Subgroups — C₂×C₇×C₁₉×D₁₅ #22547752

Order 7980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₉	D₁₅
commutator, hypocenter	C₃×C₅	C₂²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×D₁₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₁₉	C₂	semidirect
4. C₃×C₅×C₇×C₁₉	C₂²	semidirect
6. C₂×C₅×C₇×C₁₉	D₃	semidirect
8. C₂×C₁₉×D₁₅	C₇	direct (N × H)
9. C₂×C₃×C₇×C₁₉	D₅	semidirect
11. C₅×C₇×C₁₉	C₂×D₃	semidirect
12. C₂×C₃×C₅×C₁₉	C₂×C₇	semidirect
13. C₁₉×D₁₅	C₂×C₇	direct (N × H)
15. C₂×C₇×D₁₅	C₁₉	direct (N × H)
16. C₃×C₇×C₁₉	C₂×D₅	semidirect
18. C₃×C₅×C₁₉	C₂²×C₇	semidirect
20. C₂×C₇×C₁₉	D₁₅	direct (N × H)
22. C₂×C₃×C₅×C₇	C₂×C₁₉	semidirect
23. C₇×D₁₅	C₂×C₁₉	direct (N × H)
24. C₂×C₅×C₁₉	D₃×C₇	semidirect
27. C₇×C₁₉	C₂×D₁₅	direct (N × H)
28. C₂×C₃×C₁₉	C₇×D₅	semidirect
30. C₃×C₅×C₇	C₂²×C₁₉	semidirect
31. C₅×C₁₉	C₂×D₃×C₇	semidirect
34. C₂×C₅×C₇	D₃×C₁₉	semidirect
36. C₂×D₁₅	C₇×C₁₉	direct (N × H)
37. C₃×C₁₉	C₂×C₇×D₅	semidirect
38. C₂×C₃×C₇	D₅×C₁₉	semidirect
41. C₂×C₁₉	C₇×D₁₅	direct (N × H)
42. C₅×C₇	C₂×D₃×C₁₉	semidirect
43. C₂×C₃×C₅	C₂×C₇×C₁₉	semidirect
44. D₁₅	C₂×C₇×C₁₉	direct (N × H)
46. C₃×C₇	C₂×D₅×C₁₉	semidirect
48. C₁₉	C₂×C₇×D₁₅	direct (N × H)
49. C₃×C₅	C₂²×C₇×C₁₉	semidirect
51. C₂×C₇	C₁₉×D₁₅	direct (N × H)
53. C₂×C₅	D₃×C₇×C₁₉	semidirect
55. C₇	C₂×C₁₉×D₁₅	direct (N × H)
56. C₂×C₃	C₇×D₅×C₁₉	semidirect
58. C₅	C₂×D₃×C₇×C₁₉	semidirect
60. C₃	C₂×C₇×D₅×C₁₉	semidirect
62. C₂	C₇×C₁₉×D₁₅	direct (N × H)

Subgroups — C2×C7×C19×D15 #22547752

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×C₁₉×D₁₅ #22547752