Subgroups — C₅⋊#20266603 #44570547

Order 32490.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692433	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊#14524208	C₃	1	1	yes	maximal, characteristic
3	#20266603	—	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	#15692433	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	C₅×#4296	—	38	9	no	—
15	C₁₉×D₁₉	—	5	1	no	Hall
16	C₅⋊(D₁₉⋊C₃)	—	19	1	no	—
17	D₅×C₁₉⋊C₃	—	19	1	no	—
18	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×#4296	—	95	1	no	—
20	AGL(1,𝔽₁₉)	—	95	1	no	—
21	C₅×C₁₉⋊C₃	—	19	1	no	—
22	C₅×C₁₉⋊C₃	—	19	1	no	—
23	C₅×C₁₉⋊C₃	—	38	9	no	—
24	D₉₅	#4296	1	1	yes	characteristic, complemented
25	D₅×C₁₉	—	19	1	no	—
26	#4296	—	19	1	no	—
27	#4296	—	19	1	no	—
28	#4296	—	38	9	no	—
29	C₂×C₁₉⋊C₃	—	95	1	no	—
30	D₁₉⋊C₃	—	95	1	no	—
31	C₅×C₁₉	—	2	9	no	—
32	C₅×C₁₉	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
33	C₅×C₁₉	C₂×#4296	1	1	yes	characteristic, complemented
34	C₉×D₅	—	361	1	no	Hall
35	C₁₉⋊C₃	—	19	1	no	—
36	C₁₉⋊C₃	—	19	1	no	—
37	C₁₉⋊C₃	—	38	9	no	—
38	C₅×C₉	—	361	1	no	Hall
39	C₂×C₁₉	—	95	1	no	—
40	D₁₉	—	5	1	no	—
41	C₃×D₅	—	361	1	no	—
42	C₁₉	—	2	9	no	—
43	C₁₉	D₅×#4296	1	1	yes	characteristic, complemented
44	C₁₉	C₅⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
45	C₂×C₉	—	1805	1	no	Hall
46	C₃×C₅	—	361	1	no	—
47	D₅	—	19	1	no	Hall
48	C₉	—	361	1	no	Sylow
49	C₂×C₃	—	1805	1	no	—
50	C₅	#20266603	1	1	yes	characteristic, complemented, Sylow
51	C₃	—	361	1	no	—
52	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×#15692433	C₂	semidirect
5. C₁₉×D₉₅	C₉	semidirect
6. #15692433	D₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
18. C₁₉²	C₉×D₅	semidirect
24. D₉₅	#4296	semidirect
32. C₅×C₁₉	AGL(1,𝔽₁₉)	semidirect
33. C₅×C₁₉	C₂×#4296	semidirect
43. C₁₉	D₅×#4296	semidirect
44. C₁₉	C₅⋊AGL(1,𝔽₁₉)	semidirect
50. C₅	#20266603	semidirect

Maximal subgroups

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

subgroup	index
C₅×#15692433	2
C₅⋊#14524208	3
#20266603	5
C₅⋊AGL(1,𝔽₁₉)	19
D₅×#4296	19

Subgroups — C5⋊#20266603 #44570547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#20266603 #44570547