Subgroups — C₃×C₇²×D₅×C₁₇ #38735985

Order 24990.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₅×C₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₇²×C₁₇	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₅×C₁₇	C₇	1	8	yes	maximal, direct product factor
6	C₃×C₇²×C₁₇	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₇×C₁₇	C₂×C₇	1	8	yes	complemented
8	C₂×C₇²×C₁₇	—	5	1	no	Hall
9	C₃×C₇²×D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×D₅×C₁₇	C₃×C₇	1	8	yes	direct product factor
11	C₇²×C₁₇	C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇×C₁₇	—	5	8	no	—
14	C₅×C₇×C₁₇	C₂×C₃×C₇	1	8	yes	complemented
15	C₃×D₅×C₁₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
16	C₇²×D₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₇	C₇×D₅	1	8	yes	direct product factor
18	C₂×C₃×C₇²	—	5	1	no	Hall
19	C₃×C₅×C₁₇	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
20	C₅×C₇²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₁₇	—	5	8	no	—
22	C₃×C₇×D₅	C₇×C₁₇	1	8	yes	direct product factor
23	D₅×C₁₇	C₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇²	D₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₇×C₁₇	C₃×C₇×D₅	1	8	yes	direct product factor
26	C₃×C₅×C₇	C₂×C₇×C₁₇	1	8	yes	complemented
27	C₂×C₃×C₁₇	—	5	1	no	Hall
28	C₂×C₇²	—	5	1	no	Hall
29	C₅×C₁₇	C₂×C₃×C₇²	1	1	yes	characteristic, complemented, Hall
30	C₇×D₅	C₃×C₇×C₁₇	1	8	yes	direct product factor
31	C₃×C₁₇	C₇²×D₅	1	1	yes	characteristic, direct product factor, Hall
32	C₇²	C₃×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₇	—	5	8	no	—
34	C₅×C₇	C₂×C₃×C₇×C₁₇	1	8	yes	complemented
35	C₂×C₁₇	—	5	1	no	Hall
36	C₃×D₅	C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₇	C₇×D₅×C₁₇	1	8	yes	direct product factor
38	C₁₇	C₃×C₇²×D₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₂×C₇²×C₁₇	1	1	yes	characteristic, complemented, Hall
40	C₂×C₇	—	5	8	no	—
41	D₅	C₃×C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
42	C₇	C₃×C₇×D₅×C₁₇	1	8	yes	direct product factor
43	C₂×C₃	—	5	1	no	Hall
44	C₅	C₂×C₃×C₇²×C₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇²×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇²×C₁₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₇²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₇²×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₇	C₂	semidirect
2. C₇²×D₅×C₁₇	C₃	direct (N × H)
4. C₅×C₇²×C₁₇	C₂×C₃	semidirect
5. C₃×C₇×D₅×C₁₇	C₇	direct (N × H)
6. C₃×C₇²×C₁₇	D₅	direct (N × H)
7. C₃×C₅×C₇×C₁₇	C₂×C₇	semidirect
9. C₃×C₇²×D₅	C₁₇	direct (N × H)
10. C₇×D₅×C₁₇	C₃×C₇	direct (N × H)
11. C₇²×C₁₇	C₃×D₅	direct (N × H)
12. C₃×C₅×C₇²	C₂×C₁₇	semidirect
14. C₅×C₇×C₁₇	C₂×C₃×C₇	semidirect
15. C₃×D₅×C₁₇	C₇²	direct (N × H)
16. C₇²×D₅	C₃×C₁₇	direct (N × H)
17. C₃×C₇×C₁₇	C₇×D₅	direct (N × H)
19. C₃×C₅×C₁₇	C₂×C₇²	semidirect
20. C₅×C₇²	C₂×C₃×C₁₇	semidirect
22. C₃×C₇×D₅	C₇×C₁₇	direct (N × H)
23. D₅×C₁₇	C₃×C₇²	direct (N × H)
24. C₃×C₇²	D₅×C₁₇	direct (N × H)
25. C₇×C₁₇	C₃×C₇×D₅	direct (N × H)
26. C₃×C₅×C₇	C₂×C₇×C₁₇	semidirect
29. C₅×C₁₇	C₂×C₃×C₇²	semidirect
30. C₇×D₅	C₃×C₇×C₁₇	direct (N × H)
31. C₃×C₁₇	C₇²×D₅	direct (N × H)
32. C₇²	C₃×D₅×C₁₇	direct (N × H)
34. C₅×C₇	C₂×C₃×C₇×C₁₇	semidirect
36. C₃×D₅	C₇²×C₁₇	direct (N × H)
37. C₃×C₇	C₇×D₅×C₁₇	direct (N × H)
38. C₁₇	C₃×C₇²×D₅	direct (N × H)
39. C₃×C₅	C₂×C₇²×C₁₇	semidirect
41. D₅	C₃×C₇²×C₁₇	direct (N × H)
42. C₇	C₃×C₇×D₅×C₁₇	direct (N × H)
44. C₅	C₂×C₃×C₇²×C₁₇	semidirect
45. C₃	C₇²×D₅×C₁₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₇²×C₁₇	2
C₇²×D₅×C₁₇	3
C₂×C₃×C₇²×C₁₇	5
C₃×C₇×D₅×C₁₇	7
C₃×C₇²×D₅	17

Subgroups — C3×C72×D5×C17 #38735985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×D₅×C₁₇ #38735985