Subgroups — C₂×C₃×D₂₆₆₅ #44544492

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₆₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₆₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅₃₃	—	5	1	no	maximal, Hall
6	D₂₆₆₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₅₃₃	—	5	2	no	—
9	C₂×C₃×C₁₃×C₄₁	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₃×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₂₀₅	—	13	1	no	maximal, Hall
12	C₂×D₅₃₃	—	5	1	no	Hall
13	C₃×C₁₃×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₄₁	D₁₃	1	1	yes	characteristic, complemented
15	C₃×D₂₀₅	—	13	2	no	—
16	C₂×C₁₃×C₄₁	C₃×D₅	1	1	yes	characteristic, complemented
17	D₅₃₃	—	5	2	no	—
18	C₂×D₂₀₅	—	13	1	no	Hall
19	C₂×C₃×D₆₅	—	41	1	no	maximal, Hall
20	C₃×C₅×C₄₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₄₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×D₄₁	—	65	1	no	Hall
23	C₂×C₅×C₄₁	C₃×D₁₃	1	1	yes	characteristic, complemented
24	D₂₀₅	—	13	2	no	—
25	C₂×C₃×C₅×C₁₃	D₄₁	1	1	yes	characteristic, complemented
26	C₃×D₆₅	—	41	2	no	—
27	C₂×D₆₅	—	41	1	no	Hall
28	C₂×C₃×C₄₁	D₆₅	1	1	yes	characteristic, complemented
29	C₃×D₄₁	—	65	2	no	—
30	C₅×C₄₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₁₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
32	C₂×D₄₁	—	65	1	no	Hall
33	C₂×C₃×D₁₃	—	205	1	no	Hall
34	C₂×C₅×C₁₃	C₃×D₄₁	1	1	yes	characteristic, complemented
35	D₆₅	—	41	2	no	—
36	C₃×C₄₁	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
37	C₂×C₄₁	C₃×D₆₅	1	1	yes	characteristic, complemented
38	D₄₁	—	65	2	no	—
39	C₂×C₃×C₁₃	D₂₀₅	1	1	yes	characteristic, complemented
40	C₃×D₁₃	—	205	2	no	—
41	C₅×C₁₃	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₅	—	533	1	no	Hall
43	C₂×D₁₃	—	205	1	no	Hall
44	C₄₁	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
45	C₃×C₁₃	C₂×D₂₀₅	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₅	D₅₃₃	1	1	yes	characteristic, complemented
47	C₃×D₅	—	533	2	no	—
48	C₂×C₁₃	C₃×D₂₀₅	1	1	yes	characteristic, complemented
49	D₁₃	—	205	2	no	—
50	C₂×D₅	—	533	1	no	Hall
51	C₃×C₅	C₂×D₅₃₃	1	1	yes	characteristic, complemented, Hall
52	C₁₃	C₂×C₃×D₂₀₅	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	—	2665	1	no	Hall
54	C₂×C₅	C₃×D₅₃₃	1	1	yes	characteristic, complemented
55	D₅	—	533	2	no	—
56	C₂×C₃	—	2665	2	no	—
57	C₂×C₃	D₂₆₆₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×D₅₃₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2665	1	no	Sylow
60	C₃	C₂×D₂₆₆₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2665	2	no	—
62	C₂	C₃×D₂₆₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₆₆₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₄₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₄₁	C₂
LCS	G ▷ C₅×C₁₃×C₄₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₆₆₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃×C₄₁	C₂	semidirect
3. C₂×D₂₆₆₅	C₃	direct (N × H)
4. C₃×C₅×C₁₃×C₄₁	C₂²	semidirect
6. D₂₆₆₅	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₃×C₄₁	C₂×C₃	semidirect
9. C₂×C₃×C₁₃×C₄₁	D₅	semidirect
10. C₅×C₁₃×C₄₁	C₂²×C₃	semidirect
13. C₃×C₁₃×C₄₁	C₂×D₅	semidirect
14. C₂×C₃×C₅×C₄₁	D₁₃	semidirect
16. C₂×C₁₃×C₄₁	C₃×D₅	semidirect
20. C₃×C₅×C₄₁	C₂×D₁₃	semidirect
21. C₁₃×C₄₁	C₂×C₃×D₅	semidirect
23. C₂×C₅×C₄₁	C₃×D₁₃	semidirect
25. C₂×C₃×C₅×C₁₃	D₄₁	semidirect
28. C₂×C₃×C₄₁	D₆₅	semidirect
30. C₅×C₄₁	C₂×C₃×D₁₃	semidirect
31. C₃×C₅×C₁₃	C₂×D₄₁	semidirect
34. C₂×C₅×C₁₃	C₃×D₄₁	semidirect
36. C₃×C₄₁	C₂×D₆₅	semidirect
37. C₂×C₄₁	C₃×D₆₅	semidirect
39. C₂×C₃×C₁₃	D₂₀₅	semidirect
41. C₅×C₁₃	C₂×C₃×D₄₁	semidirect
44. C₄₁	C₂×C₃×D₆₅	semidirect
45. C₃×C₁₃	C₂×D₂₀₅	semidirect
46. C₂×C₃×C₅	D₅₃₃	semidirect
48. C₂×C₁₃	C₃×D₂₀₅	semidirect
51. C₃×C₅	C₂×D₅₃₃	semidirect
52. C₁₃	C₂×C₃×D₂₀₅	semidirect
54. C₂×C₅	C₃×D₅₃₃	semidirect
57. C₂×C₃	D₂₆₆₅	direct (N × H)
58. C₅	C₂×C₃×D₅₃₃	semidirect
60. C₃	C₂×D₂₆₆₅	direct (N × H)
62. C₂	C₃×D₂₆₆₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₂₆₆₅	2
C₂×C₃×C₅×C₁₃×C₄₁	2
C₂×D₂₆₆₅	3
C₂×C₃×D₅₃₃	5
C₂×C₃×D₂₀₅	13
C₂×C₃×D₆₅	41

Subgroups — C2×C3×D2665 #44544492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₆₆₅ #44544492