Subgroups — C₅×D₁₀₇₁ #24924198

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	C₅×D₃₅₇	—	3	1	no	maximal
3	D₁₀₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	D₃	1	1	yes	characteristic
5	C₅×D₁₅₃	—	7	1	no	maximal, Hall
6	C₅×D₁₁₉	—	9	1	no	Hall
7	C₇×C₉×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
9	D₃₅₇	—	3	1	no	—
10	C₅×D₆₃	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	D₉	1	1	yes	characteristic, complemented, Hall
12	C₅×D₅₁	—	21	1	no	—
13	C₃×C₇×C₁₇	C₅×D₃	1	1	yes	characteristic
14	C₅×C₇×C₉	D₁₇	1	1	yes	characteristic, complemented, Hall
15	D₁₅₃	—	7	1	no	Hall
16	C₃×C₅×C₁₇	D₂₁	1	1	yes	characteristic
17	D₁₁₉	—	9	1	no	Hall
18	C₅×D₂₁	—	51	1	no	—
19	C₅×D₁₇	—	63	1	no	Hall
20	C₉×C₁₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
21	D₆₃	—	17	1	no	Hall
22	C₇×C₁₇	C₅×D₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	D₅₁	1	1	yes	characteristic
24	D₅₁	—	21	1	no	—
25	C₅×D₉	—	119	1	no	Hall
26	C₅×C₁₇	D₆₃	1	1	yes	characteristic, complemented, Hall
27	C₅×D₇	—	153	1	no	Hall
28	C₇×C₉	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₅×D₂₁	1	1	yes	characteristic
30	C₅×C₉	D₁₁₉	1	1	yes	characteristic, complemented, Hall
31	D₂₁	—	51	1	no	—
32	C₅×C₇	D₁₅₃	1	1	yes	characteristic, complemented, Hall
33	D₁₇	—	63	1	no	Hall
34	C₅×D₃	—	357	1	no	—
35	C₃×C₇	C₅×D₅₁	1	1	yes	characteristic
36	D₉	—	119	1	no	Hall
37	C₁₇	C₅×D₆₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	D₃₅₇	1	1	yes	characteristic
39	D₇	—	153	1	no	Hall
40	C₂×C₅	—	1071	1	no	Hall
41	C₉	C₅×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	357	1	no	—
44	C₅	D₁₀₇₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₃₅₇	1	1	yes	characteristic
46	C₂	—	1071	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₀₇₁
commutator, cosocle, hypocenter	C₇×C₉×C₁₇	C₂×C₅
Frattini	C₃	C₅×D₃₅₇
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	D₃
LCS	G ▷ C₇×C₉×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₇	C₂	semidirect
3. D₁₀₇₁	C₅	direct (N × H)
7. C₇×C₉×C₁₇	C₂×C₅	semidirect
8. C₅×C₉×C₁₇	D₇	semidirect
11. C₅×C₇×C₁₇	D₉	semidirect
14. C₅×C₇×C₉	D₁₇	semidirect
20. C₉×C₁₇	C₅×D₇	semidirect
22. C₇×C₁₇	C₅×D₉	semidirect
26. C₅×C₁₇	D₆₃	semidirect
28. C₇×C₉	C₅×D₁₇	semidirect
30. C₅×C₉	D₁₁₉	semidirect
32. C₅×C₇	D₁₅₃	semidirect
37. C₁₇	C₅×D₆₃	semidirect
41. C₉	C₅×D₁₁₉	semidirect
42. C₇	C₅×D₁₅₃	semidirect
44. C₅	D₁₀₇₁	direct (N × H)

Subgroups — C5×D1071 #24924198

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₁₀₇₁ #24924198