Subgroups — C₅×D₃×C₇×D₁₉ #22547708

Order 7980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇×D₁₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇×D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₇×C₁₉	—	3	1	no	—
8	C₅×C₇×D₁₉	—	3	1	no	—
9	C₅×C₇×D₁₉	D₃	1	1	yes	characteristic, direct product factor
10	C₅×D₃×D₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×D₅₇	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×C₇×D₁₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₅₇	C₂×C₇	1	1	yes	characteristic, complemented
16	C₅×D₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×C₅×D₁₉	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×D₁₉	—	3	1	no	Hall
19	C₂×C₅×D₃×C₇	—	19	1	no	maximal, Hall
20	C₃×C₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×D₁₉	—	3	1	no	Hall
22	C₃×C₅×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₉	—	3	1	no	—
24	C₇×D₁₉	—	3	1	no	—
25	C₇×D₁₉	C₅×D₃	1	1	yes	characteristic, direct product factor
26	D₃×D₁₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃×C₅×C₇	—	19	1	no	—
28	C₅×D₃×C₇	—	19	1	no	—
29	C₅×D₃×C₇	D₁₉	1	1	yes	characteristic, direct product factor
30	C₂×C₅×C₁₉	—	3	1	no	—
31	C₅×D₁₉	—	3	1	no	—
32	C₅×D₁₉	D₃×C₇	1	1	yes	characteristic, direct product factor
33	C₂²×C₅×C₇	—	57	1	no	Hall
34	C₇×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
35	D₅₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented
36	C₃×D₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
37	D₃×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
38	C₃×C₅×C₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃×C₇	—	19	1	no	Hall
41	C₂×D₁₉	—	3	1	no	Hall
42	C₂×C₅×C₇	—	3	1	no	—
43	C₂×C₅×C₇	—	19	1	no	—
44	C₂×C₅×C₇	—	57	1	no	—
45	C₂×C₅×D₃	—	19	1	no	Hall
46	C₃×C₁₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃×C₇	—	19	1	no	—
48	D₃×C₇	—	19	1	no	—
49	D₃×C₇	C₅×D₁₉	1	1	yes	characteristic, direct product factor
50	C₂×C₁₉	—	3	1	no	—
51	D₁₉	—	3	1	no	—
52	D₁₉	C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
53	C₅×C₇	D₃×D₁₉	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₃×C₅	—	19	1	no	—
55	C₅×D₃	—	19	1	no	—
56	C₅×D₃	C₇×D₁₉	1	1	yes	characteristic, direct product factor
57	C₂²×C₇	—	57	1	no	Hall
58	C₃×C₇	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₅	—	57	1	no	Hall
60	C₁₉	C₂×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	C₂×C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	3	1	no	—
63	C₂×C₇	—	19	1	no	—
64	C₂×C₇	—	57	1	no	—
65	C₂×D₃	—	19	1	no	Hall
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	19	1	no	—
68	C₂×C₅	—	57	1	no	—
69	C₇	C₅×D₃×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	19	1	no	—
71	D₃	—	19	1	no	—
72	D₃	C₅×C₇×D₁₉	1	1	yes	characteristic, direct product factor
73	C₅	D₃×C₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	57	1	no	Sylow
75	C₃	C₂×C₅×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	19	1	no	—
78	C₂	—	57	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	D₃×D₁₉
commutator, hypocenter	C₃×C₁₉	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₅₇	C₂	semidirect
2. C₅×D₃×C₇×C₁₉	C₂	semidirect
3. C₃×C₅×C₇×D₁₉	C₂	semidirect
5. C₃×C₅×C₇×C₁₉	C₂²	semidirect
6. D₃×C₇×D₁₉	C₅	direct (N × H)
9. C₅×C₇×D₁₉	D₃	direct (N × H)
10. C₅×D₃×D₁₉	C₇	direct (N × H)
11. C₇×D₅₇	C₂×C₅	semidirect
12. D₃×C₇×C₁₉	C₂×C₅	semidirect
13. C₃×C₇×D₁₉	C₂×C₅	semidirect
14. C₅×C₇×C₁₉	C₂×D₃	semidirect
15. C₅×D₅₇	C₂×C₇	semidirect
16. C₅×D₃×C₁₉	C₂×C₇	semidirect
17. C₃×C₅×D₁₉	C₂×C₇	semidirect
20. C₃×C₇×C₁₉	C₂²×C₅	semidirect
22. C₃×C₅×C₁₉	C₂²×C₇	semidirect
25. C₇×D₁₉	C₅×D₃	direct (N × H)
26. D₃×D₁₉	C₅×C₇	direct (N × H)
29. C₅×D₃×C₇	D₁₉	direct (N × H)
32. C₅×D₁₉	D₃×C₇	direct (N × H)
34. C₇×C₁₉	C₂×C₅×D₃	semidirect
35. D₅₇	C₂×C₅×C₇	semidirect
36. C₃×D₁₉	C₂×C₅×C₇	semidirect
37. D₃×C₁₉	C₂×C₅×C₇	semidirect
38. C₃×C₅×C₇	C₂×D₁₉	semidirect
39. C₅×C₁₉	C₂×D₃×C₇	semidirect
46. C₃×C₁₉	C₂²×C₅×C₇	semidirect
49. D₃×C₇	C₅×D₁₉	direct (N × H)
52. D₁₉	C₅×D₃×C₇	direct (N × H)
53. C₅×C₇	D₃×D₁₉	direct (N × H)
56. C₅×D₃	C₇×D₁₉	direct (N × H)
58. C₃×C₇	C₂×C₅×D₁₉	semidirect
60. C₁₉	C₂×C₅×D₃×C₇	semidirect
61. C₃×C₅	C₂×C₇×D₁₉	semidirect
69. C₇	C₅×D₃×D₁₉	direct (N × H)
72. D₃	C₅×C₇×D₁₉	direct (N × H)
73. C₅	D₃×C₇×D₁₉	direct (N × H)
75. C₃	C₂×C₅×C₇×D₁₉	semidirect

Subgroups — C5×D3×C7×D19 #22547708

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃×C₇×D₁₉ #22547708