Subgroups — C₂×C₅×D₃×C₁₇×C₁₉ #34084409

Order 19380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₁₇×C₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₁₇×C₁₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₇×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₇×C₁₉	—	3	2	no	—
7	C₂×C₅×C₁₇×C₁₉	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₃×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
9	D₃×C₁₇×C₁₉	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₁₇×C₁₉	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₁₇×C₁₉	—	3	1	no	Hall
12	C₂×C₅×D₃×C₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×D₃×C₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₁₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₇×C₁₉	—	3	2	no	—
16	C₂×C₁₇×C₁₉	C₅×D₃	1	1	yes	characteristic, direct product factor
17	C₂×C₃×C₅×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₅×D₃×C₁₉	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×C₃×C₅×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented
20	C₅×D₃×C₁₇	C₂×C₁₉	1	2	yes	direct product factor
21	C₂²×C₅×C₁₉	—	3	1	no	Hall
22	C₂²×C₅×C₁₇	—	3	1	no	Hall
23	C₁₇×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅×C₁₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×C₁₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃×C₁₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×D₃×C₁₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₅×C₁₉	—	3	2	no	—
29	C₂×C₅×C₁₉	D₃×C₁₇	1	1	yes	characteristic, direct product factor
30	C₂×C₅×C₁₇	—	3	2	no	—
31	C₂×C₅×C₁₇	D₃×C₁₉	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₁₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
33	D₃×C₁₉	C₂×C₅×C₁₇	1	2	yes	direct product factor
34	C₂×C₃×C₁₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
35	D₃×C₁₇	C₂×C₅×C₁₉	1	2	yes	direct product factor
36	C₅×C₁₉	C₂×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
37	C₅×C₁₇	C₂×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
38	C₂²×C₁₉	—	3	1	no	Hall
39	C₂²×C₁₇	—	3	1	no	Hall
40	C₂×C₅×D₃	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
41	C₃×C₁₉	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₇	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₁₉	—	3	2	no	—
44	C₂×C₁₉	C₅×D₃×C₁₇	1	1	yes	characteristic, direct product factor
45	C₂×C₁₇	—	3	2	no	—
46	C₂×C₁₇	C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₅	C₂×C₁₇×C₁₉	1	1	yes	characteristic, complemented
48	C₅×D₃	C₂×C₁₇×C₁₉	1	2	yes	direct product factor
49	C₂²×C₅	—	3	1	no	Hall
50	C₁₉	C₂×C₅×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
51	C₁₇	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	C₂²×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃	C₅×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₅	—	3	2	no	—
55	C₂×C₅	D₃×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor
56	C₂×C₃	C₂×C₅×C₁₇×C₁₉	1	1	yes	characteristic, complemented
57	D₃	C₂×C₅×C₁₇×C₁₉	1	2	yes	direct product factor
58	C₅	C₂×D₃×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	3	1	no	Sylow
60	C₃	C₂²×C₅×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	3	2	no	—
62	C₂	C₅×D₃×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₁₇×C₁₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₇×C₁₉	C₂²	semidirect
5. C₂×D₃×C₁₇×C₁₉	C₅	direct (N × H)
7. C₂×C₅×C₁₇×C₁₉	D₃	direct (N × H)
8. C₂×C₃×C₁₇×C₁₉	C₂×C₅	semidirect
9. D₃×C₁₇×C₁₉	C₂×C₅	direct (N × H)
10. C₅×C₁₇×C₁₉	C₂×D₃	direct (N × H)
12. C₂×C₅×D₃×C₁₉	C₁₇	direct (N × H)
13. C₂×C₅×D₃×C₁₇	C₁₉	direct (N × H)
14. C₃×C₁₇×C₁₉	C₂²×C₅	semidirect
16. C₂×C₁₇×C₁₉	C₅×D₃	direct (N × H)
17. C₂×C₃×C₅×C₁₉	C₂×C₁₇	semidirect
18. C₅×D₃×C₁₉	C₂×C₁₇	direct (N × H)
19. C₂×C₃×C₅×C₁₇	C₂×C₁₉	semidirect
20. C₅×D₃×C₁₇	C₂×C₁₉	direct (N × H)
23. C₁₇×C₁₉	C₂×C₅×D₃	direct (N × H)
24. C₃×C₅×C₁₉	C₂²×C₁₇	semidirect
25. C₃×C₅×C₁₇	C₂²×C₁₉	semidirect
26. C₂×D₃×C₁₉	C₅×C₁₇	direct (N × H)
27. C₂×D₃×C₁₇	C₅×C₁₉	direct (N × H)
29. C₂×C₅×C₁₉	D₃×C₁₇	direct (N × H)
31. C₂×C₅×C₁₇	D₃×C₁₉	direct (N × H)
32. C₂×C₃×C₁₉	C₂×C₅×C₁₇	semidirect
33. D₃×C₁₉	C₂×C₅×C₁₇	direct (N × H)
34. C₂×C₃×C₁₇	C₂×C₅×C₁₉	semidirect
35. D₃×C₁₇	C₂×C₅×C₁₉	direct (N × H)
36. C₅×C₁₉	C₂×D₃×C₁₇	direct (N × H)
37. C₅×C₁₇	C₂×D₃×C₁₉	direct (N × H)
40. C₂×C₅×D₃	C₁₇×C₁₉	direct (N × H)
41. C₃×C₁₉	C₂²×C₅×C₁₇	semidirect
42. C₃×C₁₇	C₂²×C₅×C₁₉	semidirect
44. C₂×C₁₉	C₅×D₃×C₁₇	direct (N × H)
46. C₂×C₁₇	C₅×D₃×C₁₉	direct (N × H)
47. C₂×C₃×C₅	C₂×C₁₇×C₁₉	semidirect
48. C₅×D₃	C₂×C₁₇×C₁₉	direct (N × H)
50. C₁₉	C₂×C₅×D₃×C₁₇	direct (N × H)
51. C₁₇	C₂×C₅×D₃×C₁₉	direct (N × H)
52. C₃×C₅	C₂²×C₁₇×C₁₉	semidirect
53. C₂×D₃	C₅×C₁₇×C₁₉	direct (N × H)
55. C₂×C₅	D₃×C₁₇×C₁₉	direct (N × H)
56. C₂×C₃	C₂×C₅×C₁₇×C₁₉	semidirect
57. D₃	C₂×C₅×C₁₇×C₁₉	direct (N × H)
58. C₅	C₂×D₃×C₁₇×C₁₉	direct (N × H)
60. C₃	C₂²×C₅×C₁₇×C₁₉	semidirect
62. C₂	C₅×D₃×C₁₇×C₁₉	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×D₃×C₁₇×C₁₉	2
C₂×C₃×C₅×C₁₇×C₁₉	2
C₂²×C₅×C₁₇×C₁₉	3
C₂×D₃×C₁₇×C₁₉	5
C₂×C₅×D₃×C₁₉	17
C₂×C₅×D₃×C₁₇	19

Subgroups — C2×C5×D3×C17×C19 #34084409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₁₇×C₁₉ #34084409