Subgroups — D₅×C₁₉×#4296 #44570530

Order 32490.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×#4296	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#4296	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	D₅×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×#4296	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₉×C₁₉⋊C₃	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	D₅×#4296	C₁₉	1	1	yes	maximal, characteristic, direct product factor
10	C₉×D₅×C₁₉	—	19	1	no	maximal
11	C₁₉×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic
12	C₅×#4296	C₂×C₁₉	1	1	yes	characteristic, complemented
13	C₅×C₉×C₁₉	—	19	1	no	—
14	C₂×C₁₉²	—	5	1	no	Hall
15	C₃×D₅×C₁₉	—	19	1	no	—
16	D₅×C₁₉⋊C₃	C₃×C₁₉	1	1	yes	characteristic
17	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×#4296	—	5	1	no	—
19	C₂×C₉×C₁₉	—	95	1	no	—
20	C₃×C₅×C₁₉	—	19	1	no	—
21	C₅×C₁₉⋊C₃	C₂×C₃×C₁₉	1	1	yes	characteristic
22	D₅×C₁₉	—	9	2	no	—
23	D₅×C₁₉	C₉×C₁₉	1	1	yes	characteristic, complemented
24	D₅×C₁₉	#4296	1	1	yes	characteristic, direct product factor
25	#4296	D₅×C₁₉	1	1	yes	characteristic, direct product factor
26	C₉×C₁₉	—	19	1	no	—
27	C₂×C₃×C₁₉	—	95	1	no	—
28	C₂×C₁₉⋊C₃	—	5	1	no	—
29	C₅×C₁₉	—	9	2	no	—
30	C₅×C₁₉	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
31	C₅×C₁₉	C₂×#4296	1	1	yes	characteristic, complemented
32	C₉×D₅	—	19	1	no	Hall
33	C₃×C₁₉	—	19	1	no	—
34	C₁₉⋊C₃	C₃×D₅×C₁₉	1	1	yes	characteristic
35	C₅×C₉	—	19	1	no	Hall
36	C₂×C₁₉	—	5	1	no	—
37	C₂×C₁₉	—	5	1	no	—
38	C₂×C₁₉	—	45	2	no	—
39	C₃×D₅	—	19	1	no	—
40	C₁₉	—	9	2	no	—
41	C₁₉	C₉×D₅×C₁₉	1	1	yes	characteristic, complemented
42	C₁₉	D₅×#4296	1	1	yes	characteristic, direct product factor
43	C₂×C₉	—	95	1	no	Hall
44	C₃×C₅	—	19	1	no	—
45	D₅	C₁₉×#4296	1	1	yes	characteristic, direct product factor, Hall
46	C₉	—	19	1	no	Sylow
47	C₂×C₃	—	95	1	no	—
48	C₅	C₂×C₁₉×#4296	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	19	1	no	—
50	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₅×#4296
commutator, hypocenter	C₅×C₁₉	C₂×C₉×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂×C₉
prime radical	D₅×C₁₉×C₁₉⋊C₃	C₃
cosocle	C₅×C₁₉⋊C₃	C₂×C₃×C₁₉
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×#4296	C₂	semidirect
5. D₅×C₁₉²	C₉	semidirect
6. C₁₉×#4296	D₅	direct (N × H)
8. C₅×C₁₉²	C₂×C₉	semidirect
9. D₅×#4296	C₁₉	direct (N × H)
12. C₅×#4296	C₂×C₁₉	semidirect
17. C₁₉²	C₉×D₅	semidirect
23. D₅×C₁₉	C₉×C₁₉	semidirect
24. D₅×C₁₉	#4296	direct (N × H)
25. #4296	D₅×C₁₉	direct (N × H)
30. C₅×C₁₉	C₂×C₉×C₁₉	semidirect
31. C₅×C₁₉	C₂×#4296	semidirect
41. C₁₉	C₉×D₅×C₁₉	semidirect
42. C₁₉	D₅×#4296	direct (N × H)
45. D₅	C₁₉×#4296	direct (N × H)
48. C₅	C₂×C₁₉×#4296	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₉×#4296	2
D₅×C₁₉×C₁₉⋊C₃	3
C₂×C₁₉×#4296	5
D₅×#4296	19
C₉×D₅×C₁₉	19

Subgroups — D5×C19×#4296 #44570530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₉×#4296 #44570530