Subgroups — C₃×C₅×C₁₉×D₅₇ #44570627

Order 32490.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₉×D₁₉	—	3	1	no	maximal
3	C₅×C₁₉×D₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₁₉×D₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₉²	—	2	1	no	—
6	C₃×C₅×C₁₉²	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×C₁₉×D₁₉	—	3	1	no	Hall
9	C₃²×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₁₉×D₅₇	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₃×C₁₉×D₁₉	—	3	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×D₅₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor
14	C₃×C₅×D₃×C₁₉	—	19	1	no	maximal
15	C₃×C₁₉²	—	2	1	no	—
16	C₃×C₁₉²	C₅×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₃²×C₅×C₁₉	—	2	9	no	—
19	C₃²×C₅×C₁₉	D₁₉	1	1	yes	characteristic, complemented
20	C₃²×C₅×C₁₉	C₂×C₁₉	1	1	yes	characteristic, complemented
21	C₁₉×D₁₉	—	3	1	no	Hall
22	C₂×C₃×C₅×C₁₉	—	57	1	no	—
23	C₅×D₅₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor
24	C₅×D₃×C₁₉	—	19	1	no	—
25	C₃×C₅×D₁₉	—	3	1	no	—
26	C₁₉²	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₅₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor
28	C₃×D₃×C₁₉	—	19	1	no	—
29	C₃×C₅×C₁₉	—	2	18	no	—
30	C₃×C₅×C₁₉	—	2	9	no	—
31	C₃×C₅×C₁₉	—	2	9	no	—
32	C₃×C₅×C₁₉	—	2	1	no	—
33	C₃×C₅×C₁₉	—	2	1	no	—
34	C₃×C₅×C₁₉	D₃×C₁₉	1	1	yes	characteristic, complemented
35	C₃×C₅×C₁₉	C₃×D₁₉	1	1	yes	characteristic, complemented
36	C₃×C₅×C₁₉	D₅₇	1	1	yes	characteristic, direct product factor
37	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
38	C₂×C₅×C₁₉	—	57	1	no	—
39	C₅×D₁₉	—	3	1	no	—
40	C₃²×C₁₉	—	2	9	no	—
41	C₃²×C₁₉	C₅×D₁₉	1	1	yes	characteristic, complemented
42	C₃²×C₁₉	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
43	C₂×C₃×C₁₉	—	57	1	no	—
44	D₅₇	C₃×C₅×C₁₉	1	1	yes	characteristic, direct product factor
45	C₃×D₁₉	—	3	1	no	—
46	D₃×C₁₉	—	19	1	no	—
47	C₅×C₁₉	—	2	9	no	—
48	C₅×C₁₉	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented
49	C₅×C₁₉	C₃×D₅₇	1	1	yes	characteristic, direct product factor
50	C₃×C₅×D₃	—	19	1	no	Hall
51	C₃×C₁₉	—	2	18	no	—
52	C₃×C₁₉	—	2	1	no	—
53	C₃×C₁₉	—	2	1	no	—
54	C₃×C₁₉	—	2	9	no	—
55	C₃×C₁₉	—	2	9	no	—
56	C₃×C₁₉	C₃×C₅×D₁₉	1	1	yes	characteristic, complemented
57	C₃×C₁₉	C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
58	C₃×C₁₉	C₅×D₅₇	1	1	yes	characteristic, direct product factor
59	C₃×C₁₉	C₂×C₃×C₅×C₁₉	1	1	yes	characteristic, complemented
60	C₃²×C₅	C₁₉×D₁₉	1	1	yes	characteristic, complemented, Hall
61	C₂×C₁₉	—	57	1	no	—
62	D₁₉	—	3	1	no	—
63	C₂×C₃×C₅	—	57	1	no	—
64	C₅×D₃	—	19	1	no	—
65	C₁₉	—	2	9	no	—
66	C₁₉	C₃×C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
67	C₁₉	C₃×C₅×D₅₇	1	1	yes	characteristic, direct product factor
68	C₃×D₃	—	19	1	no	Hall
69	C₃×C₅	—	2	1	no	—
70	C₃×C₅	C₃×C₁₉×D₁₉	1	1	yes	characteristic, complemented
71	C₃×C₅	C₁₉×D₅₇	1	1	yes	characteristic, direct product factor
72	C₂×C₅	—	57	1	no	Hall
73	C₃²	C₅×C₁₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	57	1	no	—
75	D₃	—	19	1	no	—
76	C₅	C₃×C₁₉×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
77	C₃	—	2	1	no	—
78	C₃	C₅×C₁₉×D₅₇	1	1	yes	characteristic, direct product factor
79	C₃	C₃×C₅×C₁₉×D₁₉	1	1	yes	characteristic, complemented
80	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₉	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉²	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₃×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
3. C₅×C₁₉×D₅₇	C₃	direct (N × H)
4. C₃×C₁₉×D₅₇	C₅	direct (N × H)
6. C₃×C₅×C₁₉²	D₃	semidirect
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃²×C₁₉²	C₂×C₅	semidirect
10. C₁₉×D₅₇	C₃×C₅	direct (N × H)
12. C₅×C₁₉²	C₃×D₃	semidirect
13. C₃×C₅×D₅₇	C₁₉	direct (N × H)
16. C₃×C₁₉²	C₅×D₃	semidirect
17. C₃×C₁₉²	C₂×C₃×C₅	semidirect
19. C₃²×C₅×C₁₉	D₁₉	semidirect
20. C₃²×C₅×C₁₉	C₂×C₁₉	semidirect
23. C₅×D₅₇	C₃×C₁₉	direct (N × H)
26. C₁₉²	C₃×C₅×D₃	semidirect
27. C₃×D₅₇	C₅×C₁₉	direct (N × H)
34. C₃×C₅×C₁₉	D₃×C₁₉	semidirect
35. C₃×C₅×C₁₉	C₃×D₁₉	semidirect
36. C₃×C₅×C₁₉	D₅₇	direct (N × H)
37. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
41. C₃²×C₁₉	C₅×D₁₉	semidirect
42. C₃²×C₁₉	C₂×C₅×C₁₉	semidirect
44. D₅₇	C₃×C₅×C₁₉	direct (N × H)
48. C₅×C₁₉	C₃×D₃×C₁₉	semidirect
49. C₅×C₁₉	C₃×D₅₇	direct (N × H)
56. C₃×C₁₉	C₃×C₅×D₁₉	semidirect
57. C₃×C₁₉	C₅×D₃×C₁₉	semidirect
58. C₃×C₁₉	C₅×D₅₇	direct (N × H)
59. C₃×C₁₉	C₂×C₃×C₅×C₁₉	semidirect
60. C₃²×C₅	C₁₉×D₁₉	semidirect
66. C₁₉	C₃×C₅×D₃×C₁₉	semidirect
67. C₁₉	C₃×C₅×D₅₇	direct (N × H)
70. C₃×C₅	C₃×C₁₉×D₁₉	semidirect
71. C₃×C₅	C₁₉×D₅₇	direct (N × H)
73. C₃²	C₅×C₁₉×D₁₉	semidirect
76. C₅	C₃×C₁₉×D₅₇	direct (N × H)
78. C₃	C₅×C₁₉×D₅₇	direct (N × H)
79. C₃	C₃×C₅×C₁₉×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₉²	2
C₃×C₅×C₁₉×D₁₉	3
C₅×C₁₉×D₅₇	3
C₃×C₁₉×D₅₇	5
C₃×C₅×D₅₇	19
C₃×C₅×D₃×C₁₉	19

Subgroups — C3×C5×C19×D57 #44570627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₉×D₅₇ #44570627