Subgroups — C₅×C₇×AGL(1,𝔽₁₃) #19129708

Order 5460.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₇×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×AGL(1,𝔽₁₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×D₁₃	C₂×C₃	1	1	yes	characteristic
6	C₅×AGL(1,𝔽₁₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×D₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×C₄×C₅×C₇	—	13	1	no	maximal, Hall
10	C₅×D₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic
11	C₇×#261	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₃⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₅×#261	C₃×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₇	—	13	1	no	—
15	C₅×C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₃	C₂×C₃×C₅	1	1	yes	characteristic
17	AGL(1,𝔽₁₃)	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₄×C₅×C₇	—	13	1	no	Hall
19	C₅×D₁₃	C₂×C₃×C₇	1	1	yes	characteristic
20	C₃×C₅×C₇	—	13	1	no	Hall
21	C₇×C₁₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
22	C₃×C₄×C₇	—	13	1	no	Hall
23	D₁₃⋊C₃	C₂×C₅×C₇	1	1	yes	characteristic
24	C₂×C₅×C₇	—	13	1	no	—
25	C₅×C₁₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
26	C₃×C₄×C₅	—	13	1	no	Hall
27	#261	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₇	—	13	1	no	—
29	C₁₃⋊C₃	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
30	C₅×C₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₅	—	13	1	no	—
32	C₄×C₇	—	13	1	no	Hall
33	D₁₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic
34	C₃×C₇	—	13	1	no	Hall
35	C₄×C₅	—	13	1	no	Hall
36	C₃×C₅	—	13	1	no	Hall
37	C₂×C₇	—	13	1	no	—
38	C₁₃	C₃×C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₄	—	13	1	no	Hall
40	C₂×C₅	—	13	1	no	—
41	C₇	C₅×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	—	13	1	no	—
43	C₅	C₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	13	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃	C₃×C₄×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃	C₃×C₄
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×#261	C₃	semidirect
3. C₅×C₇×C₁₃⋊C₃	C₄	semidirect
4. C₇×AGL(1,𝔽₁₃)	C₅	direct (N × H)
6. C₅×AGL(1,𝔽₁₃)	C₇	direct (N × H)
8. C₅×C₇×C₁₃	C₃×C₄	semidirect
11. C₇×#261	C₃×C₅	semidirect
12. C₇×C₁₃⋊C₃	C₄×C₅	semidirect
13. C₅×#261	C₃×C₇	semidirect
15. C₅×C₁₃⋊C₃	C₄×C₇	semidirect
17. AGL(1,𝔽₁₃)	C₅×C₇	direct (N × H)
21. C₇×C₁₃	C₃×C₄×C₅	semidirect
25. C₅×C₁₃	C₃×C₄×C₇	semidirect
27. #261	C₃×C₅×C₇	semidirect
29. C₁₃⋊C₃	C₄×C₅×C₇	semidirect
30. C₅×C₇	AGL(1,𝔽₁₃)	direct (N × H)
38. C₁₃	C₃×C₄×C₅×C₇	semidirect
41. C₇	C₅×AGL(1,𝔽₁₃)	direct (N × H)
43. C₅	C₇×AGL(1,𝔽₁₃)	direct (N × H)

Subgroups — C5×C7×AGL(1,𝔽13) #19129708

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₇×AGL(1,𝔽₁₃) #19129708