Subgroups — C₃×C₅×D₅×D₁₉ #19152853

Order 5700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₁₉	—	5	1	no	maximal
7	C₃×D₅×D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×D₉₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅²×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₁₉	—	5	1	no	—
12	C₃×D₉₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×D₅×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×D₁₉	—	2	2	no	—
15	C₃×C₅×D₁₉	—	5	1	no	—
16	C₃×C₅×D₁₉	D₅	1	1	yes	characteristic, direct product factor
17	C₃×C₅×D₁₉	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₁₉	—	5	1	no	—
20	D₅×D₁₉	C₃×C₅	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₅×D₅	—	19	1	no	maximal, Hall
22	C₃×C₅×C₁₉	—	2	2	no	—
23	C₃×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
25	C₂×C₃×D₁₉	—	5	1	no	Hall
26	C₂×C₅×C₁₉	—	5	1	no	—
27	D₉₅	C₂×C₃×C₅	1	1	yes	characteristic, complemented
28	C₅×D₁₉	—	2	2	no	—
29	C₅×D₁₉	—	5	1	no	—
30	C₅×D₁₉	C₃×D₅	1	1	yes	characteristic, direct product factor
31	C₅×D₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
32	D₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
33	C₂×C₃×C₅²	—	19	1	no	—
34	C₃×C₅×D₅	—	19	1	no	—
35	C₃×C₅×D₅	D₁₉	1	1	yes	characteristic, direct product factor
36	C₂×C₃×C₁₉	—	5	1	no	—
37	C₃×D₁₉	—	5	1	no	—
38	C₃×D₁₉	C₅×D₅	1	1	yes	characteristic, direct product factor
39	C₂×C₅×D₅	—	19	1	no	Hall
40	C₅×C₁₉	—	2	2	no	—
41	C₅×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
43	C₂×D₁₉	—	5	1	no	Hall
44	C₃×C₅²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃×C₅	—	95	1	no	—
46	C₂×C₃×D₅	—	19	1	no	—
47	C₃×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅²	—	19	1	no	—
49	C₅×D₅	—	19	1	no	—
50	C₅×D₅	C₃×D₁₉	1	1	yes	characteristic, direct product factor
51	C₂×C₁₉	—	5	1	no	—
52	D₁₉	—	5	1	no	—
53	D₁₉	C₃×C₅×D₅	1	1	yes	characteristic, direct product factor
54	C₂×C₃×C₅	—	5	1	no	—
55	C₂×C₃×C₅	—	19	1	no	—
56	C₂×C₃×C₅	—	19	1	no	—
57	C₂×C₃×C₅	—	38	2	no	—
58	C₂×C₃×C₅	—	95	1	no	—
59	C₃×D₅	—	19	1	no	—
60	C₃×D₅	C₅×D₁₉	1	1	yes	characteristic, direct product factor
61	C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₅	—	95	1	no	—
63	C₂×D₅	—	19	1	no	—
64	C₁₉	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₁₉	1	1	yes	characteristic, direct product factor
67	C₃×C₅	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
68	C₂²×C₃	—	95	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	19	1	no	—
71	C₂×C₅	—	19	1	no	—
72	C₂×C₅	—	38	2	no	—
73	C₂×C₅	—	95	1	no	—
74	D₅	—	19	1	no	—
75	D₅	C₃×C₅×D₁₉	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	5	1	no	—
77	C₂×C₃	—	19	1	no	—
78	C₂×C₃	—	95	1	no	—
79	C₅	—	2	2	no	—
80	C₅	C₃×D₅×D₁₉	1	1	yes	characteristic, direct product factor
81	C₅	C₂×C₃×C₅×D₁₉	1	1	yes	characteristic, complemented
82	C₂²	—	95	1	no	Sylow
83	C₃	C₅×D₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	19	1	no	—
86	C₂	—	95	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	D₅×D₁₉
commutator, hypocenter	C₅×C₁₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₉₅	C₂	semidirect
2. C₃×C₅×D₅×C₁₉	C₂	semidirect
3. C₃×C₅²×D₁₉	C₂	semidirect
4. C₅×D₅×D₁₉	C₃	direct (N × H)
5. C₃×C₅²×C₁₉	C₂²	semidirect
7. C₃×D₅×D₁₉	C₅	direct (N × H)
8. C₅×D₉₅	C₂×C₃	semidirect
9. C₅×D₅×C₁₉	C₂×C₃	semidirect
10. C₅²×D₁₉	C₂×C₃	semidirect
12. C₃×D₉₅	C₂×C₅	semidirect
13. C₃×D₅×C₁₉	C₂×C₅	semidirect
16. C₃×C₅×D₁₉	D₅	direct (N × H)
17. C₃×C₅×D₁₉	C₂×C₅	semidirect
18. C₅²×C₁₉	C₂²×C₃	semidirect
20. D₅×D₁₉	C₃×C₅	direct (N × H)
23. C₃×C₅×C₁₉	C₂×D₅	semidirect
24. C₃×C₅×C₁₉	C₂²×C₅	semidirect
27. D₉₅	C₂×C₃×C₅	semidirect
30. C₅×D₁₉	C₃×D₅	direct (N × H)
31. C₅×D₁₉	C₂×C₃×C₅	semidirect
32. D₅×C₁₉	C₂×C₃×C₅	semidirect
35. C₃×C₅×D₅	D₁₉	direct (N × H)
38. C₃×D₁₉	C₅×D₅	direct (N × H)
41. C₅×C₁₉	C₂×C₃×D₅	semidirect
42. C₅×C₁₉	C₂²×C₃×C₅	semidirect
44. C₃×C₅²	C₂×D₁₉	semidirect
47. C₃×C₁₉	C₂×C₅×D₅	semidirect
50. C₅×D₅	C₃×D₁₉	direct (N × H)
53. D₁₉	C₃×C₅×D₅	direct (N × H)
60. C₃×D₅	C₅×D₁₉	direct (N × H)
61. C₅²	C₂×C₃×D₁₉	semidirect
64. C₁₉	C₂×C₃×C₅×D₅	semidirect
66. C₃×C₅	D₅×D₁₉	direct (N × H)
67. C₃×C₅	C₂×C₅×D₁₉	semidirect
75. D₅	C₃×C₅×D₁₉	direct (N × H)
80. C₅	C₃×D₅×D₁₉	direct (N × H)
81. C₅	C₂×C₃×C₅×D₁₉	semidirect
83. C₃	C₅×D₅×D₁₉	direct (N × H)

Subgroups — C3×C5×D5×D19 #19152853

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×D₅×D₁₉ #19152853