Subgroups — C₂×C₃×C₅×D₁₂₉ #21440957

Order 7740.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅×D₄₃	—	3	1	no	maximal
5	C₃²×C₅×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₁₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₄₃	—	2	1	no	—
8	C₂×C₃×C₅×C₄₃	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅×D₁₂₉	C₂×C₃	1	2	yes	direct product factor
11	C₃×C₅×D₄₃	—	3	2	no	—
12	C₂×C₅×D₄₃	—	3	1	no	Hall
13	C₂×C₃²×C₄₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×D₁₂₉	C₂×C₅	1	2	yes	direct product factor
15	C₃×C₅×C₄₃	—	2	1	no	—
16	C₃×C₅×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×D₁₂₉	C₃×C₅	1	1	yes	characteristic, direct product factor
19	C₂×C₃×D₄₃	—	3	1	no	—
20	C₂×C₅×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented
21	C₅×D₄₃	—	3	2	no	—
22	C₃²×C₄₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₄₃	—	2	1	no	—
24	C₂×C₃×C₄₃	C₅×D₃	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	D₁₂₉	C₂×C₃×C₅	1	2	yes	direct product factor
27	C₃×D₄₃	—	3	2	no	—
28	C₅×C₄₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₅×D₃	—	43	1	no	maximal, Hall
30	C₂×D₄₃	—	3	1	no	Hall
31	C₃×C₄₃	—	2	1	no	—
32	C₃×C₄₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
33	C₃×C₄₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
34	C₂×C₃²×C₅	D₄₃	1	1	yes	characteristic, complemented
35	C₃×C₅×D₃	—	43	2	no	—
36	C₂×C₄₃	C₃×C₅×D₃	1	1	yes	characteristic, complemented
37	D₄₃	—	3	2	no	—
38	C₂²×C₃×C₅	—	129	1	no	—
39	C₂×C₅×D₃	—	43	1	no	—
40	C₃²×C₅	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
41	C₄₃	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×D₃	—	43	1	no	Hall
43	C₂×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅	—	129	2	no	—
45	C₂×C₃×C₅	C₃×D₄₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅	D₁₂₉	1	1	yes	characteristic, direct product factor
47	C₅×D₃	—	43	2	no	—
48	C₂²×C₅	—	129	1	no	Hall
49	C₂×C₃²	C₅×D₄₃	1	1	yes	characteristic, complemented
50	C₃×D₃	—	43	2	no	—
51	C₃×C₅	—	2	1	no	—
52	C₃×C₅	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented
53	C₃×C₅	C₂×D₁₂₉	1	1	yes	characteristic, direct product factor
54	C₂²×C₃	—	129	1	no	—
55	C₂×D₃	—	43	1	no	—
56	C₂×C₅	—	129	2	no	—
57	C₂×C₅	C₃×D₁₂₉	1	1	yes	characteristic, direct product factor
58	C₃²	C₂×C₅×D₄₃	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	129	2	no	—
61	C₂×C₃	C₃×C₅×D₄₃	1	1	yes	characteristic, complemented
62	C₂×C₃	C₅×D₁₂₉	1	1	yes	characteristic, direct product factor
63	D₃	—	43	2	no	—
64	C₅	C₂×C₃×D₁₂₉	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²	—	129	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×C₅×D₄₃	1	1	yes	characteristic, complemented
68	C₃	C₂×C₅×D₁₂₉	1	1	yes	characteristic, direct product factor
69	C₂	—	129	2	no	—
70	C₂	C₃×C₅×D₁₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₁₂₉
commutator, hypocenter	C₃×C₄₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₄₃	C₂
LCS	G ▷ C₃×C₄₃
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₁₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₄₃	C₂	semidirect
3. C₂×C₅×D₁₂₉	C₃	direct (N × H)
5. C₃²×C₅×C₄₃	C₂²	semidirect
6. C₂×C₃×D₁₂₉	C₅	direct (N × H)
8. C₂×C₃×C₅×C₄₃	D₃	semidirect
9. C₂×C₃×C₅×C₄₃	C₂×C₃	semidirect
10. C₅×D₁₂₉	C₂×C₃	direct (N × H)
13. C₂×C₃²×C₄₃	C₂×C₅	semidirect
14. C₃×D₁₂₉	C₂×C₅	direct (N × H)
16. C₃×C₅×C₄₃	C₂×D₃	semidirect
17. C₃×C₅×C₄₃	C₂²×C₃	semidirect
18. C₂×D₁₂₉	C₃×C₅	direct (N × H)
20. C₂×C₅×C₄₃	C₃×D₃	semidirect
22. C₃²×C₄₃	C₂²×C₅	semidirect
24. C₂×C₃×C₄₃	C₅×D₃	semidirect
25. C₂×C₃×C₄₃	C₂×C₃×C₅	semidirect
26. D₁₂₉	C₂×C₃×C₅	direct (N × H)
28. C₅×C₄₃	C₂×C₃×D₃	semidirect
32. C₃×C₄₃	C₂×C₅×D₃	semidirect
33. C₃×C₄₃	C₂²×C₃×C₅	semidirect
34. C₂×C₃²×C₅	D₄₃	semidirect
36. C₂×C₄₃	C₃×C₅×D₃	semidirect
40. C₃²×C₅	C₂×D₄₃	semidirect
41. C₄₃	C₂×C₃×C₅×D₃	semidirect
45. C₂×C₃×C₅	C₃×D₄₃	semidirect
46. C₂×C₃×C₅	D₁₂₉	direct (N × H)
49. C₂×C₃²	C₅×D₄₃	semidirect
52. C₃×C₅	C₂×C₃×D₄₃	semidirect
53. C₃×C₅	C₂×D₁₂₉	direct (N × H)
57. C₂×C₅	C₃×D₁₂₉	direct (N × H)
58. C₃²	C₂×C₅×D₄₃	semidirect
61. C₂×C₃	C₃×C₅×D₄₃	semidirect
62. C₂×C₃	C₅×D₁₂₉	direct (N × H)
64. C₅	C₂×C₃×D₁₂₉	direct (N × H)
67. C₃	C₂×C₃×C₅×D₄₃	semidirect
68. C₃	C₂×C₅×D₁₂₉	direct (N × H)
70. C₂	C₃×C₅×D₁₂₉	direct (N × H)

Subgroups — C2×C3×C5×D129 #21440957

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×D₁₂₉ #21440957