Subgroups — C₃×C₁₉×#1044 #19152856

Order 5700.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1044	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×AGL(1,𝔽₅)	—	5	2	no	maximal
5	C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₁₉	—	5	2	no	—
7	C₃×D₅×C₁₉	—	10	2	no	—
8	C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₁₉×AGL(1,𝔽₅)	—	5	2	no	—
10	C₃×#1044	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×C₁₉	—	2	2	no	—
12	C₃×C₅×C₁₉	AGL(1,𝔽₅)	1	2	yes	complemented
13	C₃×C₄×C₁₉	—	25	1	no	Hall
14	D₅×C₁₉	—	5	2	no	—
15	D₅×C₁₉	—	10	2	no	—
16	C₃×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic
17	C₂×C₃×C₁₉	—	25	1	no	—
18	#1044	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₉	—	2	2	no	—
20	C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
21	C₄×C₁₉	—	25	1	no	Hall
22	C₃×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃×AGL(1,𝔽₅)	—	5	2	no	—
24	C₃×C₁₉	#1044	1	1	yes	characteristic, direct product factor, Hall
25	C₅⋊D₅	C₂×C₃×C₁₉	1	1	yes	characteristic
26	C₂×C₁₉	—	25	1	no	—
27	C₃×D₅	—	5	2	no	—
28	C₃×D₅	—	10	2	no	—
29	C₅²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
30	AGL(1,𝔽₅)	—	5	2	no	—
31	C₁₉	C₃×#1044	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
34	C₃×C₄	—	25	1	no	Hall
35	D₅	—	5	2	no	—
36	D₅	—	10	2	no	—
37	C₂×C₃	—	25	1	no	—
38	C₅	—	2	2	no	—
39	C₅	C₃×C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
40	C₄	—	25	1	no	Sylow
41	C₃	C₁₉×#1044	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#1044
commutator, hypocenter	C₅²	C₃×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₄
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1044	C₃	direct (N × H)
3. C₃×C₅²×C₁₉	C₄	semidirect
8. C₅²×C₁₉	C₃×C₄	semidirect
10. C₃×#1044	C₁₉	direct (N × H)
12. C₃×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
18. #1044	C₃×C₁₉	direct (N × H)
20. C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
22. C₃×C₅²	C₄×C₁₉	semidirect
24. C₃×C₁₉	#1044	direct (N × H)
29. C₅²	C₃×C₄×C₁₉	semidirect
31. C₁₉	C₃×#1044	direct (N × H)
33. C₃×C₅	C₁₉×AGL(1,𝔽₅)	semidirect
39. C₅	C₃×C₁₉×AGL(1,𝔽₅)	semidirect
41. C₃	C₁₉×#1044	direct (N × H)

Subgroups — C3×C19×#1044 #19152856

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₉×#1044 #19152856