Subgroups — C₂×C₃×C₂₉×D₁₅ #19104897

Order 5220.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×D₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×D₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₅×C₂₉	—	3	1	no	maximal
5	C₃²×C₅×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃×C₂₉	—	5	1	no	maximal, Hall
7	C₂×C₃×C₅×C₂₉	—	2	1	no	—
8	C₂×C₃×C₅×C₂₉	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂₉×D₁₅	C₂×C₃	1	2	yes	direct product factor
11	C₃×D₅×C₂₉	—	3	2	no	—
12	C₂×D₅×C₂₉	—	3	1	no	Hall
13	C₂×C₃²×C₂₉	D₅	1	1	yes	characteristic, complemented
14	C₃×D₃×C₂₉	—	5	2	no	—
15	C₃×C₅×C₂₉	—	2	1	no	—
16	C₃×C₅×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₂₉	—	15	1	no	—
19	C₂×D₃×C₂₉	—	5	1	no	—
20	C₂×C₅×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented
21	D₅×C₂₉	—	3	2	no	—
22	C₃²×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×D₁₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₃×C₂₉	—	2	1	no	—
25	C₂×C₃×C₂₉	—	15	2	no	—
26	C₂×C₃×C₂₉	C₃×D₅	1	1	yes	characteristic, complemented
27	C₂×C₃×C₂₉	D₁₅	1	1	yes	characteristic, direct product factor
28	D₃×C₂₉	—	5	2	no	—
29	C₅×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₂₉	—	15	1	no	Hall
31	C₂×C₃²×C₅	C₂×C₂₉	1	1	yes	characteristic, complemented
32	C₃×D₁₅	C₂×C₂₉	1	2	yes	direct product factor
33	C₃×C₂₉	—	2	1	no	—
34	C₃×C₂₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
35	C₃×C₂₉	C₂×D₁₅	1	1	yes	characteristic, direct product factor
36	C₂×D₁₅	C₃×C₂₉	1	1	yes	characteristic, direct product factor
37	C₂×C₃×D₅	—	3	1	no	—
38	C₂×C₂₉	—	15	2	no	—
39	C₂×C₂₉	C₃×D₁₅	1	1	yes	characteristic, direct product factor
40	C₃²×C₅	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×D₃	—	5	1	no	Hall
42	C₂×C₃×C₅	—	2	1	no	—
43	C₂×C₃×C₅	D₃×C₂₉	1	1	yes	characteristic, complemented
44	C₂×C₃×C₅	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
45	D₁₅	C₂×C₃×C₂₉	1	2	yes	direct product factor
46	C₃×D₅	—	3	2	no	—
47	C₂₉	C₂×C₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₅	—	3	1	no	Hall
49	C₂×C₃²	D₅×C₂₉	1	1	yes	characteristic, complemented
50	C₃×D₃	—	5	2	no	—
51	C₃×C₅	—	2	1	no	—
52	C₃×C₅	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
53	C₃×C₅	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	15	1	no	—
55	C₂×D₃	—	5	1	no	—
56	C₂×C₅	C₃×D₃×C₂₉	1	1	yes	characteristic, complemented
57	D₅	—	3	2	no	—
58	C₃²	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	15	2	no	—
61	C₂×C₃	C₃×D₅×C₂₉	1	1	yes	characteristic, complemented
62	C₂×C₃	C₂₉×D₁₅	1	1	yes	characteristic, direct product factor
63	D₃	—	5	2	no	—
64	C₅	C₂×C₃×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	15	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₅×C₂₉	1	1	yes	characteristic, complemented
68	C₃	C₂×C₂₉×D₁₅	1	1	yes	characteristic, direct product factor
69	C₂	—	15	2	no	—
70	C₂	C₃×C₂₉×D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	D₁₅
commutator, hypocenter	C₃×C₅	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₂₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×D₁₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₂₉	C₂	semidirect
3. C₂×C₂₉×D₁₅	C₃	direct (N × H)
5. C₃²×C₅×C₂₉	C₂²	semidirect
8. C₂×C₃×C₅×C₂₉	D₃	semidirect
9. C₂×C₃×C₅×C₂₉	C₂×C₃	semidirect
10. C₂₉×D₁₅	C₂×C₃	direct (N × H)
13. C₂×C₃²×C₂₉	D₅	semidirect
16. C₃×C₅×C₂₉	C₂×D₃	semidirect
17. C₃×C₅×C₂₉	C₂²×C₃	semidirect
20. C₂×C₅×C₂₉	C₃×D₃	semidirect
22. C₃²×C₂₉	C₂×D₅	semidirect
23. C₂×C₃×D₁₅	C₂₉	direct (N × H)
26. C₂×C₃×C₂₉	C₃×D₅	semidirect
27. C₂×C₃×C₂₉	D₁₅	direct (N × H)
29. C₅×C₂₉	C₂×C₃×D₃	semidirect
31. C₂×C₃²×C₅	C₂×C₂₉	semidirect
32. C₃×D₁₅	C₂×C₂₉	direct (N × H)
34. C₃×C₂₉	C₂×C₃×D₅	semidirect
35. C₃×C₂₉	C₂×D₁₅	direct (N × H)
36. C₂×D₁₅	C₃×C₂₉	direct (N × H)
39. C₂×C₂₉	C₃×D₁₅	direct (N × H)
40. C₃²×C₅	C₂²×C₂₉	semidirect
43. C₂×C₃×C₅	D₃×C₂₉	semidirect
44. C₂×C₃×C₅	C₂×C₃×C₂₉	semidirect
45. D₁₅	C₂×C₃×C₂₉	direct (N × H)
47. C₂₉	C₂×C₃×D₁₅	direct (N × H)
49. C₂×C₃²	D₅×C₂₉	semidirect
52. C₃×C₅	C₂×D₃×C₂₉	semidirect
53. C₃×C₅	C₂²×C₃×C₂₉	semidirect
56. C₂×C₅	C₃×D₃×C₂₉	semidirect
58. C₃²	C₂×D₅×C₂₉	semidirect
61. C₂×C₃	C₃×D₅×C₂₉	semidirect
62. C₂×C₃	C₂₉×D₁₅	direct (N × H)
64. C₅	C₂×C₃×D₃×C₂₉	semidirect
67. C₃	C₂×C₃×D₅×C₂₉	semidirect
68. C₃	C₂×C₂₉×D₁₅	direct (N × H)
70. C₂	C₃×C₂₉×D₁₅	direct (N × H)

Subgroups — C2×C3×C29×D15 #19104897

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₂₉×D₁₅ #19104897