Subgroups — C₅⋊(C₁₇⋊(D₇⋊C₉)) #24924209

Order 10710.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅₉₅	C₃	1	1	yes	maximal, characteristic
3	C₁₇⋊(D₇⋊C₉)	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₉×D₈₅	—	7	1	no	maximal, Hall
6	D₅₉₅	C₉	1	1	yes	characteristic, complemented, Hall
7	C₁₇×C₇⋊C₉	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₁₇	—	7	1	no	Hall
9	C₃×D₁₁₉	—	5	1	no	—
10	C₅⋊(D₇⋊C₉)	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×D₈₅	—	7	1	no	—
13	C₃×C₇×C₁₇	C₃×D₅	1	1	yes	characteristic
14	C₅×C₇⋊C₉	D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₉×D₁₇	—	35	1	no	Hall
16	C₃×C₅×C₁₇	AGL(1,𝔽₇)	1	1	yes	characteristic
17	D₁₁₉	—	5	1	no	Hall
18	C₃×D₃₅	—	17	1	no	—
19	D₈₅	—	7	1	no	Hall
20	C₉×C₁₇	—	7	1	no	Hall
21	D₇⋊C₉	—	85	1	no	Hall
22	C₇×C₁₇	C₉×D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	C₃×D₁₇	1	1	yes	characteristic
24	C₃×D₁₇	—	35	1	no	—
25	C₉×D₅	—	119	1	no	Hall
26	C₅×C₁₇	D₇⋊C₉	1	1	yes	characteristic, complemented, Hall
27	D₃₅	—	17	1	no	Hall
28	C₇⋊C₉	D₈₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic
30	C₅×C₉	—	7	1	no	Hall
31	C₃×D₇	—	85	1	no	—
32	C₅×C₇	C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
33	D₁₇	—	35	1	no	Hall
34	C₃×D₅	—	119	1	no	—
35	C₃×C₇	C₃×D₈₅	1	1	yes	characteristic
36	C₂×C₉	—	595	1	no	Hall
37	C₁₇	C₅⋊(D₇⋊C₉)	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	C₁₇⋊AGL(1,𝔽₇)	1	1	yes	characteristic
39	D₇	—	85	1	no	Hall
40	D₅	—	119	1	no	Hall
41	C₉	—	7	1	no	Sylow
42	C₇	C₉×D₈₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	595	1	no	—
44	C₅	C₁₇⋊(D₇⋊C₉)	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₅⋊(C₁₇⋊AGL(1,𝔽₇))	1	1	yes	characteristic
46	C₂	—	595	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊(C₁₇⋊AGL(1,𝔽₇))
commutator, hypocenter	C₅×C₇×C₁₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×D₅₉₅	C₃
LCS	G ▷ C₅×C₇×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₇⋊C₉	C₂	semidirect
6. D₅₉₅	C₉	semidirect
7. C₁₇×C₇⋊C₉	D₅	semidirect
11. C₅×C₇×C₁₇	C₂×C₉	semidirect
14. C₅×C₇⋊C₉	D₁₇	semidirect
22. C₇×C₁₇	C₉×D₅	semidirect
26. C₅×C₁₇	D₇⋊C₉	semidirect
28. C₇⋊C₉	D₈₅	semidirect
32. C₅×C₇	C₉×D₁₇	semidirect
37. C₁₇	C₅⋊(D₇⋊C₉)	semidirect
42. C₇	C₉×D₈₅	semidirect
44. C₅	C₁₇⋊(D₇⋊C₉)	semidirect

Subgroups — C5⋊(C17⋊(D7⋊C9)) #24924209

Conjugacy classes of subgroups

Complements

Subgroups — C₅⋊(C₁₇⋊(D₇⋊C₉)) #24924209