Subgroups — C₂²×C₃×C₅×C₉×C₁₉ #72188917

Order 10260.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₉×C₁₉	C₂	1	3	yes	maximal, direct product factor
2	C₃×C₅×C₉×C₁₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₃×C₉×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃²×C₅×C₁₉	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₅×C₉×C₁₉	C₃	1	3	yes	maximal, direct product factor
6	C₂×C₃²×C₅×C₁₉	C₂×C₃	1	3	yes	—
7	C₂×C₅×C₉×C₁₉	C₂×C₃	1	9	yes	direct product factor
8	C₂²×C₃×C₅×C₁₉	C₉	1	3	yes	direct product factor
9	C₂²×C₃×C₅×C₁₉	C₃²	1	1	yes	characteristic
10	C₂×C₃×C₉×C₁₉	C₂×C₅	1	3	yes	direct product factor
11	C₃²×C₅×C₁₉	C₂²×C₃	1	1	yes	characteristic
12	C₅×C₉×C₁₉	C₂²×C₃	1	3	yes	direct product factor
13	C₂²×C₃²×C₁₉	C₃×C₅	1	1	yes	characteristic
14	C₂²×C₉×C₁₉	C₃×C₅	1	3	yes	direct product factor
15	C₂×C₃×C₅×C₁₉	C₂×C₉	1	9	yes	direct product factor
16	C₂×C₃×C₅×C₁₉	C₂×C₃²	1	3	yes	—
17	C₂²×C₃×C₅×C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₃×C₉×C₁₉	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅×C₁₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃²×C₁₉	C₂×C₃×C₅	1	3	yes	—
21	C₂×C₉×C₁₉	C₂×C₃×C₅	1	9	yes	direct product factor
22	C₃×C₅×C₁₉	C₂²×C₉	1	3	yes	direct product factor
23	C₃×C₅×C₁₉	C₂²×C₃²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₉	C₂×C₁₉	1	3	yes	direct product factor
25	C₂²×C₃×C₁₉	C₅×C₉	1	3	yes	direct product factor
26	C₂²×C₃×C₁₉	C₃²×C₅	1	1	yes	characteristic
27	C₂×C₅×C₁₉	C₂×C₃×C₉	1	3	yes	direct product factor
28	C₂²×C₃²×C₅	C₃×C₁₉	1	1	yes	characteristic
29	C₂²×C₅×C₉	C₃×C₁₉	1	3	yes	direct product factor
30	C₃²×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₉×C₁₉	C₂²×C₃×C₅	1	3	yes	direct product factor
32	C₃×C₅×C₉	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₁₉	C₂×C₅×C₉	1	9	yes	direct product factor
34	C₂×C₃×C₁₉	C₂×C₃²×C₅	1	3	yes	—
35	C₂²×C₃×C₉	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₁₉	C₂²×C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₃²×C₅	C₂×C₃×C₁₉	1	3	yes	—
38	C₂×C₅×C₉	C₂×C₃×C₁₉	1	9	yes	direct product factor
39	C₂²×C₁₉	C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₃×C₅	C₉×C₁₉	1	3	yes	direct product factor
41	C₂²×C₃×C₅	C₃²×C₁₉	1	1	yes	characteristic
42	C₃×C₁₉	C₂²×C₅×C₉	1	3	yes	direct product factor
43	C₃×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic
44	C₂×C₃×C₉	C₂×C₅×C₁₉	1	3	yes	direct product factor
45	C₃²×C₅	C₂²×C₃×C₁₉	1	1	yes	characteristic
46	C₅×C₉	C₂²×C₃×C₁₉	1	3	yes	direct product factor
47	C₂×C₁₉	C₂×C₃×C₅×C₉	1	3	yes	direct product factor
48	C₂²×C₃²	C₃×C₅×C₁₉	1	1	yes	characteristic
49	C₂²×C₉	C₃×C₅×C₁₉	1	3	yes	direct product factor
50	C₂×C₃×C₅	C₂×C₉×C₁₉	1	9	yes	direct product factor
51	C₂×C₃×C₅	C₂×C₃²×C₁₉	1	3	yes	—
52	C₃×C₉	C₂²×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²×C₅	C₃×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
