Subgroups — C₅×C₁₇×#64423 #38735948

Order 24990.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₇×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×#64423	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₇×AGL(1,𝔽₇)	—	7	1	no	maximal
6	C₂×C₅×C₁₇×ΓL(1,𝔽₈)	—	7	1	no	maximal
7	C₁₇×#3861	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₇×ΓL(1,𝔽₈)	—	7	1	no	—
9	C₅×C₁₇×ΓL(1,𝔽₈)	—	7	1	no	—
10	C₅×C₁₇×ΓL(1,𝔽₈)	—	14	3	no	—
11	C₇×D₇×C₁₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×#64423	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₇×C₁₇	—	7	1	no	—
14	C₅×D₇×C₁₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₇²×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₅×#3861	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₇×ΓL(1,𝔽₈)	—	7	1	no	—
18	C₁₇×AGL(1,𝔽₇)	—	7	1	no	—
19	C₅×C₇×C₁₇	—	2	3	no	—
20	C₅×C₇×C₁₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₅×C₇×C₁₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×C₁₇	—	49	1	no	Hall
23	C₅×C₇×D₇	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₁₇×ΓL(1,𝔽₈)	—	7	1	no	—
25	C₁₇×ΓL(1,𝔽₈)	—	7	1	no	—
26	C₁₇×ΓL(1,𝔽₈)	—	14	3	no	—
27	#64423	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅×C₁₇	—	49	1	no	Hall
29	C₅×C₇²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₇	—	7	1	no	—
31	D₇×C₁₇	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
32	C₂×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
33	C₅×AGL(1,𝔽₇)	—	7	1	no	—
34	C₂×C₅×C₁₇	—	7	1	no	Hall
35	#3861	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
36	C₇×C₁₇	—	2	3	no	—
37	C₇×C₁₇	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
38	C₇×C₁₇	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
40	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
41	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
42	C₂×C₃×C₁₇	—	49	1	no	Hall
43	C₇×D₇	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
44	C₅×C₁₇	#64423	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₅×C₇	—	7	1	no	—
46	C₅×D₇	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
47	C₃×C₁₇	—	49	1	no	Hall
48	C₇²	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
50	AGL(1,𝔽₇)	—	7	1	no	—
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	C₁₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
53	C₅×C₇	C₂×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
54	C₂×C₁₇	—	7	1	no	Hall
55	C₂×C₃×C₅	—	49	1	no	Hall
56	ΓL(1,𝔽₈)	—	7	1	no	—
57	ΓL(1,𝔽₈)	—	7	1	no	—
58	ΓL(1,𝔽₈)	—	14	3	no	—
59	C₁₇	C₅×#64423	1	1	yes	characteristic, direct product factor, Sylow
60	C₃×C₅	—	49	1	no	Hall
61	C₂×C₇	—	7	1	no	—
62	D₇	C₅×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
63	C₂×C₅	—	7	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	C₂×C₅×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
66	C₇	C₅×C₁₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
67	C₂×C₃	—	49	1	no	Hall
68	C₅	C₁₇×#64423	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	—	49	1	no	Sylow
70	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	#64423
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×#3861	C₂	semidirect
2. C₅×C₇×D₇×C₁₇	C₃	semidirect
3. C₁₇×#64423	C₅	direct (N × H)
4. C₅×C₇²×C₁₇	C₂×C₃	semidirect
7. C₁₇×#3861	C₂×C₅	semidirect
11. C₇×D₇×C₁₇	C₃×C₅	semidirect
12. C₅×#64423	C₁₇	direct (N × H)
14. C₅×D₇×C₁₇	ΓL(1,𝔽₈)	semidirect
15. C₇²×C₁₇	C₂×C₃×C₅	semidirect
16. C₅×#3861	C₂×C₁₇	semidirect
20. C₅×C₇×C₁₇	AGL(1,𝔽₇)	semidirect
21. C₅×C₇×C₁₇	C₂×ΓL(1,𝔽₈)	semidirect
23. C₅×C₇×D₇	C₃×C₁₇	semidirect
27. #64423	C₅×C₁₇	direct (N × H)
29. C₅×C₇²	C₂×C₃×C₁₇	semidirect
31. D₇×C₁₇	C₅×ΓL(1,𝔽₈)	semidirect
35. #3861	C₂×C₅×C₁₇	semidirect
37. C₇×C₁₇	C₅×AGL(1,𝔽₇)	semidirect
38. C₇×C₁₇	C₂×C₅×ΓL(1,𝔽₈)	semidirect
43. C₇×D₇	C₃×C₅×C₁₇	semidirect
44. C₅×C₁₇	#64423	direct (N × H)
46. C₅×D₇	C₁₇×ΓL(1,𝔽₈)	semidirect
48. C₇²	C₂×C₃×C₅×C₁₇	semidirect
52. C₅×C₇	C₁₇×AGL(1,𝔽₇)	semidirect
53. C₅×C₇	C₂×C₁₇×ΓL(1,𝔽₈)	semidirect
59. C₁₇	C₅×#64423	direct (N × H)
62. D₇	C₅×C₁₇×ΓL(1,𝔽₈)	semidirect
65. C₇	C₂×C₅×C₁₇×ΓL(1,𝔽₈)	semidirect
66. C₇	C₅×C₁₇×AGL(1,𝔽₇)	semidirect
68. C₅	C₁₇×#64423	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₇×#3861	2
C₅×C₇×D₇×C₁₇	3
C₁₇×#64423	5
C₅×C₁₇×AGL(1,𝔽₇)	7
C₂×C₅×C₁₇×ΓL(1,𝔽₈)	7
C₅×#64423	17

Subgroups — C5×C17×#64423 #38735948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×#64423 #38735948