Subgroups — C₂×C₅×D₆₀₉ #27131819

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₂₀₃	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₆₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₂₀₃	—	3	2	no	—
7	C₂×C₅×C₇×C₂₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₅×D₈₇	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
10	D₆₀₉	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₂₉	D₇	1	1	yes	characteristic, complemented
13	C₅×D₈₇	—	7	2	no	—
14	C₂×D₂₀₃	—	3	1	no	Hall
15	C₃×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₂₉	—	21	1	no	Hall
17	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×D₂₁	—	29	1	no	maximal, Hall
19	C₂×C₇×C₂₉	C₅×D₃	1	1	yes	characteristic, complemented
20	D₂₀₃	—	3	2	no	—
21	C₂×D₈₇	—	7	1	no	Hall
22	C₂×C₅×C₂₉	D₂₁	1	1	yes	characteristic, complemented
23	C₅×D₂₉	—	21	2	no	—
24	C₂×C₃×C₅×C₇	D₂₉	1	1	yes	characteristic, complemented
25	C₅×D₂₁	—	29	2	no	—
26	C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₂₉	C₅×D₇	1	1	yes	characteristic, complemented
28	D₈₇	—	7	2	no	—
29	C₅×C₂₉	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×D₇	—	87	1	no	Hall
31	C₂×D₂₉	—	21	1	no	Hall
32	C₃×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
34	C₂×D₂₁	—	29	1	no	Hall
35	C₂×C₅×C₇	D₈₇	1	1	yes	characteristic, complemented
36	C₅×D₇	—	87	2	no	—
37	C₂×C₅×D₃	—	203	1	no	Hall
38	C₂×C₂₉	C₅×D₂₁	1	1	yes	characteristic, complemented
39	D₂₉	—	21	2	no	—
40	C₂×C₃×C₇	C₅×D₂₉	1	1	yes	characteristic, complemented
41	D₂₁	—	29	2	no	—
42	C₅×C₇	C₂×D₈₇	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	D₂₀₃	1	1	yes	characteristic, complemented
44	C₅×D₃	—	203	2	no	—
45	C₂₉	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₇	—	87	1	no	Hall
47	C₃×C₇	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅	—	609	1	no	Hall
49	C₃×C₅	C₂×D₂₀₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	C₅×D₈₇	1	1	yes	characteristic, complemented
51	D₇	—	87	2	no	—
52	C₂×D₃	—	203	1	no	Hall
53	C₂×C₅	—	609	2	no	—
54	C₂×C₅	D₆₀₉	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₈₇	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	C₅×D₂₀₃	1	1	yes	characteristic, complemented
57	D₃	—	203	2	no	—
58	C₅	C₂×D₆₀₉	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	609	1	no	Sylow
60	C₃	C₂×C₅×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	609	2	no	—
62	C₂	C₅×D₆₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₆₀₉
commutator, hypocenter	C₃×C₇×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₆₀₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₉	C₂	semidirect
4. C₃×C₅×C₇×C₂₉	C₂²	semidirect
5. C₂×D₆₀₉	C₅	direct (N × H)
7. C₂×C₅×C₇×C₂₉	D₃	semidirect
9. C₂×C₃×C₇×C₂₉	C₂×C₅	semidirect
10. D₆₀₉	C₂×C₅	direct (N × H)
11. C₅×C₇×C₂₉	C₂×D₃	semidirect
12. C₂×C₃×C₅×C₂₉	D₇	semidirect
15. C₃×C₇×C₂₉	C₂²×C₅	semidirect
17. C₃×C₅×C₂₉	C₂×D₇	semidirect
19. C₂×C₇×C₂₉	C₅×D₃	semidirect
22. C₂×C₅×C₂₉	D₂₁	semidirect
24. C₂×C₃×C₅×C₇	D₂₉	semidirect
26. C₇×C₂₉	C₂×C₅×D₃	semidirect
27. C₂×C₃×C₂₉	C₅×D₇	semidirect
29. C₅×C₂₉	C₂×D₂₁	semidirect
32. C₃×C₅×C₇	C₂×D₂₉	semidirect
33. C₃×C₂₉	C₂×C₅×D₇	semidirect
35. C₂×C₅×C₇	D₈₇	semidirect
38. C₂×C₂₉	C₅×D₂₁	semidirect
40. C₂×C₃×C₇	C₅×D₂₉	semidirect
42. C₅×C₇	C₂×D₈₇	semidirect
43. C₂×C₃×C₅	D₂₀₃	semidirect
45. C₂₉	C₂×C₅×D₂₁	semidirect
47. C₃×C₇	C₂×C₅×D₂₉	semidirect
49. C₃×C₅	C₂×D₂₀₃	semidirect
50. C₂×C₇	C₅×D₈₇	semidirect
54. C₂×C₅	D₆₀₉	direct (N × H)
55. C₇	C₂×C₅×D₈₇	semidirect
56. C₂×C₃	C₅×D₂₀₃	semidirect
58. C₅	C₂×D₆₀₉	direct (N × H)
60. C₃	C₂×C₅×D₂₀₃	semidirect
62. C₂	C₅×D₆₀₉	direct (N × H)

Subgroups — C2×C5×D609 #27131819

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₆₀₉ #27131819