Subgroups — C₅⋊#20266604 #44570549

Order 32490.

60 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⋊#14524208	C₃	1	1	yes	maximal, characteristic
3	#20266604	—	5	1	no	maximal, Hall
4	C₅×#11762245	C₂×C₃	1	1	yes	characteristic
5	C₁₉×D₉₅	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692434	D₅	1	1	yes	characteristic, complemented, Hall
7	#14524208	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅⋊AGL(1,𝔽₁₉)	—	19	1	no	maximal
10	D₅×#4296	—	19	1	no	maximal
11	#11762245	C₃×D₅	1	1	yes	characteristic
12	C₅×#4296	—	19	1	no	—
13	C₅×#4296	—	19	1	no	—
14	C₁₉×D₁₉	—	5	1	no	Hall
15	C₅⋊(D₁₉⋊C₃)	—	19	1	no	—
16	D₅×C₁₉⋊C₃	—	19	1	no	—
17	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×#4296	—	95	1	no	—
19	AGL(1,𝔽₁₉)	—	95	1	no	—
20	C₅×C₁₉⋊C₃	—	19	1	no	—
21	C₅×C₁₉⋊C₃	—	19	1	no	—
22	C₅×C₁₉⋊C₃	—	114	3	no	—
23	D₉₅	#4296	1	1	yes	characteristic, complemented
24	D₅×C₁₉	—	19	1	no	—
25	#4296	—	19	1	no	—
26	#4296	—	19	1	no	—
27	C₂×C₁₉⋊C₃	—	95	1	no	—
28	D₁₉⋊C₃	—	95	1	no	—
29	C₅×C₁₉	—	6	3	no	—
30	C₅×C₁₉	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
31	C₅×C₁₉	C₂×#4296	1	1	yes	characteristic, complemented
32	C₉×D₅	—	361	1	no	Hall
33	C₁₉⋊C₃	—	19	1	no	—
34	C₁₉⋊C₃	—	19	1	no	—
35	C₁₉⋊C₃	—	114	3	no	—
36	C₅×C₉	—	361	1	no	Hall
37	C₂×C₁₉	—	95	1	no	—
38	D₁₉	—	5	1	no	—
39	C₃×D₅	—	361	1	no	—
40	C₁₉	—	6	3	no	—
41	C₁₉	D₅×#4296	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	—	361	1	no	—
45	D₅	—	19	1	no	Hall
46	C₉	—	361	1	no	Sylow
47	C₂×C₃	—	1805	1	no	—
48	C₅	#20266604	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	361	1	no	—
50	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉²	C₂×C₉
prime radical	C₅⋊#14524208	C₃
cosocle	C₅×#11762245	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×#15692434	C₂	semidirect
5. C₁₉×D₉₅	C₉	semidirect
6. #15692434	D₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
17. C₁₉²	C₉×D₅	semidirect
23. D₉₅	#4296	semidirect
30. C₅×C₁₉	AGL(1,𝔽₁₉)	semidirect
31. C₅×C₁₉	C₂×#4296	semidirect
41. C₁₉	D₅×#4296	semidirect
42. C₁₉	C₅⋊AGL(1,𝔽₁₉)	semidirect
48. C₅	#20266604	semidirect

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⋊#14524208	3
#20266604	5
C₅⋊AGL(1,𝔽₁₉)	19
D₅×#4296	19

Subgroups — C5⋊#20266604 #44570549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#20266604 #44570549