Subgroups — C₂₉×D₁₅⋊D₅ #22576490

Order 8700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₂₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅²×C₂₉	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×D₅×C₂₉	—	5	2	no	maximal
6	C₂₉×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₂₉	—	3	2	no	—
8	C₂₉×D₁₅	D₅	1	2	yes	complemented
9	C₅×D₃×C₂₉	—	5	2	no	—
10	C₃×D₅×C₂₉	—	5	2	no	—
11	C₃×D₅×C₂₉	—	10	2	no	—
12	C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₅×C₂₉	—	15	2	no	—
14	C₃×C₅×C₂₉	—	2	2	no	—
15	C₃×C₅×C₂₉	C₂×D₅	1	2	yes	complemented
16	C₂×D₃×C₂₉	—	25	1	no	Hall
17	D₁₅⋊D₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₅×C₂₉	—	15	2	no	—
19	D₅×C₂₉	—	3	2	no	—
20	D₅×C₂₉	—	5	2	no	—
21	D₅×C₂₉	—	10	2	no	—
22	C₂×C₃×C₂₉	—	25	1	no	—
23	D₃×C₂₉	—	5	2	no	—
24	C₅×D₁₅	C₂×C₂₉	1	2	yes	complemented
25	C₃×C₅⋊D₅	C₂×C₂₉	1	1	yes	characteristic, complemented
26	C₅×C₂₉	—	2	2	no	—
27	C₅×C₂₉	D₃×D₅	1	2	yes	complemented
28	C₂²×C₂₉	—	75	1	no	Hall
29	D₅²	—	3	1	no	Hall
30	C₃×C₂₉	D₅²	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
32	D₃×D₅	—	5	2	no	—
33	C₂×C₂₉	—	15	2	no	—
34	C₂×C₂₉	—	25	1	no	—
35	C₅⋊D₅	D₃×C₂₉	1	1	yes	characteristic, complemented
36	C₅×D₅	—	3	2	no	—
37	D₁₅	D₅×C₂₉	1	2	yes	complemented
38	C₃×D₅	—	5	2	no	—
39	C₃×D₅	—	10	2	no	—
40	C₅×D₃	—	5	2	no	—
41	C₂₉	D₁₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₅²	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	15	2	no	—
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	C₂×D₅×C₂₉	1	2	yes	complemented
46	C₂×D₃	—	25	1	no	Hall
47	C₂×C₅	—	15	2	no	—
48	D₅	—	3	2	no	—
49	D₅	—	5	2	no	—
50	D₅	—	10	2	no	—
51	C₂×C₃	—	25	1	no	—
52	D₃	—	5	2	no	—
53	C₅	—	2	2	no	—
54	C₅	D₃×D₅×C₂₉	1	2	yes	complemented
55	C₂²	—	75	1	no	Sylow
56	C₃	D₅²×C₂₉	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	15	2	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₁₅⋊D₅
commutator, hypocenter	C₃×C₅²	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×D₁₅	C₂	semidirect
2. C₃×C₂₉×C₅⋊D₅	C₂	semidirect
4. C₃×C₅²×C₂₉	C₂²	semidirect
6. C₂₉×C₅⋊D₅	D₃	semidirect
8. C₂₉×D₁₅	D₅	semidirect
12. C₅²×C₂₉	C₂×D₃	semidirect
15. C₃×C₅×C₂₉	C₂×D₅	semidirect
17. D₁₅⋊D₅	C₂₉	direct (N × H)
24. C₅×D₁₅	C₂×C₂₉	semidirect
25. C₃×C₅⋊D₅	C₂×C₂₉	semidirect
27. C₅×C₂₉	D₃×D₅	semidirect
30. C₃×C₂₉	D₅²	semidirect
31. C₃×C₅²	C₂²×C₂₉	semidirect
35. C₅⋊D₅	D₃×C₂₉	semidirect
37. D₁₅	D₅×C₂₉	semidirect
41. C₂₉	D₁₅⋊D₅	direct (N × H)
42. C₅²	C₂×D₃×C₂₉	semidirect
45. C₃×C₅	C₂×D₅×C₂₉	semidirect
54. C₅	D₃×D₅×C₂₉	semidirect
56. C₃	D₅²×C₂₉	semidirect

Subgroups — C29×D15⋊D5 #22576490

Conjugacy classes of subgroups

Complements

Subgroups — C₂₉×D₁₅⋊D₅ #22576490