Subgroups — C₂×D₄₂₀ #13132892

Order 1680.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₀₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₂₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₄₀	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×D₁₀₅	—	2	4	no	—
7	C₂×D₁₀₅	C₂²	1	4	yes	complemented
8	C₃×C₄×C₅×C₇	C₂²	1	2	yes	complemented
9	C₂×D₈₄	—	5	1	no	maximal, Hall
10	C₂²×D₃₅	—	3	2	no	—
11	C₂×C₄×C₅×C₇	D₃	1	1	yes	characteristic, complemented
12	D₁₄₀	—	3	4	no	—
13	C₂×D₆₀	—	7	1	no	maximal, Hall
14	C₂×C₃×C₅×C₇	D₄	1	2	yes	complemented
15	C₂×C₃×C₅×C₇	C₂³	1	1	yes	characteristic
16	D₁₀₅	—	2	4	no	—
17	C₂²×D₂₁	—	5	2	no	—
18	C₂×C₃×C₄×C₇	D₅	1	1	yes	characteristic, complemented
19	D₈₄	—	5	4	no	—
20	C₂²×C₅×C₇	C₂×D₃	1	1	yes	characteristic
21	C₂×D₃₅	—	3	4	no	—
22	C₂×D₃₅	—	6	4	no	—
23	C₄×C₅×C₇	C₂×D₃	1	2	yes	complemented
24	C₂²×D₁₅	—	7	2	no	—
25	C₂×C₃×C₄×C₅	D₇	1	1	yes	characteristic, complemented
26	D₆₀	—	7	4	no	—
27	C₂×D₂₈	—	15	1	no	Hall
28	C₃×C₅×C₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₃×C₇	C₂×D₅	1	1	yes	characteristic
30	C₂×D₂₁	—	5	4	no	—
31	C₂×D₂₁	—	10	4	no	—
32	C₃×C₄×C₇	C₂×D₅	1	2	yes	complemented
33	C₂×D₂₀	—	21	1	no	Hall
34	C₂×C₅×C₇	D₁₂	1	2	yes	complemented
35	C₂×C₅×C₇	C₂²×D₃	1	1	yes	characteristic
36	D₃₅	—	6	4	no	—
37	C₂²×C₃×C₅	C₂×D₇	1	1	yes	characteristic
38	C₂×D₁₅	—	7	4	no	—
39	C₂×D₁₅	—	14	4	no	—
40	C₃×C₄×C₅	C₂×D₇	1	2	yes	complemented
41	C₂²×D₇	—	15	2	no	—
42	C₂×C₄×C₇	D₁₅	1	1	yes	characteristic, complemented
43	D₂₈	—	15	4	no	—
44	C₂×D₁₂	—	35	1	no	Hall
45	C₂×C₃×C₇	D₂₀	1	2	yes	complemented
46	C₂×C₃×C₇	C₂²×D₅	1	1	yes	characteristic
47	D₂₁	—	10	4	no	—
48	C₂²×D₅	—	21	2	no	—
49	C₂×C₄×C₅	D₂₁	1	1	yes	characteristic, complemented
50	D₂₀	—	21	4	no	—
51	C₅×C₇	C₂×D₁₂	1	1	yes	characteristic, complemented, Hall
52	C₂×C₃×C₅	D₂₈	1	2	yes	complemented
53	C₂×C₃×C₅	C₂²×D₇	1	1	yes	characteristic
54	D₁₅	—	14	4	no	—
55	C₂²×C₇	C₂×D₁₅	1	1	yes	characteristic
56	C₂×D₇	—	15	4	no	—
57	C₂×D₇	—	30	4	no	—
58	C₄×C₇	C₂×D₁₅	1	2	yes	complemented
59	C₂²×D₃	—	35	2	no	—
60	C₂×C₃×C₄	D₃₅	1	1	yes	characteristic, complemented
61	D₁₂	—	35	4	no	—
62	C₃×C₇	C₂×D₂₀	1	1	yes	characteristic, complemented, Hall
63	C₂²×C₅	C₂×D₂₁	1	1	yes	characteristic
64	C₂×D₅	—	21	4	no	—
65	C₂×D₅	—	42	4	no	—
66	C₄×C₅	C₂×D₂₁	1	2	yes	complemented
67	C₂×D₄	—	105	1	no	Sylow
