Subgroups — C₅⋊#20266610 #44570538

Order 32490.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692438	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊((C₁₉⋊C₃)⋊D₁₉)	C₃	1	1	yes	maximal, characteristic
3	#20266610	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₅⋊(C₁₉⋊D₁₉)	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692438	D₅	1	1	yes	characteristic, complemented, Hall
7	(C₁₉⋊C₃)⋊D₁₉	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅⋊AGL(1,𝔽₁₉)	—	19	1	no	maximal
10	C₅⋊(#4294⋊C₂)	—	19	1	no	maximal
11	C₁₉×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic
12	C₅×#4296	—	19	1	no	—
13	C₅×#4294	—	19	1	no	—
14	C₁₉⋊D₁₉	—	5	1	no	Hall
15	C₃×D₉₅	—	19	1	no	—
16	C₅⋊(D₁₉⋊C₃)	—	19	1	no	—
17	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₁₉)	—	95	1	no	—
19	#4294⋊C₂	—	95	1	no	—
20	C₃×C₅×C₁₉	—	19	1	no	—
21	C₅×C₁₉⋊C₃	D₁₉⋊C₃	1	1	yes	characteristic
22	D₉₅	—	19	1	no	—
23	D₉₅	—	19	1	no	—
24	D₉₅	—	171	2	no	—
25	#4296	—	19	1	no	—
26	#4294	—	19	1	no	—
27	C₃×D₁₉	—	95	1	no	—
28	D₁₉⋊C₃	—	95	1	no	—
29	C₅×C₁₉	—	9	2	no	—
30	C₅×C₁₉	#4294⋊C₂	1	1	yes	characteristic, complemented
31	C₅×C₁₉	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
32	C₉×D₅	—	361	1	no	Hall
33	C₃×C₁₉	—	19	1	no	—
34	C₁₉⋊C₃	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic
35	C₅×C₉	—	361	1	no	Hall
36	D₁₉	—	855	2	no	—
37	D₁₉	—	95	1	no	—
38	D₁₉	—	95	1	no	—
39	C₃×D₅	—	361	1	no	—
40	C₁₉	—	9	2	no	—
41	C₁₉	C₅⋊(#4294⋊C₂)	1	1	yes	characteristic, complemented
42	C₁₉	C₅⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
43	C₂×C₉	—	1805	1	no	Hall
44	C₃×C₅	—	19	1	no	—
45	D₅	—	361	1	no	Hall
46	C₉	—	361	1	no	Sylow
47	C₂×C₃	—	1805	1	no	—
48	C₅	#20266610	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	19	1	no	—
50	C₂	—	1805	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×#15692438	C₂	semidirect
5. C₅⋊(C₁₉⋊D₁₉)	C₉	semidirect
6. #15692438	D₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
17. C₁₉²	C₉×D₅	semidirect
30. C₅×C₁₉	#4294⋊C₂	semidirect
31. C₅×C₁₉	AGL(1,𝔽₁₉)	semidirect
41. C₁₉	C₅⋊(#4294⋊C₂)	semidirect
42. C₁₉	C₅⋊AGL(1,𝔽₁₉)	semidirect
48. C₅	#20266610	semidirect

Maximal subgroups

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

subgroup	index
C₅×#15692438	2
C₅⋊((C₁₉⋊C₃)⋊D₁₉)	3
#20266610	5
C₅⋊AGL(1,𝔽₁₉)	19
C₅⋊(#4294⋊C₂)	19

Subgroups — C5⋊#20266610 #44570538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#20266610 #44570538