Subgroups — C₁₇×C₅⋊#64425 #38735975

Order 24990.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₅⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×#64425	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₅⋊AGL(1,𝔽₇)	—	7	2	no	maximal
6	C₁₇×#3862	D₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₇×ΓL(1,𝔽₈)	—	7	2	no	—
8	C₁₇×C₇⋊D₇	—	5	1	no	Hall
9	C₅⋊#64425	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₇×D₃₅	—	7	2	no	—
11	C₁₇×D₃₅	—	21	2	no	—
12	C₇²×C₁₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	C₅×#3862	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₁₇×AGL(1,𝔽₇)	—	35	2	no	—
15	C₅×C₇×C₁₇	—	3	2	no	—
16	C₅×C₇×C₁₇	AGL(1,𝔽₇)	1	2	yes	complemented
17	C₃×D₅×C₁₇	—	49	1	no	Hall
18	C₅⋊(C₇⋊D₇)	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₁₇×ΓL(1,𝔽₈)	—	7	2	no	—
20	#64425	—	5	1	no	Hall
21	C₃×C₅×C₁₇	—	49	1	no	Hall
22	C₅×C₇²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
23	D₇×C₁₇	—	35	2	no	—
24	D₇×C₁₇	—	105	2	no	—
25	C₅⋊AGL(1,𝔽₇)	—	7	2	no	—
26	D₅×C₁₇	—	49	1	no	Hall
27	#3862	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₇	—	3	2	no	—
29	C₇×C₁₇	C₅⋊AGL(1,𝔽₇)	1	2	yes	complemented
30	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
31	C₂×C₃×C₁₇	—	245	1	no	Hall
32	C₇⋊D₇	—	5	1	no	Hall
33	C₅×C₁₇	#64425	1	1	yes	characteristic, complemented, Hall
34	D₃₅	—	7	2	no	—
35	D₃₅	—	21	2	no	—
36	C₃×C₁₇	—	49	1	no	Hall
37	C₇²	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
38	AGL(1,𝔽₇)	—	35	2	no	—
39	C₅×C₇	—	3	2	no	—
40	C₅×C₇	C₁₇×AGL(1,𝔽₇)	1	2	yes	complemented
41	C₂×C₁₇	—	245	1	no	Hall
42	C₃×D₅	—	49	1	no	Hall
43	ΓL(1,𝔽₈)	—	7	2	no	—
44	C₁₇	C₅⋊#64425	1	1	yes	characteristic, direct product factor, Sylow
45	C₃×C₅	—	49	1	no	Hall
46	D₇	—	35	2	no	—
47	D₇	—	105	2	no	—
48	D₅	—	49	1	no	Hall
49	C₇	—	3	2	no	—
50	C₇	C₁₇×C₅⋊AGL(1,𝔽₇)	1	2	yes	complemented
51	C₂×C₃	—	245	1	no	Hall
52	C₅	C₁₇×#64425	1	1	yes	characteristic, complemented, Sylow
53	C₃	—	49	1	no	Sylow
54	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₅⋊#64425
commutator, cosocle, hypocenter	C₅×C₇²	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×#3862	C₂	semidirect
2. C₁₇×C₅⋊(C₇⋊D₇)	C₃	semidirect
4. C₅×C₇²×C₁₇	C₂×C₃	semidirect
6. C₁₇×#3862	D₅	semidirect
9. C₅⋊#64425	C₁₇	direct (N × H)
12. C₇²×C₁₇	C₃×D₅	semidirect
13. C₅×#3862	C₂×C₁₇	semidirect
16. C₅×C₇×C₁₇	AGL(1,𝔽₇)	semidirect
18. C₅⋊(C₇⋊D₇)	C₃×C₁₇	semidirect
22. C₅×C₇²	C₂×C₃×C₁₇	semidirect
27. #3862	D₅×C₁₇	semidirect
29. C₇×C₁₇	C₅⋊AGL(1,𝔽₇)	semidirect
33. C₅×C₁₇	#64425	semidirect
37. C₇²	C₃×D₅×C₁₇	semidirect
40. C₅×C₇	C₁₇×AGL(1,𝔽₇)	semidirect
44. C₁₇	C₅⋊#64425	direct (N × H)
50. C₇	C₁₇×C₅⋊AGL(1,𝔽₇)	semidirect
52. C₅	C₁₇×#64425	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₇×#3862	2
C₁₇×C₅⋊(C₇⋊D₇)	3
C₁₇×#64425	5
C₁₇×C₅⋊AGL(1,𝔽₇)	7
C₅⋊#64425	17

Subgroups — C17×C5⋊#64425 #38735975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₅⋊#64425 #38735975