Subgroups — C₅×C₉×C₁₉×D₁₉ #44570495

Order 32490.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₉×D₁₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉×D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₉×D₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉×D₁₉	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₉×C₁₉	—	19	1	no	maximal
10	C₅×C₉×D₁₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor
11	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic
12	C₅×C₉×C₁₉	—	2	9	no	—
13	C₅×C₉×C₁₉	D₁₉	1	1	yes	characteristic, direct product factor
14	C₅×C₉×C₁₉	C₂×C₁₉	1	1	yes	characteristic, complemented
15	C₁₉×D₁₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₅×C₁₉	—	19	1	no	—
17	C₃×C₅×D₁₉	C₃×C₁₉	1	1	yes	characteristic
18	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₉×C₁₉	—	19	1	no	—
20	C₉×D₁₉	C₅×C₁₉	1	1	yes	characteristic, direct product factor
21	C₃×C₅×C₁₉	—	2	9	no	—
22	C₃×C₅×C₁₉	C₃×D₁₉	1	1	yes	characteristic
23	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic
24	C₂×C₅×C₁₉	—	19	1	no	—
25	C₅×D₁₉	C₉×C₁₉	1	1	yes	characteristic, direct product factor
26	C₉×C₁₉	—	2	9	no	—
27	C₉×C₁₉	C₅×D₁₉	1	1	yes	characteristic, direct product factor
28	C₉×C₁₉	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
29	C₂×C₃×C₁₉	—	19	1	no	—
30	C₃×D₁₉	C₃×C₅×C₁₉	1	1	yes	characteristic
31	C₅×C₁₉	—	2	9	no	—
32	C₅×C₁₉	C₉×D₁₉	1	1	yes	characteristic, direct product factor
33	C₅×C₁₉	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
34	C₂×C₅×C₉	—	19	1	no	Hall
35	C₃×C₁₉	—	2	9	no	—
36	C₃×C₁₉	C₃×C₅×D₁₉	1	1	yes	characteristic
37	C₃×C₁₉	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic
38	C₅×C₉	C₁₉×D₁₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₁₉	—	19	1	no	—
40	D₁₉	C₅×C₉×C₁₉	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₅	—	19	1	no	—
42	C₁₉	—	2	9	no	—
43	C₁₉	C₅×C₉×D₁₉	1	1	yes	characteristic, direct product factor
44	C₁₉	C₂×C₅×C₉×C₁₉	1	1	yes	characteristic, complemented
45	C₂×C₉	—	19	1	no	Hall
46	C₃×C₅	C₃×C₁₉×D₁₉	1	1	yes	characteristic
47	C₂×C₅	—	19	1	no	Hall
48	C₉	C₅×C₁₉×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃	—	19	1	no	—
50	C₅	C₉×C₁₉×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₃×C₅×C₁₉×D₁₉	1	1	yes	characteristic
52	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉×C₁₉	D₁₉
commutator, hypocenter	C₁₉	C₂×C₅×C₉×C₁₉
Frattini	C₃	C₃×C₅×C₁₉×D₁₉
Fitting	C₅×C₉×C₁₉²	C₂
socle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×C₅×C₁₉×D₁₉	C₃
cosocle	C₃×C₁₉	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₉×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₉²	C₂	semidirect
3. C₉×C₁₉×D₁₉	C₅	direct (N × H)
5. C₅×C₁₉×D₁₉	C₉	direct (N × H)
6. C₉×C₁₉²	C₂×C₅	semidirect
8. C₅×C₁₉²	C₂×C₉	semidirect
10. C₅×C₉×D₁₉	C₁₉	direct (N × H)
13. C₅×C₉×C₁₉	D₁₉	direct (N × H)
14. C₅×C₉×C₁₉	C₂×C₁₉	semidirect
15. C₁₉×D₁₉	C₅×C₉	direct (N × H)
18. C₁₉²	C₂×C₅×C₉	semidirect
20. C₉×D₁₉	C₅×C₁₉	direct (N × H)
25. C₅×D₁₉	C₉×C₁₉	direct (N × H)
27. C₉×C₁₉	C₅×D₁₉	direct (N × H)
28. C₉×C₁₉	C₂×C₅×C₁₉	semidirect
32. C₅×C₁₉	C₉×D₁₉	direct (N × H)
33. C₅×C₁₉	C₂×C₉×C₁₉	semidirect
38. C₅×C₉	C₁₉×D₁₉	direct (N × H)
40. D₁₉	C₅×C₉×C₁₉	direct (N × H)
43. C₁₉	C₅×C₉×D₁₉	direct (N × H)
44. C₁₉	C₂×C₅×C₉×C₁₉	semidirect
48. C₉	C₅×C₁₉×D₁₉	direct (N × H)
50. C₅	C₉×C₁₉×D₁₉	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×C₉×C₁₉²	2
C₃×C₅×C₁₉×D₁₉	3
C₉×C₁₉×D₁₉	5
C₂×C₅×C₉×C₁₉	19
C₅×C₉×D₁₉	19

Subgroups — C5×C9×C19×D19 #44570495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₉×D₁₉ #44570495