Subgroups — C₅×#20266606 #44570525

Order 32490.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692435	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#14524209	C₃	1	1	yes	maximal, characteristic
3	#20266606	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×#11762246	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₉×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692435	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	#14524209	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×#4296	—	19	1	no	maximal
10	C₅×AGL(1,𝔽₁₉)	—	19	1	no	maximal
11	#11762246	C₂×C₃×C₅	1	1	yes	characteristic
12	C₅×#4296	—	19	1	no	—
13	C₅×#4296	—	19	1	no	—
14	C₁₉×D₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₉⋊C₃	—	19	1	no	—
16	C₅×D₁₉⋊C₃	—	19	1	no	—
17	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×#4296	—	19	1	no	—
19	AGL(1,𝔽₁₉)	—	19	1	no	—
20	C₅×C₁₉⋊C₃	—	19	1	no	—
21	C₅×C₁₉⋊C₃	—	19	1	no	—
22	C₂×C₅×C₁₉	—	19	1	no	—
23	C₅×D₁₉	#4296	1	1	yes	characteristic, complemented
24	#4296	—	19	1	no	—
25	#4296	—	19	1	no	—
26	C₂×C₁₉⋊C₃	—	19	1	no	—
27	D₁₉⋊C₃	—	19	1	no	—
28	C₅×C₁₉	—	18	1	no	—
29	C₅×C₁₉	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
30	C₅×C₁₉	C₂×#4296	1	1	yes	characteristic, complemented
31	C₂×C₅×C₉	—	361	1	no	Hall
32	C₁₉⋊C₃	—	19	1	no	—
33	C₁₉⋊C₃	—	19	1	no	—
34	C₅×C₉	—	361	1	no	Hall
35	C₂×C₁₉	—	19	1	no	—
36	D₁₉	C₅×#4296	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅	—	361	1	no	—
38	C₁₉	—	18	1	no	—
39	C₁₉	C₅×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
40	C₁₉	C₂×C₅×#4296	1	1	yes	characteristic, complemented
41	C₂×C₉	—	361	1	no	Hall
42	C₃×C₅	—	361	1	no	—
43	C₂×C₅	—	19	1	no	Hall
44	C₉	—	361	1	no	Sylow
45	C₂×C₃	—	361	1	no	—
46	C₅	#20266606	1	1	yes	characteristic, direct product factor, Sylow
47	C₃	—	361	1	no	—
48	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#20266606
commutator, hypocenter	C₁₉²	C₂×C₅×C₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂×C₉
prime radical	C₅×#14524209	C₃
cosocle	#11762246	C₂×C₃×C₅
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15692435	C₂	semidirect
3. #20266606	C₅	direct (N × H)
5. C₅×C₁₉×D₁₉	C₉	semidirect
6. #15692435	C₂×C₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
14. C₁₉×D₁₉	C₅×C₉	semidirect
17. C₁₉²	C₂×C₅×C₉	semidirect
23. C₅×D₁₉	#4296	semidirect
29. C₅×C₁₉	AGL(1,𝔽₁₉)	semidirect
30. C₅×C₁₉	C₂×#4296	semidirect
36. D₁₉	C₅×#4296	semidirect
39. C₁₉	C₅×AGL(1,𝔽₁₉)	semidirect
40. C₁₉	C₂×C₅×#4296	semidirect
46. C₅	#20266606	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×#15692435	2
C₅×#14524209	3
#20266606	5
C₂×C₅×#4296	19
C₅×AGL(1,𝔽₁₉)	19

Subgroups — C5×#20266606 #44570525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20266606 #44570525