Subgroups — C₂×C₃×D₁₀₁₅ #27131823

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₀₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₀₁₅	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×D₂₀₃	—	5	1	no	maximal, Hall
6	D₁₀₁₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×D₁₄₅	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇×C₂₉	D₅	1	1	yes	characteristic, complemented
10	C₃×D₂₀₃	—	5	2	no	—
11	C₅×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₂₉	D₇	1	1	yes	characteristic, complemented
13	C₃×D₁₄₅	—	7	2	no	—
14	C₂×D₂₀₃	—	5	1	no	Hall
15	C₃×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₁₄₅	—	7	1	no	Hall
17	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×D₃₅	—	29	1	no	maximal, Hall
19	C₂×C₇×C₂₉	C₃×D₅	1	1	yes	characteristic, complemented
20	D₂₀₃	—	5	2	no	—
21	C₂×C₃×D₂₉	—	35	1	no	Hall
22	C₂×C₅×C₂₉	C₃×D₇	1	1	yes	characteristic, complemented
23	D₁₄₅	—	7	2	no	—
24	C₂×C₃×C₅×C₇	D₂₉	1	1	yes	characteristic, complemented
25	C₃×D₃₅	—	29	2	no	—
26	C₇×C₂₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₂₉	D₃₅	1	1	yes	characteristic, complemented
28	C₃×D₂₉	—	35	2	no	—
29	C₅×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₃₅	—	29	1	no	Hall
31	C₂×D₂₉	—	35	1	no	Hall
32	C₃×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₇	—	145	1	no	Hall
35	C₂×C₅×C₇	C₃×D₂₉	1	1	yes	characteristic, complemented
36	D₃₅	—	29	2	no	—
37	C₂×C₃×D₅	—	203	1	no	Hall
38	C₂×C₂₉	C₃×D₃₅	1	1	yes	characteristic, complemented
39	D₂₉	—	35	2	no	—
40	C₂×C₃×C₇	D₁₄₅	1	1	yes	characteristic, complemented
41	C₃×D₇	—	145	2	no	—
42	C₅×C₇	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	D₂₀₃	1	1	yes	characteristic, complemented
44	C₃×D₅	—	203	2	no	—
45	C₂₉	C₂×C₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₇	—	145	1	no	Hall
47	C₃×C₇	C₂×D₁₄₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₅	—	203	1	no	Hall
49	C₃×C₅	C₂×D₂₀₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	C₃×D₁₄₅	1	1	yes	characteristic, complemented
51	D₇	—	145	2	no	—
52	C₂²×C₃	—	1015	1	no	Hall
53	C₂×C₅	C₃×D₂₀₃	1	1	yes	characteristic, complemented
54	D₅	—	203	2	no	—
55	C₇	C₂×C₃×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	1015	2	no	—
57	C₂×C₃	D₁₀₁₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	1015	1	no	Sylow
60	C₃	C₂×D₁₀₁₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	1015	2	no	—
62	C₂	C₃×D₁₀₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₀₁₅
commutator, hypocenter	C₅×C₇×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₀₁₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₉	C₂	semidirect
3. C₂×D₁₀₁₅	C₃	direct (N × H)
4. C₃×C₅×C₇×C₂₉	C₂²	semidirect
6. D₁₀₁₅	C₂×C₃	direct (N × H)
7. C₂×C₅×C₇×C₂₉	C₂×C₃	semidirect
9. C₂×C₃×C₇×C₂₉	D₅	semidirect
11. C₅×C₇×C₂₉	C₂²×C₃	semidirect
12. C₂×C₃×C₅×C₂₉	D₇	semidirect
15. C₃×C₇×C₂₉	C₂×D₅	semidirect
17. C₃×C₅×C₂₉	C₂×D₇	semidirect
19. C₂×C₇×C₂₉	C₃×D₅	semidirect
22. C₂×C₅×C₂₉	C₃×D₇	semidirect
24. C₂×C₃×C₅×C₇	D₂₉	semidirect
26. C₇×C₂₉	C₂×C₃×D₅	semidirect
27. C₂×C₃×C₂₉	D₃₅	semidirect
29. C₅×C₂₉	C₂×C₃×D₇	semidirect
32. C₃×C₅×C₇	C₂×D₂₉	semidirect
33. C₃×C₂₉	C₂×D₃₅	semidirect
35. C₂×C₅×C₇	C₃×D₂₉	semidirect
38. C₂×C₂₉	C₃×D₃₅	semidirect
40. C₂×C₃×C₇	D₁₄₅	semidirect
42. C₅×C₇	C₂×C₃×D₂₉	semidirect
43. C₂×C₃×C₅	D₂₀₃	semidirect
45. C₂₉	C₂×C₃×D₃₅	semidirect
47. C₃×C₇	C₂×D₁₄₅	semidirect
49. C₃×C₅	C₂×D₂₀₃	semidirect
50. C₂×C₇	C₃×D₁₄₅	semidirect
53. C₂×C₅	C₃×D₂₀₃	semidirect
55. C₇	C₂×C₃×D₁₄₅	semidirect
57. C₂×C₃	D₁₀₁₅	direct (N × H)
58. C₅	C₂×C₃×D₂₀₃	semidirect
60. C₃	C₂×D₁₀₁₅	direct (N × H)
62. C₂	C₃×D₁₀₁₅	direct (N × H)

Subgroups — C2×C3×D1015 #27131823

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₁₀₁₅ #27131823