Subgroups — C₁₉×C₃⋊AGL(1,𝔽₁₃) #22580272

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×AGL(1,𝔽₁₃)	—	3	1	no	maximal
4	C₃×C₁₉×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic
6	C₁₉×D₁₃⋊C₃	—	2	1	no	—
7	C₁₉×D₁₃⋊C₃	D₃	1	1	yes	characteristic
8	C₁₉×#261	—	3	1	no	Hall
9	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₉×C₁₃⋊C₃	—	2	1	no	—
11	C₁₉×C₁₃⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₃×Dic₃×C₁₉	—	13	1	no	maximal, Hall
13	C₁₉×D₁₃	C₃×D₃	1	1	yes	characteristic
14	C₃⋊AGL(1,𝔽₁₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃²×C₁₉	—	13	1	no	—
16	C₁₃×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic
18	C₃×C₄×C₁₉	—	39	1	no	—
19	Dic₃×C₁₉	—	13	1	no	—
20	C₃²×C₁₉	—	13	1	no	Hall
21	C₃⋊#261	C₃×C₁₉	1	1	yes	characteristic, complemented
22	AGL(1,𝔽₁₃)	—	3	1	no	—
23	C₃×C₁₃⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₉	—	13	1	no	—
25	C₂×C₃×C₁₉	—	13	1	no	—
26	C₂×C₃×C₁₉	—	26	1	no	—
27	C₃×D₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
28	D₁₃⋊C₃	—	2	1	no	—
29	D₁₃⋊C₃	D₃×C₁₉	1	1	yes	characteristic
30	C₄×C₁₉	—	39	1	no	Hall
31	C₃×C₁₉	—	13	1	no	—
32	C₃×C₁₉	—	26	1	no	—
33	C₃×C₁₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
34	#261	—	3	1	no	Hall
35	C₃×C₁₃	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
36	C₁₃⋊C₃	—	2	1	no	—
37	C₁₃⋊C₃	Dic₃×C₁₉	1	1	yes	characteristic, complemented
38	C₂×C₁₉	—	13	1	no	—
39	C₃×Dic₃	—	13	1	no	Hall
40	D₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic
41	C₁₉	C₃⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃²	—	13	1	no	—
43	C₁₃	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	39	1	no	—
45	Dic₃	—	13	1	no	—
46	C₃²	—	13	1	no	Sylow
47	C₂×C₃	—	13	1	no	—
48	C₂×C₃	—	13	1	no	—
49	C₂×C₃	—	26	1	no	—
50	C₄	—	39	1	no	Sylow
51	C₃	—	13	1	no	—
52	C₃	—	26	1	no	—
53	C₃	C₁₉×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
54	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊AGL(1,𝔽₁₃)
commutator, hypocenter	C₃×C₁₃	C₃×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₃×C₄
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×C₃⋊#261	C₃	semidirect
4. C₃×C₁₉×C₁₃⋊C₃	C₄	semidirect
9. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
11. C₁₉×C₁₃⋊C₃	Dic₃	semidirect
14. C₃⋊AGL(1,𝔽₁₃)	C₁₉	direct (N × H)
16. C₁₃×C₁₉	C₃×Dic₃	semidirect
21. C₃⋊#261	C₃×C₁₉	semidirect
23. C₃×C₁₃⋊C₃	C₄×C₁₉	semidirect
33. C₃×C₁₉	AGL(1,𝔽₁₃)	semidirect
35. C₃×C₁₃	C₃×C₄×C₁₉	semidirect
37. C₁₃⋊C₃	Dic₃×C₁₉	semidirect
41. C₁₉	C₃⋊AGL(1,𝔽₁₃)	direct (N × H)
43. C₁₃	C₃×Dic₃×C₁₉	semidirect
53. C₃	C₁₉×AGL(1,𝔽₁₃)	semidirect

Subgroups — C19×C3⋊AGL(1,𝔽13) #22580272

Conjugacy classes of subgroups

Complements

Subgroups — C₁₉×C₃⋊AGL(1,𝔽₁₃) #22580272