Subgroups — C₃×C₅×C₁₉×AGL(1,𝔽₅) #19152851

Order 5700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₉	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₃×C₄×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₄
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₉×AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃×C₅²×C₁₉	C₄	semidirect
4. C₃×C₁₉×AGL(1,𝔽₅)	C₅	direct (N × H)
9. C₅²×C₁₉	C₃×C₄	semidirect
10. C₁₉×AGL(1,𝔽₅)	C₃×C₅	direct (N × H)
12. C₃×C₅×AGL(1,𝔽₅)	C₁₉	direct (N × H)
14. C₃×C₅×C₁₉	C₄×C₅	semidirect
15. C₃×C₅×C₁₉	AGL(1,𝔽₅)	direct (N × H)
21. C₅×AGL(1,𝔽₅)	C₃×C₁₉	direct (N × H)
23. C₅×C₁₉	C₃×C₄×C₅	semidirect
24. C₅×C₁₉	C₃×AGL(1,𝔽₅)	direct (N × H)
26. C₃×C₅²	C₄×C₁₉	semidirect
27. C₃×AGL(1,𝔽₅)	C₅×C₁₉	direct (N × H)
29. C₃×C₁₉	C₅×AGL(1,𝔽₅)	direct (N × H)
34. C₅²	C₃×C₄×C₁₉	semidirect
35. AGL(1,𝔽₅)	C₃×C₅×C₁₉	direct (N × H)
37. C₁₉	C₃×C₅×AGL(1,𝔽₅)	direct (N × H)
39. C₃×C₅	C₄×C₅×C₁₉	semidirect
40. C₃×C₅	C₁₉×AGL(1,𝔽₅)	direct (N × H)
46. C₅	C₃×C₄×C₅×C₁₉	semidirect
47. C₅	C₃×C₁₉×AGL(1,𝔽₅)	direct (N × H)
49. C₃	C₅×C₁₉×AGL(1,𝔽₅)	direct (N × H)

Subgroups — C3×C5×C19×AGL(1,𝔽5) #19152851

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×C₁₉×AGL(1,𝔽₅) #19152851