Subgroups — C₅×C₁₉×AGL(1,𝔽₁₉) #44570507

Order 32490.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×#4296	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₁₉×AGL(1,𝔽₁₉)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₉×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×#4296	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₁₉×D₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅×AGL(1,𝔽₁₉)	C₁₉	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₅×C₉×C₁₉	—	19	1	no	maximal
11	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
12	C₅×#4296	C₂×C₁₉	1	1	yes	characteristic, complemented
13	C₅×C₉×C₁₉	—	19	1	no	—
14	C₁₉×D₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₉	—	19	1	no	—
16	C₅×D₁₉⋊C₃	C₃×C₁₉	1	1	yes	characteristic
17	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₁₉)	C₅×C₁₉	1	1	yes	characteristic, direct product factor
19	C₂×C₉×C₁₉	—	19	1	no	—
20	C₃×C₅×C₁₉	—	19	1	no	—
21	C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₂×C₅×C₁₉	—	19	1	no	—
23	C₅×D₁₉	C₉×C₁₉	1	1	yes	characteristic, complemented
24	#4296	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
25	C₉×C₁₉	—	19	1	no	—
26	C₂×C₃×C₁₉	—	19	1	no	—
27	D₁₉⋊C₃	C₃×C₅×C₁₉	1	1	yes	characteristic
28	C₅×C₁₉	—	18	1	no	—
29	C₅×C₁₉	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
30	C₅×C₁₉	AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor
31	C₂×C₅×C₉	—	19	1	no	Hall
32	C₃×C₁₉	—	19	1	no	—
33	C₁₉⋊C₃	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic
34	C₅×C₉	—	19	1	no	Hall
35	C₂×C₁₉	—	19	1	no	—
36	D₁₉	C₅×C₉×C₁₉	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅	—	19	1	no	—
38	C₁₉	—	18	1	no	—
39	C₁₉	C₂×C₅×C₉×C₁₉	1	1	yes	characteristic, complemented
40	C₁₉	C₅×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor
41	C₂×C₉	—	19	1	no	Hall
42	C₃×C₅	—	19	1	no	—
43	C₂×C₅	—	19	1	no	Hall
44	C₉	—	19	1	no	Sylow
45	C₂×C₃	—	19	1	no	—
46	C₅	C₁₉×AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor, Sylow
47	C₃	—	19	1	no	—
48	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉	AGL(1,𝔽₁₉)
commutator, hypocenter	C₁₉	C₂×C₅×C₉×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂×C₉
prime radical	C₅×C₁₉×D₁₉⋊C₃	C₃
cosocle	C₁₉⋊C₃	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×#4296	C₂	semidirect
3. C₁₉×AGL(1,𝔽₁₉)	C₅	direct (N × H)
5. C₅×C₁₉×D₁₉	C₉	semidirect
6. C₁₉×#4296	C₂×C₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
9. C₅×AGL(1,𝔽₁₉)	C₁₉	direct (N × H)
12. C₅×#4296	C₂×C₁₉	semidirect
14. C₁₉×D₁₉	C₅×C₉	semidirect
17. C₁₉²	C₂×C₅×C₉	semidirect
18. AGL(1,𝔽₁₉)	C₅×C₁₉	direct (N × H)
23. C₅×D₁₉	C₉×C₁₉	semidirect
24. #4296	C₂×C₅×C₁₉	semidirect
29. C₅×C₁₉	C₂×C₉×C₁₉	semidirect
30. C₅×C₁₉	AGL(1,𝔽₁₉)	direct (N × H)
36. D₁₉	C₅×C₉×C₁₉	semidirect
39. C₁₉	C₂×C₅×C₉×C₁₉	semidirect
40. C₁₉	C₅×AGL(1,𝔽₁₉)	direct (N × H)
46. C₅	C₁₉×AGL(1,𝔽₁₉)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₁₉×#4296	2
C₅×C₁₉×D₁₉⋊C₃	3
C₁₉×AGL(1,𝔽₁₉)	5
C₅×AGL(1,𝔽₁₉)	19
C₂×C₅×C₉×C₁₉	19

Subgroups — C5×C19×AGL(1,𝔽19) #44570507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×AGL(1,𝔽₁₉) #44570507