Subgroups — C₃×C₁₉×AGL(1,𝔽₁₃) #22580259

Order 8892.

72 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	C₃×C₁₉×#261	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×AGL(1,𝔽₁₃)	C₃	1	3	yes	maximal, direct product factor
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	C₂×C₃	1	3	yes	—
7	C₁₉×#261	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₉×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₃²×C₄×C₁₉	—	13	1	no	maximal, Hall
11	C₁₉×D₁₃	C₂×C₃²	1	1	yes	characteristic
12	C₃×AGL(1,𝔽₁₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃²×C₁₉	—	13	1	no	—
14	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×D₁₃⋊C₃	C₂×C₁₉	1	1	yes	characteristic
16	C₃×C₄×C₁₉	—	13	3	no	—
17	C₃×C₄×C₁₉	—	13	1	no	—
18	C₃²×C₁₉	—	13	1	no	Hall
19	C₃×#261	C₃×C₁₉	1	1	yes	characteristic, complemented
20	AGL(1,𝔽₁₃)	C₃×C₁₉	1	3	yes	direct product factor
21	C₃×C₁₃⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₉	—	13	3	no	—
23	C₂×C₃×C₁₉	—	13	1	no	—
24	C₃×D₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
25	D₁₃⋊C₃	C₂×C₃×C₁₉	1	3	yes	—
26	C₄×C₁₉	—	13	1	no	Hall
27	C₃×C₁₉	—	13	3	no	—
28	C₃×C₁₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
29	#261	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃×C₁₃	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
31	C₁₃⋊C₃	C₃×C₄×C₁₉	1	3	yes	complemented
32	C₂×C₁₉	—	13	1	no	—
33	C₃²×C₄	—	13	1	no	Hall
34	D₁₃	C₂×C₃²×C₁₉	1	1	yes	characteristic
35	C₁₉	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃²	—	13	1	no	—
37	C₁₃	C₃²×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	13	3	no	—
39	C₃×C₄	—	13	1	no	—
40	C₃²	—	13	1	no	Sylow
41	C₂×C₃	—	13	3	no	—
42	C₂×C₃	—	13	1	no	—
43	C₄	—	13	1	no	Sylow
44	C₃	—	13	3	no	—
45	C₃	C₁₉×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃	C₃²×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₃×C₄
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×#261	C₃	semidirect
3. C₁₉×AGL(1,𝔽₁₃)	C₃	direct (N × H)
4. C₃×C₁₉×C₁₃⋊C₃	C₄	semidirect
7. C₁₉×#261	C₃²	semidirect
8. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
9. C₁₉×C₁₃⋊C₃	C₃×C₄	semidirect
12. C₃×AGL(1,𝔽₁₃)	C₁₉	direct (N × H)
14. C₁₃×C₁₉	C₃²×C₄	semidirect
19. C₃×#261	C₃×C₁₉	semidirect
20. AGL(1,𝔽₁₃)	C₃×C₁₉	direct (N × H)
21. C₃×C₁₃⋊C₃	C₄×C₁₉	semidirect
28. C₃×C₁₉	AGL(1,𝔽₁₃)	direct (N × H)
29. #261	C₃²×C₁₉	semidirect
30. C₃×C₁₃	C₃×C₄×C₁₉	semidirect
31. C₁₃⋊C₃	C₃×C₄×C₁₉	semidirect
35. C₁₉	C₃×AGL(1,𝔽₁₃)	direct (N × H)
37. C₁₃	C₃²×C₄×C₁₉	semidirect
45. C₃	C₁₉×AGL(1,𝔽₁₃)	direct (N × H)

Subgroups — C3×C19×AGL(1,𝔽13) #22580259

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₉×AGL(1,𝔽₁₃) #22580259