68	C₃×C₅	C₂×D₂₈	1	1	yes	characteristic, complemented, Hall
69	C₂×C₇	D₆₀	1	2	yes	complemented
70	C₂×C₇	C₂²×D₁₅	1	1	yes	characteristic
71	D₇	—	30	4	no	—
72	C₂²×C₃	C₂×D₃₅	1	1	yes	characteristic
73	C₂×D₃	—	35	4	no	—
74	C₂×D₃	—	70	4	no	—
75	C₃×C₄	C₂×D₃₅	1	2	yes	complemented
76	C₂×C₅	D₈₄	1	2	yes	complemented
77	C₂×C₅	C₂²×D₂₁	1	1	yes	characteristic
78	D₅	—	42	4	no	—
79	C₂³	—	105	2	no	—
80	D₄	—	105	4	no	—
81	C₂×C₄	D₁₀₅	1	1	yes	characteristic, complemented
82	C₇	C₂×D₆₀	1	1	yes	characteristic, complemented, Sylow
83	C₂×C₃	D₁₄₀	1	2	yes	complemented
84	C₂×C₃	C₂²×D₃₅	1	1	yes	characteristic
85	D₃	—	70	4	no	—
86	C₅	C₂×D₈₄	1	1	yes	characteristic, complemented, Sylow
87	C₂²	—	105	4	no	—
88	C₂²	—	210	4	no	—
89	C₂²	C₂×D₁₀₅	1	1	yes	characteristic
90	C₄	C₂×D₁₀₅	1	2	yes	complemented
91	C₃	C₂×D₁₄₀	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	210	4	no	—
93	C₂	D₄₂₀	1	2	yes	direct product factor
94	C₂	C₂²×D₁₀₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₀₅
commutator, cosocle	C₂×C₃×C₅×C₇	C₂³
Frattini	C₂	C₂²×D₁₀₅
Fitting	C₂×C₃×C₄×C₅×C₇	C₂
socle	C₂²×C₃×C₅×C₇	C₂²
hypercenter	C₂×C₄	D₁₀₅
hypocenter	C₃×C₅×C₇	C₂×D₄
LCS	G ▷ C₂×C₃×C₅×C₇ ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₀₅	C₂	semidirect
2. C₂×C₃×C₄×C₅×C₇	C₂	semidirect
3. D₄₂₀	C₂	direct (N × H)
7. C₂×D₁₀₅	C₂²	semidirect
8. C₃×C₄×C₅×C₇	C₂²	semidirect
11. C₂×C₄×C₅×C₇	D₃	semidirect
14. C₂×C₃×C₅×C₇	D₄	semidirect
18. C₂×C₃×C₄×C₇	D₅	semidirect
23. C₄×C₅×C₇	C₂×D₃	semidirect
25. C₂×C₃×C₄×C₅	D₇	semidirect
28. C₃×C₅×C₇	C₂×D₄	semidirect
32. C₃×C₄×C₇	C₂×D₅	semidirect
34. C₂×C₅×C₇	D₁₂	semidirect
40. C₃×C₄×C₅	C₂×D₇	semidirect
42. C₂×C₄×C₇	D₁₅	semidirect
45. C₂×C₃×C₇	D₂₀	semidirect
49. C₂×C₄×C₅	D₂₁	semidirect
51. C₅×C₇	C₂×D₁₂	semidirect
52. C₂×C₃×C₅	D₂₈	semidirect
58. C₄×C₇	C₂×D₁₅	semidirect
60. C₂×C₃×C₄	D₃₅	semidirect
62. C₃×C₇	C₂×D₂₀	semidirect
66. C₄×C₅	C₂×D₂₁	semidirect
68. C₃×C₅	C₂×D₂₈	semidirect
69. C₂×C₇	D₆₀	semidirect
75. C₃×C₄	C₂×D₃₅	semidirect
76. C₂×C₅	D₈₄	semidirect
81. C₂×C₄	D₁₀₅	semidirect
82. C₇	C₂×D₆₀	semidirect
83. C₂×C₃	D₁₄₀	semidirect
86. C₅	C₂×D₈₄	semidirect
90. C₄	C₂×D₁₀₅	semidirect
91. C₃	C₂×D₁₄₀	semidirect
93. C₂	D₄₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₀₅	2
C₂×C₃×C₄×C₅×C₇	2
D₄₂₀	2
C₂×D₁₄₀	3
C₂×D₈₄	5
C₂×D₆₀	7

Subgroups — C2×D420 #13132892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₂₀ #13132892