54	C₁₉	C₂²×C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₃²	C₂×C₃×C₅×C₁₉	1	3	yes	—
56	C₂×C₉	C₂×C₃×C₅×C₁₉	1	9	yes	direct product factor
57	C₃×C₅	C₂²×C₉×C₁₉	1	3	yes	direct product factor
58	C₃×C₅	C₂²×C₃²×C₁₉	1	1	yes	characteristic
59	C₂²×C₃	C₅×C₉×C₁₉	1	3	yes	direct product factor
60	C₂²×C₃	C₃²×C₅×C₁₉	1	1	yes	characteristic
61	C₂×C₅	C₂×C₃×C₉×C₁₉	1	3	yes	direct product factor
62	C₃²	C₂²×C₃×C₅×C₁₉	1	1	yes	characteristic
63	C₉	C₂²×C₃×C₅×C₁₉	1	3	yes	direct product factor
64	C₂×C₃	C₂×C₅×C₉×C₁₉	1	9	yes	direct product factor
65	C₂×C₃	C₂×C₃²×C₅×C₁₉	1	3	yes	—
66	C₅	C₂²×C₃×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	C₃×C₅×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
68	C₃	C₂²×C₅×C₉×C₁₉	1	3	yes	direct product factor
69	C₃	C₂²×C₃²×C₅×C₁₉	1	1	yes	characteristic
70	C₂	C₂×C₃×C₅×C₉×C₁₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃²×C₅×C₁₉
socle, prime radical	C₂²×C₃²×C₅×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₉×C₁₉	C₂	direct (N × H)
2. C₃×C₅×C₉×C₁₉	C₂²	direct (N × H)
3. C₂²×C₃×C₉×C₁₉	C₅	direct (N × H)
5. C₂²×C₅×C₉×C₁₉	C₃	direct (N × H)
7. C₂×C₅×C₉×C₁₉	C₂×C₃	direct (N × H)
8. C₂²×C₃×C₅×C₁₉	C₉	direct (N × H)
10. C₂×C₃×C₉×C₁₉	C₂×C₅	direct (N × H)
12. C₅×C₉×C₁₉	C₂²×C₃	direct (N × H)
14. C₂²×C₉×C₁₉	C₃×C₅	direct (N × H)
15. C₂×C₃×C₅×C₁₉	C₂×C₉	direct (N × H)
17. C₂²×C₃×C₅×C₉	C₁₉	direct (N × H)
18. C₃×C₉×C₁₉	C₂²×C₅	direct (N × H)
19. C₂²×C₅×C₁₉	C₃×C₉	direct (N × H)
21. C₂×C₉×C₁₉	C₂×C₃×C₅	direct (N × H)
22. C₃×C₅×C₁₉	C₂²×C₉	direct (N × H)
24. C₂×C₃×C₅×C₉	C₂×C₁₉	direct (N × H)
25. C₂²×C₃×C₁₉	C₅×C₉	direct (N × H)
27. C₂×C₅×C₁₉	C₂×C₃×C₉	direct (N × H)
29. C₂²×C₅×C₉	C₃×C₁₉	direct (N × H)
31. C₉×C₁₉	C₂²×C₃×C₅	direct (N × H)
32. C₃×C₅×C₉	C₂²×C₁₉	direct (N × H)
33. C₂×C₃×C₁₉	C₂×C₅×C₉	direct (N × H)
35. C₂²×C₃×C₉	C₅×C₁₉	direct (N × H)
36. C₅×C₁₉	C₂²×C₃×C₉	direct (N × H)
38. C₂×C₅×C₉	C₂×C₃×C₁₉	direct (N × H)
39. C₂²×C₁₉	C₃×C₅×C₉	direct (N × H)
40. C₂²×C₃×C₅	C₉×C₁₉	direct (N × H)
42. C₃×C₁₉	C₂²×C₅×C₉	direct (N × H)
44. C₂×C₃×C₉	C₂×C₅×C₁₉	direct (N × H)
46. C₅×C₉	C₂²×C₃×C₁₉	direct (N × H)
47. C₂×C₁₉	C₂×C₃×C₅×C₉	direct (N × H)
49. C₂²×C₉	C₃×C₅×C₁₉	direct (N × H)
50. C₂×C₃×C₅	C₂×C₉×C₁₉	direct (N × H)
52. C₃×C₉	C₂²×C₅×C₁₉	direct (N × H)
53. C₂²×C₅	C₃×C₉×C₁₉	direct (N × H)
54. C₁₉	C₂²×C₃×C₅×C₉	direct (N × H)
56. C₂×C₉	C₂×C₃×C₅×C₁₉	direct (N × H)
57. C₃×C₅	C₂²×C₉×C₁₉	direct (N × H)
59. C₂²×C₃	C₅×C₉×C₁₉	direct (N × H)
61. C₂×C₅	C₂×C₃×C₉×C₁₉	direct (N × H)
63. C₉	C₂²×C₃×C₅×C₁₉	direct (N × H)
64. C₂×C₃	C₂×C₅×C₉×C₁₉	direct (N × H)
66. C₅	C₂²×C₃×C₉×C₁₉	direct (N × H)
67. C₂²	C₃×C₅×C₉×C₁₉	direct (N × H)
68. C₃	C₂²×C₅×C₉×C₁₉	direct (N × H)
70. C₂	C₂×C₃×C₅×C₉×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
C₂×C₃×C₅×C₉×C₁₉	2
C₂²×C₃×C₉×C₁₉	5
C₂²×C₃²×C₅×C₁₉	3
C₂²×C₅×C₉×C₁₉	3
C₂²×C₃×C₅×C₉	19

Subgroups — C22×C3×C5×C9×C19 #72188917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₅×C₉×C₁₉ #72188917