Subgroups — C₅×#20266600 #44570521

Order 32490.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692434	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#14524206	C₃	1	1	yes	maximal, characteristic
3	#20266600	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×#11762245	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₉⋊D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692434	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	#14524206	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅×AGL(1,𝔽₁₉)	—	19	2	no	maximal
10	#11762245	C₂×C₃×C₅	1	1	yes	characteristic
11	C₅×#4296	—	19	2	no	—
12	C₁₉⋊D₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
13	C₅×D₁₉⋊C₃	—	19	2	no	—
14	C₅×D₁₉⋊C₃	—	57	6	no	—
15	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
16	AGL(1,𝔽₁₉)	—	19	2	no	—
17	C₅×C₁₉⋊C₃	—	19	2	no	—
18	C₅×C₁₉⋊C₃	—	57	6	no	—
19	C₅×D₁₉	—	19	2	no	—
20	C₅×D₁₉	—	57	6	no	—
21	#4296	—	19	2	no	—
22	D₁₉⋊C₃	—	19	2	no	—
23	D₁₉⋊C₃	—	57	6	no	—
24	C₅×C₁₉	—	3	6	no	—
25	C₅×C₁₉	AGL(1,𝔽₁₉)	1	2	yes	complemented
26	C₂×C₅×C₉	—	361	1	no	Hall
27	C₁₉⋊C₃	—	19	2	no	—
28	C₁₉⋊C₃	—	57	6	no	—
29	C₅×C₉	—	361	1	no	Hall
30	D₁₉	—	19	2	no	—
31	D₁₉	—	57	6	no	—
32	C₂×C₃×C₅	—	361	1	no	—
33	C₁₉	—	3	6	no	—
34	C₁₉	C₅×AGL(1,𝔽₁₉)	1	2	yes	complemented
35	C₂×C₉	—	361	1	no	Hall
36	C₃×C₅	—	361	1	no	—
37	C₂×C₅	—	361	1	no	Hall
38	C₉	—	361	1	no	Sylow
39	C₂×C₃	—	361	1	no	—
40	C₅	#20266600	1	1	yes	characteristic, direct product factor, Sylow
41	C₃	—	361	1	no	—
42	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#20266600
commutator, hypocenter	C₁₉²	C₂×C₅×C₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂×C₉
prime radical	C₅×#14524206	C₃
cosocle	#11762245	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×#15692434	C₂	semidirect
3. #20266600	C₅	direct (N × H)
5. C₅×C₁₉⋊D₁₉	C₉	semidirect
6. #15692434	C₂×C₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
12. C₁₉⋊D₁₉	C₅×C₉	semidirect
15. C₁₉²	C₂×C₅×C₉	semidirect
25. C₅×C₁₉	AGL(1,𝔽₁₉)	semidirect
34. C₁₉	C₅×AGL(1,𝔽₁₉)	semidirect
40. C₅	#20266600	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×#15692434	2
C₅×#14524206	3
#20266600	5
C₅×AGL(1,𝔽₁₉)	19

Subgroups — C5×#20266600 #44570521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20266600 #44570521