Subgroups — C₃×C₁₉⋊#1044 #19152857

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	—	19	1	no	maximal, Hall
11	C₃×C₅×C₁₉	—	2	2	no	—
12	C₃×C₅×C₁₉	AGL(1,𝔽₅)	1	2	yes	complemented
13	C₃×Dic₁₉	—	25	1	no	Hall
14	D₅×C₁₉	—	5	2	no	—
15	D₅×C₁₉	—	10	2	no	—
16	C₃×C₅⋊D₅	D₁₉	1	1	yes	characteristic
17	C₂×C₃×C₁₉	—	25	1	no	—
18	#1044	—	19	1	no	Hall
19	C₅×C₁₉	—	2	2	no	—
20	C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
21	Dic₁₉	—	25	1	no	Hall
22	C₃×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃×AGL(1,𝔽₅)	—	95	2	no	—
24	C₃×C₁₉	#1044	1	1	yes	characteristic, complemented, Hall
25	C₅⋊D₅	C₃×D₁₉	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×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
30	AGL(1,𝔽₅)	—	95	2	no	—
31	C₁₉	C₃×#1044	1	1	yes	characteristic, complemented, Sylow
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	C₁₉⋊AGL(1,𝔽₅)	1	2	yes	complemented
34	C₃×C₄	—	475	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	—	475	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×C₁₉	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₄
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

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
12. C₃×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
20. C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
22. C₃×C₅²	Dic₁₉	semidirect
24. C₃×C₁₉	#1044	semidirect
29. C₅²	C₃×Dic₁₉	semidirect
31. C₁₉	C₃×#1044	semidirect
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 #19152857

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₉⋊#1044 #19152857