Subgroups — D₅×C₁₉×D₂₁ #22547728

Order 7980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₇×C₁₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₉×D₂₁	—	5	1	no	maximal, Hall
7	C₁₉×D₃₅	—	3	1	no	—
8	C₇×D₅×C₁₉	D₃	1	1	yes	characteristic, complemented
9	C₅×D₇×C₁₉	—	3	1	no	—
10	D₃×D₅×C₁₉	—	7	1	no	maximal, Hall
11	C₂×C₃×C₇×C₁₉	—	5	1	no	—
12	C₁₉×D₂₁	—	5	1	no	—
13	C₁₉×D₂₁	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₁₉×D₁₅	—	7	1	no	—
16	C₅×D₃×C₁₉	—	7	1	no	—
17	C₃×D₅×C₁₉	D₇	1	1	yes	characteristic, complemented
18	C₂×D₇×C₁₉	—	15	1	no	Hall
19	D₅×D₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₃×C₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×D₅×C₁₉	—	21	1	no	Hall
22	C₃×C₅×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₉	—	5	1	no	—
24	D₇×C₁₉	—	3	1	no	—
25	D₇×C₁₉	—	15	1	no	—
26	C₂×D₃×C₁₉	—	35	1	no	Hall
27	D₁₀₅	C₂×C₁₉	1	1	yes	characteristic, complemented
28	C₅×D₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented
29	C₃×C₇×D₅	C₂×C₁₉	1	1	yes	characteristic, complemented
30	C₂×C₅×C₁₉	—	21	1	no	—
31	D₅×C₁₉	—	21	1	no	—
32	D₅×C₁₉	D₂₁	1	1	yes	characteristic, direct product factor
33	D₅×D₇	—	3	1	no	Hall
34	C₇×C₁₉	D₃×D₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₁₉	—	5	1	no	—
36	D₃×C₁₉	—	7	1	no	—
37	D₃×C₁₉	—	35	1	no	—
38	C₃×C₅×C₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₉	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
40	C₂×D₂₁	—	5	1	no	Hall
41	C₂²×C₁₉	—	105	1	no	Hall
42	D₃₅	—	3	1	no	—
43	C₅×D₇	—	3	1	no	—
44	C₇×D₅	D₃×C₁₉	1	1	yes	characteristic, complemented
45	D₃×D₅	—	7	1	no	Hall
46	C₃×C₁₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃×C₇	—	5	1	no	—
48	D₂₁	—	5	1	no	—
49	D₂₁	D₅×C₁₉	1	1	yes	characteristic, direct product factor
50	C₂×C₁₉	—	5	1	no	—
51	C₂×C₁₉	—	21	1	no	—
52	C₂×C₁₉	—	105	1	no	—
53	C₅×C₇	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
54	D₁₅	—	7	1	no	—
55	C₃×D₅	D₇×C₁₉	1	1	yes	characteristic, complemented
56	C₅×D₃	—	7	1	no	—
57	C₂×D₇	—	15	1	no	Hall
58	C₃×C₇	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
59	C₂×D₅	—	21	1	no	Hall
60	C₁₉	D₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₃×C₅	C₂×D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	5	1	no	—
63	D₇	—	3	1	no	—
64	D₇	—	15	1	no	—
65	C₂×D₃	—	35	1	no	Hall
66	C₂×C₅	—	21	1	no	—
67	D₅	—	21	1	no	—
68	D₅	C₁₉×D₂₁	1	1	yes	characteristic, direct product factor
69	C₇	D₃×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	5	1	no	—
71	D₃	—	7	1	no	—
72	D₃	—	35	1	no	—
73	C₅	C₂×C₁₉×D₂₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	105	1	no	Sylow
75	C₃	D₅×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	21	1	no	—
78	C₂	—	105	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₂₁
commutator, hypocenter	C₃×C₅×C₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₁₀₅	C₂	semidirect
2. C₅×C₁₉×D₂₁	C₂	semidirect
3. C₃×C₇×D₅×C₁₉	C₂	semidirect
5. C₃×C₅×C₇×C₁₉	C₂²	semidirect
8. C₇×D₅×C₁₉	D₃	semidirect
13. C₁₉×D₂₁	D₅	direct (N × H)
14. C₅×C₇×C₁₉	C₂×D₃	semidirect
17. C₃×D₅×C₁₉	D₇	semidirect
19. D₅×D₂₁	C₁₉	direct (N × H)
20. C₃×C₇×C₁₉	C₂×D₅	semidirect
22. C₃×C₅×C₁₉	C₂×D₇	semidirect
27. D₁₀₅	C₂×C₁₉	semidirect
28. C₅×D₂₁	C₂×C₁₉	semidirect
29. C₃×C₇×D₅	C₂×C₁₉	semidirect
32. D₅×C₁₉	D₂₁	direct (N × H)
34. C₇×C₁₉	D₃×D₅	semidirect
38. C₃×C₅×C₇	C₂²×C₁₉	semidirect
39. C₅×C₁₉	C₂×D₂₁	semidirect
44. C₇×D₅	D₃×C₁₉	semidirect
46. C₃×C₁₉	D₅×D₇	semidirect
49. D₂₁	D₅×C₁₉	direct (N × H)
53. C₅×C₇	C₂×D₃×C₁₉	semidirect
55. C₃×D₅	D₇×C₁₉	semidirect
58. C₃×C₇	C₂×D₅×C₁₉	semidirect
60. C₁₉	D₅×D₂₁	direct (N × H)
61. C₃×C₅	C₂×D₇×C₁₉	semidirect
68. D₅	C₁₉×D₂₁	direct (N × H)
69. C₇	D₃×D₅×C₁₉	semidirect
73. C₅	C₂×C₁₉×D₂₁	semidirect
75. C₃	D₅×D₇×C₁₉	semidirect

Subgroups — D5×C19×D21 #22547728

Conjugacy classes of subgroups

Complements

Subgroups — D₅×C₁₉×D₂₁ #22547728