Subgroups — C₂×C₇×C₂₉×D₁₅ #27131818

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×D₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₅×C₂₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₇×C₂₉	—	5	1	no	maximal, Hall
6	C₇×D₅×C₂₉	—	3	2	no	—
7	C₂×C₅×C₇×C₂₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₂₉×D₁₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₂₉	D₅	1	1	yes	characteristic, complemented
10	D₃×C₇×C₂₉	—	5	2	no	—
11	C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
13	C₂₉×D₁₅	C₂×C₇	1	2	yes	direct product factor
14	C₂²×C₇×C₂₉	—	15	1	no	Hall
15	C₃×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅×C₂₉	—	3	1	no	Hall
17	C₃×C₅×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×D₁₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₇×C₂₉	—	15	2	no	—
20	C₂×C₇×C₂₉	D₁₅	1	1	yes	characteristic, direct product factor
21	C₂×D₃×C₂₉	—	5	1	no	Hall
22	C₂×C₅×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented
23	D₅×C₂₉	—	3	2	no	—
24	C₂×C₃×C₅×C₇	C₂×C₂₉	1	1	yes	characteristic, complemented
25	C₇×D₁₅	C₂×C₂₉	1	2	yes	direct product factor
26	C₇×C₂₉	C₂×D₁₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃×C₂₉	C₇×D₅	1	1	yes	characteristic, complemented
28	D₃×C₂₉	—	5	2	no	—
29	C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×D₅	—	3	1	no	Hall
31	C₂²×C₂₉	—	15	1	no	Hall
32	C₃×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₂₉	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃×C₇	—	5	1	no	Hall
35	C₂×C₅×C₇	D₃×C₂₉	1	1	yes	characteristic, complemented
36	C₇×D₅	—	3	2	no	—
37	C₂×D₁₅	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₂₉	—	15	2	no	—
39	C₂×C₂₉	C₇×D₁₅	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₇	D₅×C₂₉	1	1	yes	characteristic, complemented
41	D₃×C₇	—	5	2	no	—
42	C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
44	D₁₅	C₂×C₇×C₂₉	1	2	yes	direct product factor
45	C₂₉	C₂×C₇×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₇	—	15	1	no	Hall
47	C₃×C₇	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
48	C₂×D₅	—	3	1	no	Hall
49	C₃×C₅	C₂²×C₇×C₂₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	—	15	2	no	—
51	C₂×C₇	C₂₉×D₁₅	1	1	yes	characteristic, direct product factor
52	C₂×D₃	—	5	1	no	Hall
53	C₂×C₅	D₃×C₇×C₂₉	1	1	yes	characteristic, complemented
54	D₅	—	3	2	no	—
55	C₇	C₂×C₂₉×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	C₇×D₅×C₂₉	1	1	yes	characteristic, complemented
57	D₃	—	5	2	no	—
58	C₅	C₂×D₃×C₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	15	1	no	Sylow
60	C₃	C₂×C₇×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	15	2	no	—
62	C₂	C₇×C₂₉×D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₉	D₁₅
commutator, hypocenter	C₃×C₅	C₂²×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₇×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉×D₁₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₉	C₂	semidirect
4. C₃×C₅×C₇×C₂₉	C₂²	semidirect
7. C₂×C₅×C₇×C₂₉	D₃	semidirect
8. C₂×C₂₉×D₁₅	C₇	direct (N × H)
9. C₂×C₃×C₇×C₂₉	D₅	semidirect
11. C₅×C₇×C₂₉	C₂×D₃	semidirect
12. C₂×C₃×C₅×C₂₉	C₂×C₇	semidirect
13. C₂₉×D₁₅	C₂×C₇	direct (N × H)
15. C₃×C₇×C₂₉	C₂×D₅	semidirect
17. C₃×C₅×C₂₉	C₂²×C₇	semidirect
18. C₂×C₇×D₁₅	C₂₉	direct (N × H)
20. C₂×C₇×C₂₉	D₁₅	direct (N × H)
22. C₂×C₅×C₂₉	D₃×C₇	semidirect
24. C₂×C₃×C₅×C₇	C₂×C₂₉	semidirect
25. C₇×D₁₅	C₂×C₂₉	direct (N × H)
26. C₇×C₂₉	C₂×D₁₅	direct (N × H)
27. C₂×C₃×C₂₉	C₇×D₅	semidirect
29. C₅×C₂₉	C₂×D₃×C₇	semidirect
32. C₃×C₅×C₇	C₂²×C₂₉	semidirect
33. C₃×C₂₉	C₂×C₇×D₅	semidirect
35. C₂×C₅×C₇	D₃×C₂₉	semidirect
37. C₂×D₁₅	C₇×C₂₉	direct (N × H)
39. C₂×C₂₉	C₇×D₁₅	direct (N × H)
40. C₂×C₃×C₇	D₅×C₂₉	semidirect
42. C₅×C₇	C₂×D₃×C₂₉	semidirect
43. C₂×C₃×C₅	C₂×C₇×C₂₉	semidirect
44. D₁₅	C₂×C₇×C₂₉	direct (N × H)
45. C₂₉	C₂×C₇×D₁₅	direct (N × H)
47. C₃×C₇	C₂×D₅×C₂₉	semidirect
49. C₃×C₅	C₂²×C₇×C₂₉	semidirect
51. C₂×C₇	C₂₉×D₁₅	direct (N × H)
53. C₂×C₅	D₃×C₇×C₂₉	semidirect
55. C₇	C₂×C₂₉×D₁₅	direct (N × H)
56. C₂×C₃	C₇×D₅×C₂₉	semidirect
58. C₅	C₂×D₃×C₇×C₂₉	semidirect
60. C₃	C₂×C₇×D₅×C₂₉	semidirect
62. C₂	C₇×C₂₉×D₁₅	direct (N × H)

Subgroups — C2×C7×C29×D15 #27131818

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×C₂₉×D₁₅ #27131818