Subgroups — C₂×C₁₃×AGL(1,𝔽₁₉) #22580247

Order 8892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×AGL(1,𝔽₁₉)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₁₃×D₁₉⋊C₃	C₂×C₃	1	2	yes	—
7	C₂×C₁₃×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
8	C₁₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×AGL(1,𝔽₁₉)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
11	C₁₃×D₁₉	C₂×C₉	1	2	yes	complemented
12	C₂²×C₉×C₁₃	—	19	1	no	maximal, Hall
13	C₂×#4296	C₂×C₁₃	1	1	yes	characteristic, complemented
14	AGL(1,𝔽₁₉)	C₂×C₁₃	1	2	yes	direct product factor
15	C₁₃×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₉×C₁₃	—	19	2	no	—
17	C₂×C₉×C₁₃	—	19	1	no	—
18	C₂×D₁₉⋊C₃	C₃×C₁₃	1	1	yes	characteristic
19	#4296	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃×C₁₃	—	19	1	no	—
21	C₉×C₁₃	—	19	1	no	Hall
22	C₂×C₁₉⋊C₃	C₂×C₃×C₁₃	1	1	yes	characteristic
23	D₁₉⋊C₃	C₂×C₃×C₁₃	1	2	yes	—
24	C₂×C₃×C₁₃	—	19	2	no	—
25	C₂×C₃×C₁₃	—	19	1	no	—
26	C₂×D₁₉	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₁₉⋊C₃	C₂²×C₃×C₁₃	1	1	yes	characteristic
28	C₂²×C₁₃	—	19	1	no	Hall
29	C₃×C₁₃	—	19	1	no	—
30	C₂×C₁₉	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented
31	D₁₉	C₂×C₉×C₁₃	1	2	yes	complemented
32	C₂²×C₉	—	19	1	no	Hall
33	C₂×C₁₃	—	19	2	no	—
34	C₂×C₁₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor
35	C₁₉	C₂²×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₉	—	19	2	no	—
37	C₂×C₉	—	19	1	no	—
38	C₁₃	C₂×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃	—	19	1	no	—
40	C₉	—	19	1	no	Sylow
41	C₂×C₃	—	19	2	no	—
42	C₂×C₃	—	19	1	no	—
43	C₂²	—	19	1	no	Sylow
44	C₃	—	19	1	no	—
45	C₂	—	19	2	no	—
46	C₂	C₁₃×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	AGL(1,𝔽₁₉)
commutator, hypocenter	C₁₉	C₂²×C₉×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₉	C₂×C₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#4296	C₂	semidirect
2. C₁₃×AGL(1,𝔽₁₉)	C₂	direct (N × H)
4. C₁₃×#4296	C₂²	semidirect
7. C₂×C₁₃×D₁₉	C₉	semidirect
9. C₂×AGL(1,𝔽₁₉)	C₁₃	direct (N × H)
10. C₂×C₁₃×C₁₉	C₂×C₉	semidirect
11. C₁₃×D₁₉	C₂×C₉	semidirect
13. C₂×#4296	C₂×C₁₃	semidirect
14. AGL(1,𝔽₁₉)	C₂×C₁₃	direct (N × H)
15. C₁₃×C₁₉	C₂²×C₉	semidirect
19. #4296	C₂²×C₁₃	semidirect
26. C₂×D₁₉	C₉×C₁₃	semidirect
30. C₂×C₁₉	C₂×C₉×C₁₃	semidirect
31. D₁₉	C₂×C₉×C₁₃	semidirect
34. C₂×C₁₃	AGL(1,𝔽₁₉)	direct (N × H)
35. C₁₉	C₂²×C₉×C₁₃	semidirect
38. C₁₃	C₂×AGL(1,𝔽₁₉)	direct (N × H)
46. C₂	C₁₃×AGL(1,𝔽₁₉)	direct (N × H)

Subgroups — C2×C13×AGL(1,𝔽19) #22580247

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×AGL(1,𝔽₁₉) #22580247