Subgroups — C₂×C₅×C₁₃×D₂₁ #19129889

Order 5460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₃×D₇	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₃	D₃	1	1	yes	characteristic, complemented
7	C₅×C₁₃×D₇	—	3	2	no	—
8	C₂×C₅×D₃×C₁₃	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₁₃×D₂₁	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₁₃	D₇	1	1	yes	characteristic, complemented
14	C₅×D₃×C₁₃	—	7	2	no	—
15	C₂×C₁₃×D₇	—	3	1	no	Hall
16	C₃×C₇×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅×C₁₃	—	21	1	no	Hall
18	C₂×C₃×C₅×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₅×D₂₁	C₂×C₁₃	1	2	yes	direct product factor
20	C₃×C₅×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₁₃	C₅×D₃	1	1	yes	characteristic, complemented
22	C₁₃×D₇	—	3	2	no	—
23	C₂×D₃×C₁₃	—	7	1	no	Hall
24	C₂×C₅×D₇	—	3	1	no	Hall
25	C₂×C₅×C₁₃	—	21	2	no	—
26	C₂×C₅×C₁₃	D₂₁	1	1	yes	characteristic, direct product factor
27	C₃×C₅×C₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₂₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₃	C₅×D₇	1	1	yes	characteristic, complemented
31	D₃×C₁₃	—	7	2	no	—
32	C₂×C₅×C₇	D₃×C₁₃	1	1	yes	characteristic, complemented
33	C₅×D₇	—	3	2	no	—
34	C₅×C₁₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₅×D₃	—	7	1	no	Hall
36	C₂²×C₁₃	—	21	1	no	Hall
37	C₂×C₃×C₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
38	D₂₁	C₂×C₅×C₁₃	1	2	yes	direct product factor
39	C₃×C₁₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
40	C₅×C₇	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₅	C₁₃×D₇	1	1	yes	characteristic, complemented
42	C₅×D₃	—	7	2	no	—
43	C₂×D₇	—	3	1	no	Hall
44	C₂×C₁₃	—	21	2	no	—
45	C₂×C₁₃	C₅×D₂₁	1	1	yes	characteristic, direct product factor
46	C₃×C₇	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
47	C₂²×C₅	—	21	1	no	Hall
48	C₃×C₅	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇	C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
50	D₇	—	3	2	no	—
51	C₁₃	C₂×C₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×D₃	—	7	1	no	Hall
53	C₂×C₅	—	21	2	no	—
54	C₂×C₅	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	C₅×C₁₃×D₇	1	1	yes	characteristic, complemented
57	D₃	—	7	2	no	—
58	C₅	C₂×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	21	1	no	Sylow
60	C₃	C₂×C₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	21	2	no	—
62	C₂	C₅×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃	D₂₁
commutator, hypocenter	C₃×C₇	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×D₂₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₁₃	C₂	semidirect
4. C₃×C₅×C₇×C₁₃	C₂²	semidirect
5. C₂×C₁₃×D₂₁	C₅	direct (N × H)
6. C₂×C₅×C₇×C₁₃	D₃	semidirect
9. C₂×C₃×C₇×C₁₃	C₂×C₅	semidirect
10. C₁₃×D₂₁	C₂×C₅	direct (N × H)
11. C₅×C₇×C₁₃	C₂×D₃	semidirect
12. C₂×C₅×D₂₁	C₁₃	direct (N × H)
13. C₂×C₃×C₅×C₁₃	D₇	semidirect
16. C₃×C₇×C₁₃	C₂²×C₅	semidirect
18. C₂×C₃×C₅×C₇	C₂×C₁₃	semidirect
19. C₅×D₂₁	C₂×C₁₃	direct (N × H)
20. C₃×C₅×C₁₃	C₂×D₇	semidirect
21. C₂×C₇×C₁₃	C₅×D₃	semidirect
26. C₂×C₅×C₁₃	D₂₁	direct (N × H)
27. C₃×C₅×C₇	C₂²×C₁₃	semidirect
28. C₇×C₁₃	C₂×C₅×D₃	semidirect
29. C₂×D₂₁	C₅×C₁₃	direct (N × H)
30. C₂×C₃×C₁₃	C₅×D₇	semidirect
32. C₂×C₅×C₇	D₃×C₁₃	semidirect
34. C₅×C₁₃	C₂×D₂₁	direct (N × H)
37. C₂×C₃×C₇	C₂×C₅×C₁₃	semidirect
38. D₂₁	C₂×C₅×C₁₃	direct (N × H)
39. C₃×C₁₃	C₂×C₅×D₇	semidirect
40. C₅×C₇	C₂×D₃×C₁₃	semidirect
41. C₂×C₃×C₅	C₁₃×D₇	semidirect
45. C₂×C₁₃	C₅×D₂₁	direct (N × H)
46. C₃×C₇	C₂²×C₅×C₁₃	semidirect
48. C₃×C₅	C₂×C₁₃×D₇	semidirect
49. C₂×C₇	C₅×D₃×C₁₃	semidirect
51. C₁₃	C₂×C₅×D₂₁	direct (N × H)
54. C₂×C₅	C₁₃×D₂₁	direct (N × H)
55. C₇	C₂×C₅×D₃×C₁₃	semidirect
56. C₂×C₃	C₅×C₁₃×D₇	semidirect
58. C₅	C₂×C₁₃×D₂₁	direct (N × H)
60. C₃	C₂×C₅×C₁₃×D₇	semidirect
62. C₂	C₅×C₁₃×D₂₁	direct (N × H)

Subgroups — C2×C5×C13×D21 #19129889

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₁₃×D₂₁ #19129889