Subgroups — D₅×C₁₉×#4294 #44570471

Order 32490.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₅×C₁₉⋊C₃
commutator, hypocenter	C₅×C₁₉	C₂×C₉×C₁₉
Frattini	C₃	D₅×C₁₉×C₁₉⋊C₃
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×D₅×C₁₉²	C₃
cosocle	C₃×C₅×C₁₉	C₂×C₃×C₁₉
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×#4294	C₂	semidirect
5. D₅×C₁₉²	C₉	semidirect
6. C₁₉×#4294	D₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₉	semidirect
10. D₅×#4294	C₁₉	direct (N × H)
13. C₅×#4294	C₂×C₁₉	semidirect
18. C₁₉²	C₉×D₅	semidirect
25. D₅×C₁₉	#4294	direct (N × H)
26. D₅×C₁₉	C₉×C₁₉	semidirect
28. #4294	D₅×C₁₉	direct (N × H)
33. C₅×C₁₉	C₂×#4294	semidirect
34. C₅×C₁₉	C₂×C₉×C₁₉	semidirect
45. C₁₉	D₅×#4294	direct (N × H)
46. C₁₉	C₉×D₅×C₁₉	semidirect
49. D₅	C₁₉×#4294	direct (N × H)
52. C₅	C₂×C₁₉×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₉×#4294	2
C₃×D₅×C₁₉²	3
C₂×C₁₉×#4294	5
C₉×D₅×C₁₉	19
D₅×#4294	19

Subgroups — D5×C19×#4294 #44570471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₉×#4294 #44570471