Subgroups — C₂×C₃×C₅×C₇×D₂₉ #27131829

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₇	D₂₉
commutator, hypocenter	C₂₉	C₂²×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×D₂₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₉	C₂	semidirect
3. C₂×C₅×C₇×D₂₉	C₃	direct (N × H)
4. C₃×C₅×C₇×C₂₉	C₂²	semidirect
5. C₂×C₃×C₇×D₂₉	C₅	direct (N × H)
6. C₅×C₇×D₂₉	C₂×C₃	direct (N × H)
7. C₂×C₅×C₇×C₂₉	C₂×C₃	semidirect
8. C₂×C₃×C₅×D₂₉	C₇	direct (N × H)
9. C₂×C₃×C₇×C₂₉	C₂×C₅	semidirect
10. C₃×C₇×D₂₉	C₂×C₅	direct (N × H)
11. C₅×C₇×C₂₉	C₂²×C₃	semidirect
12. C₂×C₃×C₅×C₂₉	C₂×C₇	semidirect
13. C₃×C₅×D₂₉	C₂×C₇	direct (N × H)
14. C₂×C₇×D₂₉	C₃×C₅	direct (N × H)
15. C₃×C₇×C₂₉	C₂²×C₅	semidirect
16. C₂×C₅×D₂₉	C₃×C₇	direct (N × H)
17. C₃×C₅×C₂₉	C₂²×C₇	semidirect
19. C₂×C₇×C₂₉	C₂×C₃×C₅	semidirect
20. C₇×D₂₉	C₂×C₃×C₅	direct (N × H)
21. C₂×C₃×D₂₉	C₅×C₇	direct (N × H)
22. C₂×C₅×C₂₉	C₂×C₃×C₇	semidirect
23. C₅×D₂₉	C₂×C₃×C₇	direct (N × H)
25. C₂×C₃×C₅×C₇	D₂₉	direct (N × H)
26. C₇×C₂₉	C₂²×C₃×C₅	semidirect
27. C₂×C₃×C₂₉	C₂×C₅×C₇	semidirect
28. C₃×D₂₉	C₂×C₅×C₇	direct (N × H)
29. C₅×C₂₉	C₂²×C₃×C₇	semidirect
31. C₂×D₂₉	C₃×C₅×C₇	direct (N × H)
32. C₃×C₅×C₇	C₂×D₂₉	direct (N × H)
33. C₃×C₂₉	C₂²×C₅×C₇	semidirect
36. C₂×C₅×C₇	C₃×D₂₉	direct (N × H)
38. C₂×C₂₉	C₂×C₃×C₅×C₇	semidirect
39. D₂₉	C₂×C₃×C₅×C₇	direct (N × H)
41. C₂×C₃×C₇	C₅×D₂₉	direct (N × H)
42. C₅×C₇	C₂×C₃×D₂₉	direct (N × H)
44. C₂×C₃×C₅	C₇×D₂₉	direct (N × H)
45. C₂₉	C₂²×C₃×C₅×C₇	semidirect
47. C₃×C₇	C₂×C₅×D₂₉	direct (N × H)
49. C₃×C₅	C₂×C₇×D₂₉	direct (N × H)
51. C₂×C₇	C₃×C₅×D₂₉	direct (N × H)
54. C₂×C₅	C₃×C₇×D₂₉	direct (N × H)
55. C₇	C₂×C₃×C₅×D₂₉	direct (N × H)
57. C₂×C₃	C₅×C₇×D₂₉	direct (N × H)
58. C₅	C₂×C₃×C₇×D₂₉	direct (N × H)
60. C₃	C₂×C₅×C₇×D₂₉	direct (N × H)
62. C₂	C₃×C₅×C₇×D₂₉	direct (N × H)

Subgroups — C2×C3×C5×C7×D29 #27131829

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×C₇×D₂₉ #27131829