Subgroups — D₃×D₂₆₆₅ #44544477

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₉₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₆₆₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅₃₃	—	5	1	no	maximal, Hall
7	D₂₆₆₅	—	3	1	no	—
8	D₂₆₆₅	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₁₃×C₄₁	—	3	1	no	—
10	D₁₅₉₉	—	5	1	no	—
11	D₃×C₁₃×C₄₁	D₅	1	1	yes	characteristic, complemented
12	C₃×D₅₃₃	—	5	1	no	—
13	C₅×C₁₃×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₃×D₂₀₅	—	13	1	no	maximal, Hall
15	C₂×D₅₃₃	—	15	1	no	Hall
16	C₃×C₁₃×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₆₁₅	—	13	1	no	—
18	C₅×D₃×C₄₁	D₁₃	1	1	yes	characteristic, complemented
19	C₃×D₂₀₅	—	13	1	no	—
20	C₂×C₁₃×C₄₁	—	3	1	no	—
21	D₅₃₃	—	5	1	no	—
22	D₅₃₃	—	15	1	no	—
23	C₂×D₂₀₅	—	39	1	no	Hall
24	D₃×D₆₅	—	41	1	no	maximal, Hall
25	C₃×C₅×C₄₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×C₄₁	D₃×D₅	1	1	yes	characteristic, complemented, Hall
27	D₃×D₄₁	—	65	1	no	Hall
28	C₂×C₅×C₄₁	—	3	1	no	—
29	D₂₀₅	—	13	1	no	—
30	D₂₀₅	—	39	1	no	—
31	D₁₉₅	—	41	1	no	—
32	C₅×D₃×C₁₃	D₄₁	1	1	yes	characteristic, complemented
33	C₃×D₆₅	—	41	1	no	—
34	C₂×D₆₅	—	123	1	no	Hall
35	D₁₂₃	—	65	1	no	—
36	C₃×D₄₁	—	65	1	no	—
37	D₃×C₄₁	D₆₅	1	1	yes	characteristic, complemented
38	C₅×C₄₁	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
40	C₂×D₄₁	—	195	1	no	Hall
41	D₃×D₁₃	—	205	1	no	Hall
42	C₂×C₅×C₁₃	—	3	1	no	—
43	D₆₅	—	41	1	no	—
44	D₆₅	—	123	1	no	—
45	C₃×C₄₁	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
46	C₂×C₄₁	—	3	1	no	—
47	D₄₁	—	65	1	no	—
48	D₄₁	—	195	1	no	—
49	D₃₉	—	205	1	no	—
50	C₃×D₁₃	—	205	1	no	—
51	D₃×C₁₃	D₂₀₅	1	1	yes	characteristic, complemented
52	C₅×C₁₃	D₃×D₄₁	1	1	yes	characteristic, complemented, Hall
53	D₃×D₅	—	533	1	no	Hall
54	C₂×D₁₃	—	615	1	no	Hall
55	C₄₁	D₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₁₃	C₂×D₂₀₅	1	1	yes	characteristic, complemented, Hall
57	D₁₅	—	533	1	no	—
58	C₃×D₅	—	533	1	no	—
59	C₅×D₃	D₅₃₃	1	1	yes	characteristic, complemented
60	C₂×C₁₃	—	3	1	no	—
61	D₁₃	—	615	1	no	—
62	D₁₃	—	205	1	no	—
63	C₂×D₅	—	1599	1	no	Hall
64	C₃×C₅	C₂×D₅₃₃	1	1	yes	characteristic, complemented, Hall
65	C₁₃	D₃×D₂₀₅	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₃	—	2665	1	no	Hall
67	C₂×C₅	—	3	1	no	—
68	D₅	—	533	1	no	—
69	D₅	—	1599	1	no	—
70	C₂×C₃	—	2665	1	no	—
71	D₃	—	2665	1	no	—
72	D₃	D₂₆₆₅	1	1	yes	characteristic, direct product factor
73	C₅	D₃×D₅₃₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	7995	1	no	Sylow
75	C₃	C₂×D₂₆₆₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	7995	1	no	—
78	C₂	—	2665	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₇₉₉₅	C₂	semidirect
2. C₅×D₃×C₁₃×C₄₁	C₂	semidirect
3. C₃×D₂₆₆₅	C₂	semidirect
5. C₃×C₅×C₁₃×C₄₁	C₂²	semidirect
8. D₂₆₆₅	D₃	direct (N × H)
11. D₃×C₁₃×C₄₁	D₅	semidirect
13. C₅×C₁₃×C₄₁	C₂×D₃	semidirect
16. C₃×C₁₃×C₄₁	C₂×D₅	semidirect
18. C₅×D₃×C₄₁	D₁₃	semidirect
25. C₃×C₅×C₄₁	C₂×D₁₃	semidirect
26. C₁₃×C₄₁	D₃×D₅	semidirect
32. C₅×D₃×C₁₃	D₄₁	semidirect
37. D₃×C₄₁	D₆₅	semidirect
38. C₅×C₄₁	D₃×D₁₃	semidirect
39. C₃×C₅×C₁₃	C₂×D₄₁	semidirect
45. C₃×C₄₁	C₂×D₆₅	semidirect
51. D₃×C₁₃	D₂₀₅	semidirect
52. C₅×C₁₃	D₃×D₄₁	semidirect
55. C₄₁	D₃×D₆₅	semidirect
56. C₃×C₁₃	C₂×D₂₀₅	semidirect
59. C₅×D₃	D₅₃₃	semidirect
64. C₃×C₅	C₂×D₅₃₃	semidirect
65. C₁₃	D₃×D₂₀₅	semidirect
72. D₃	D₂₆₆₅	direct (N × H)
73. C₅	D₃×D₅₃₃	semidirect
75. C₃	C₂×D₂₆₆₅	semidirect

Maximal subgroups

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

subgroup	index
D₇₉₉₅	2
C₅×D₃×C₁₃×C₄₁	2
C₃×D₂₆₆₅	2
C₂×D₂₆₆₅	3
D₃×D₅₃₃	5
D₃×D₂₀₅	13
D₃×D₆₅	41

Subgroups — D3×D2665 #44544477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₆₆₅ #44544477