Subgroups — C₁₇×D₃₁₅ #24924201

Order 10710.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₁₀₅	—	3	1	no	maximal
3	C₁₇×D₆₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₁₇	D₃	1	1	yes	characteristic
5	C₁₇×D₄₅	—	7	1	no	maximal, Hall
6	C₁₇×D₃₅	—	9	1	no	Hall
7	C₇×C₉×C₁₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×D₂₁	—	15	1	no	—
10	D₃₁₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×C₁₇	D₉	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₁₅	—	21	1	no	—
13	C₃×C₇×C₁₇	D₁₅	1	1	yes	characteristic
14	C₅×C₇×C₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₇×D₉	—	35	1	no	Hall
16	C₃×C₅×C₁₇	D₂₁	1	1	yes	characteristic
17	D₇×C₁₇	—	45	1	no	Hall
18	D₁₀₅	—	3	1	no	—
19	D₅×C₁₇	—	63	1	no	Hall
20	C₉×C₁₇	D₃₅	1	1	yes	characteristic, complemented, Hall
21	D₆₃	—	5	1	no	Hall
22	C₇×C₁₇	D₄₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	D₃×C₁₇	1	1	yes	characteristic
24	D₃×C₁₇	—	105	1	no	—
25	D₄₅	—	7	1	no	Hall
26	C₅×C₁₇	D₆₃	1	1	yes	characteristic, complemented, Hall
27	D₃₅	—	9	1	no	Hall
28	C₇×C₉	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	D₁₀₅	1	1	yes	characteristic
30	C₅×C₉	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
31	D₂₁	—	15	1	no	—
32	C₅×C₇	C₁₇×D₉	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₇	—	315	1	no	Hall
34	D₁₅	—	21	1	no	—
35	C₃×C₇	C₁₇×D₁₅	1	1	yes	characteristic
36	D₉	—	35	1	no	Hall
37	C₁₇	D₃₁₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₁₇×D₂₁	1	1	yes	characteristic
39	D₇	—	45	1	no	Hall
40	D₅	—	63	1	no	Hall
41	C₉	C₁₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₁₇×D₄₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	105	1	no	—
44	C₅	C₁₇×D₆₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₁₇×D₁₀₅	1	1	yes	characteristic
46	C₂	—	315	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₃₁₅
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂×C₁₇
Frattini	C₃	C₁₇×D₁₀₅
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₇	C₂	semidirect
7. C₇×C₉×C₁₇	D₅	semidirect
8. C₅×C₉×C₁₇	D₇	semidirect
10. D₃₁₅	C₁₇	direct (N × H)
11. C₅×C₇×C₁₇	D₉	semidirect
14. C₅×C₇×C₉	C₂×C₁₇	semidirect
20. C₉×C₁₇	D₃₅	semidirect
22. C₇×C₁₇	D₄₅	semidirect
26. C₅×C₁₇	D₆₃	semidirect
28. C₇×C₉	D₅×C₁₇	semidirect
30. C₅×C₉	D₇×C₁₇	semidirect
32. C₅×C₇	C₁₇×D₉	semidirect
37. C₁₇	D₃₁₅	direct (N × H)
41. C₉	C₁₇×D₃₅	semidirect
42. C₇	C₁₇×D₄₅	semidirect
44. C₅	C₁₇×D₆₃	semidirect

Subgroups — C17×D315 #24924201

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×D₃₁₅ #24924201