇	direct (N × H)
41. C₃²	C₅×C₇×D₁₇	direct (N × H)
42. C₇	C₃²×C₅×D₁₇	direct (N × H)
44. C₅	C₃²×C₇×D₁₇	direct (N × H)
45. C₃	C₃×C₅×C₇×D₁₇	direct (N × H)

Subgroups — C32×C5×C7×D17 #24924249

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₅×C₇×D₁₇ #24924249