Subgroups — C₂×C₁₃×C₅⋊AGL(1,𝔽₇) #19129798

Order 5460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₅⋊AGL(1,𝔽₇)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₃×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₃×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×AGL(1,𝔽₇)	—	5	1	no	maximal, Hall
6	C₂×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₃₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₃×D₅×C₁₃	—	7	1	no	maximal, Hall
9	C₂×C₁₃×ΓL(1,𝔽₈)	D₅	1	1	yes	characteristic, complemented
10	C₁₃×AGL(1,𝔽₇)	—	5	2	no	—
11	C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅⋊AGL(1,𝔽₇)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₁₃	—	7	1	no	—
14	C₃×D₅×C₁₃	—	7	2	no	—
15	C₂×C₁₃×D₇	—	5	1	no	Hall
16	C₁₃×ΓL(1,𝔽₈)	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×D₅×C₁₃	—	7	1	no	Hall
18	C₂×C₅×ΓL(1,𝔽₈)	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₅⋊AGL(1,𝔽₇)	C₂×C₁₃	1	2	yes	direct product factor
20	C₃×C₅×C₁₃	—	7	1	no	Hall
21	C₂×C₇×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
22	C₁₃×D₇	—	5	2	no	—
23	C₂²×C₃×C₁₃	—	35	1	no	Hall
24	C₂×D₃₅	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
26	D₅×C₁₃	—	7	2	no	—
27	C₅×ΓL(1,𝔽₈)	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
29	C₂×AGL(1,𝔽₇)	—	5	1	no	Hall
30	C₂×C₃×C₁₃	—	7	1	no	—
31	C₂×C₃×C₁₃	—	35	2	no	—
32	C₂×C₅×C₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
33	D₃₅	C₂×C₃×C₁₃	1	2	yes	complemented
34	C₅×C₁₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×D₅	—	7	1	no	Hall
36	C₂²×C₁₃	—	35	1	no	Hall
37	C₂×ΓL(1,𝔽₈)	D₅×C₁₃	1	1	yes	characteristic, complemented
38	AGL(1,𝔽₇)	—	5	2	no	—
39	C₃×C₁₃	—	7	1	no	Hall
40	C₅×C₇	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₅	—	7	1	no	—
42	C₃×D₅	—	7	2	no	—
43	C₂×D₇	—	5	1	no	Hall
44	C₂×C₁₃	—	35	2	no	—
45	C₂×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
46	ΓL(1,𝔽₈)	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
47	C₂×D₅	—	7	1	no	Hall
48	C₃×C₅	—	7	1	no	Hall
49	C₂×C₇	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented
50	D₇	—	5	2	no	—
51	C₁₃	C₂×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₃	—	35	1	no	Hall
53	C₂×C₅	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
54	D₅	—	7	2	no	—
55	C₇	C₂×C₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	7	1	no	—
57	C₂×C₃	—	35	2	no	—
58	C₅	C₂×C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	35	1	no	Sylow
60	C₃	—	7	1	no	Sylow
61	C₂	—	35	2	no	—
62	C₂	C₁₃×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₅⋊AGL(1,𝔽₇)
commutator, hypocenter	C₅×C₇	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₅⋊AGL(1,𝔽₇)	C₂	direct (N × H)
2. C₂×C₅×C₁₃×ΓL(1,𝔽₈)	C₂	semidirect
3. C₂×C₁₃×D₃₅	C₃	semidirect
4. C₅×C₁₃×ΓL(1,𝔽₈)	C₂²	semidirect
6. C₂×C₅×C₇×C₁₃	C₂×C₃	semidirect
7. C₁₃×D₃₅	C₂×C₃	semidirect
9. C₂×C₁₃×ΓL(1,𝔽₈)	D₅	semidirect
11. C₅×C₇×C₁₃	C₂²×C₃	semidirect
12. C₂×C₅⋊AGL(1,𝔽₇)	C₁₃	direct (N × H)
16. C₁₃×ΓL(1,𝔽₈)	C₂×D₅	semidirect
18. C₂×C₅×ΓL(1,𝔽₈)	C₂×C₁₃	semidirect
19. C₅⋊AGL(1,𝔽₇)	C₂×C₁₃	direct (N × H)
21. C₂×C₇×C₁₃	C₃×D₅	semidirect
24. C₂×D₃₅	C₃×C₁₃	semidirect
25. C₂×C₅×C₁₃	AGL(1,𝔽₇)	semidirect
27. C₅×ΓL(1,𝔽₈)	C₂²×C₁₃	semidirect
28. C₇×C₁₃	C₂×C₃×D₅	semidirect
32. C₂×C₅×C₇	C₂×C₃×C₁₃	semidirect
33. D₃₅	C₂×C₃×C₁₃	semidirect
34. C₅×C₁₃	C₂×AGL(1,𝔽₇)	semidirect
37. C₂×ΓL(1,𝔽₈)	D₅×C₁₃	semidirect
40. C₅×C₇	C₂²×C₃×C₁₃	semidirect
45. C₂×C₁₃	C₅⋊AGL(1,𝔽₇)	direct (N × H)
46. ΓL(1,𝔽₈)	C₂×D₅×C₁₃	semidirect
49. C₂×C₇	C₃×D₅×C₁₃	semidirect
51. C₁₃	C₂×C₅⋊AGL(1,𝔽₇)	direct (N × H)
53. C₂×C₅	C₁₃×AGL(1,𝔽₇)	semidirect
55. C₇	C₂×C₃×D₅×C₁₃	semidirect
58. C₅	C₂×C₁₃×AGL(1,𝔽₇)	semidirect
62. C₂	C₁₃×C₅⋊AGL(1,𝔽₇)	direct (N × H)

Subgroups — C2×C13×C5⋊AGL(1,𝔽7) #19129798

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×C₅⋊AGL(1,𝔽₇) #19129798