Subgroups — C₃×C₅×C₁₇⋊AGL(1,𝔽₇) #24924212

Order 10710.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₇⋊AGL(1,𝔽₇)	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅×D₁₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇⋊AGL(1,𝔽₇)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₁₇×ΓL(1,𝔽₈)	C₂×C₃	1	3	yes	complemented
7	C₃²×C₅×D₁₇	—	7	1	no	maximal, Hall
8	C₅×D₁₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₇×ΓL(1,𝔽₈)	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₅×C₁₇	—	7	1	no	Hall
11	C₃×D₁₁₉	C₃×C₅	1	1	yes	characteristic, complemented
12	C₁₇⋊AGL(1,𝔽₇)	C₃×C₅	1	3	yes	direct product factor
13	C₃×C₅×AGL(1,𝔽₇)	—	17	1	no	maximal, Hall
14	C₅×C₇×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×D₁₇	—	7	3	no	—
16	C₃×C₅×D₁₇	—	7	1	no	—
17	C₃×C₇×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₁₇×ΓL(1,𝔽₈)	C₂×C₃×C₅	1	3	yes	complemented
19	C₃×C₅×ΓL(1,𝔽₈)	D₁₇	1	1	yes	characteristic, complemented, Hall
20	C₃²×D₁₇	—	7	1	no	Hall
21	C₃×C₅×C₁₇	—	7	3	no	—
22	C₃×C₅×C₁₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
23	D₁₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×D₇	—	17	1	no	—
25	C₅×AGL(1,𝔽₇)	—	17	3	no	—
26	C₅×D₁₇	—	7	1	no	Hall
27	C₃²×C₁₇	—	7	1	no	Hall
28	C₃×AGL(1,𝔽₇)	—	17	1	no	Hall
29	C₇×C₁₇	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₇	C₃×D₁₇	1	1	yes	characteristic, complemented
31	C₅×ΓL(1,𝔽₈)	C₃×D₁₇	1	3	yes	complemented
32	C₃×D₁₇	—	7	3	no	—
33	C₃×D₁₇	—	7	1	no	—
34	C₂×C₃²×C₅	—	119	1	no	Hall
35	C₅×C₁₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
36	C₅×D₇	—	17	1	no	Hall
37	C₃×ΓL(1,𝔽₈)	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
38	C₃×C₁₇	—	7	3	no	—
39	C₃×C₁₇	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
40	C₃²×C₅	—	7	1	no	Hall
41	C₃×D₇	—	17	1	no	—
42	AGL(1,𝔽₇)	—	17	3	no	—
43	C₅×C₇	C₃²×D₁₇	1	1	yes	characteristic, complemented, Hall
44	D₁₇	—	7	1	no	Hall
45	C₂×C₃×C₅	—	119	3	no	—
46	C₂×C₃×C₅	—	119	1	no	—
47	C₃×C₇	C₃×C₅×D₁₇	1	1	yes	characteristic, complemented
48	ΓL(1,𝔽₈)	C₃×C₅×D₁₇	1	3	yes	complemented
49	C₂×C₃²	—	119	1	no	Hall
50	C₁₇	C₃×C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₅	—	7	3	no	—
52	C₃×C₅	C₁₇⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
53	D₇	—	17	1	no	Hall
54	C₂×C₅	—	119	1	no	Hall
55	C₃²	—	7	1	no	Sylow
56	C₇	C₃²×C₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	119	3	no	—
58	C₂×C₃	—	119	1	no	—
59	C₅	C₃×C₁₇⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Sylow
60	C₃	—	7	3	no	—
61	C₃	C₅×C₁₇⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
62	C₂	—	119	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	C₁₇⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇×C₁₇	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂×C₃
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×ΓL(1,𝔽₈)	C₂	semidirect
2. C₅×C₁₇⋊AGL(1,𝔽₇)	C₃	direct (N × H)
3. C₃×C₅×D₁₁₉	C₃	semidirect
4. C₃×C₁₇⋊AGL(1,𝔽₇)	C₅	direct (N × H)
5. C₃×C₅×C₇×C₁₇	C₂×C₃	semidirect
6. C₅×C₁₇×ΓL(1,𝔽₈)	C₂×C₃	semidirect
8. C₅×D₁₁₉	C₃²	semidirect
9. C₃×C₁₇×ΓL(1,𝔽₈)	C₂×C₅	semidirect
11. C₃×D₁₁₉	C₃×C₅	semidirect
12. C₁₇⋊AGL(1,𝔽₇)	C₃×C₅	direct (N × H)
14. C₅×C₇×C₁₇	C₂×C₃²	semidirect
17. C₃×C₇×C₁₇	C₂×C₃×C₅	semidirect
18. C₁₇×ΓL(1,𝔽₈)	C₂×C₃×C₅	semidirect
19. C₃×C₅×ΓL(1,𝔽₈)	D₁₇	semidirect
22. C₃×C₅×C₁₇	AGL(1,𝔽₇)	semidirect
23. D₁₁₉	C₃²×C₅	semidirect
29. C₇×C₁₇	C₂×C₃²×C₅	semidirect
30. C₃×C₅×C₇	C₃×D₁₇	semidirect
31. C₅×ΓL(1,𝔽₈)	C₃×D₁₇	semidirect
35. C₅×C₁₇	C₃×AGL(1,𝔽₇)	semidirect
37. C₃×ΓL(1,𝔽₈)	C₅×D₁₇	semidirect
39. C₃×C₁₇	C₅×AGL(1,𝔽₇)	semidirect
43. C₅×C₇	C₃²×D₁₇	semidirect
47. C₃×C₇	C₃×C₅×D₁₇	semidirect
48. ΓL(1,𝔽₈)	C₃×C₅×D₁₇	semidirect
50. C₁₇	C₃×C₅×AGL(1,𝔽₇)	semidirect
52. C₃×C₅	C₁₇⋊AGL(1,𝔽₇)	direct (N × H)
56. C₇	C₃²×C₅×D₁₇	semidirect
59. C₅	C₃×C₁₇⋊AGL(1,𝔽₇)	direct (N × H)
61. C₃	C₅×C₁₇⋊AGL(1,𝔽₇)	direct (N × H)

Subgroups — C3×C5×C17⋊AGL(1,𝔽7) #24924212

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×C₁₇⋊AGL(1,𝔽₇) #24924212