Subgroups — C₂×C₃×D₄₀ #91620

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₄₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₅	—	2	2	no	—
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×D₂₀	—	2	2	no	—
8	C₃×D₂₀	C₂²	1	4	yes	complemented
9	C₃×C₅×C₈	C₂²	1	2	yes	complemented
10	C₂×C₃×D₈	—	5	1	no	maximal, Hall
11	C₂×D₂₀	C₂×C₃	1	2	yes	complemented
12	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
13	D₄₀	C₂×C₃	1	4	yes	direct product factor
14	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
15	C₂×C₃×D₅	—	2	4	no	—
16	C₂×C₃×D₅	—	4	4	no	—
17	C₃×C₄×C₅	D₄	1	1	yes	characteristic
18	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×C₃×D₄	—	5	2	no	—
20	C₃×D₈	—	5	4	no	—
21	C₂×C₃×C₈	D₅	1	1	yes	characteristic, complemented
22	C₂²×D₅	—	2	2	no	—
23	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
24	D₂₀	—	2	2	no	—
25	D₂₀	C₂²×C₃	1	4	yes	complemented
26	C₅×C₈	C₂²×C₃	1	2	yes	complemented
27	C₂×D₈	—	5	1	no	Sylow
28	C₂×C₃×C₅	D₈	1	2	yes	complemented
29	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
30	C₃×D₅	—	4	4	no	—
31	C₂³×C₃	—	10	2	no	—
32	C₃×D₄	—	5	4	no	—
33	C₃×D₄	—	10	2	no	—
34	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
35	C₃×C₈	C₂×D₅	1	2	yes	complemented
36	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
37	C₂×D₅	—	2	4	no	—
38	C₂×D₅	—	4	4	no	—
39	C₄×C₅	C₃×D₄	1	1	yes	characteristic
40	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
41	C₂×D₄	—	5	2	no	—
42	D₈	—	5	4	no	—
43	C₂×C₈	C₃×D₅	1	1	yes	characteristic, complemented
44	C₃×C₅	C₂×D₈	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	—	10	4	no	—
46	C₂²×C₃	—	20	4	no	—
47	C₂²×C₃	D₂₀	1	1	yes	characteristic
48	C₃×C₄	D₂₀	1	1	yes	characteristic
49	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
50	C₂×C₅	C₃×D₈	1	2	yes	complemented
51	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
52	D₅	—	4	4	no	—
53	C₂³	—	10	2	no	—
54	D₄	—	5	4	no	—
55	D₄	—	10	2	no	—
56	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
57	C₈	C₂×C₃×D₅	1	2	yes	complemented
58	C₂×C₃	—	20	4	no	—
59	C₂×C₃	D₄₀	1	2	yes	direct product factor
60	C₂×C₃	C₂×D₂₀	1	1	yes	characteristic
61	C₅	C₂×C₃×D₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²	—	10	4	no	—
63	C₂²	—	20	4	no	—
64	C₂²	C₃×D₂₀	1	1	yes	characteristic
65	C₄	C₃×D₂₀	1	1	yes	characteristic
66	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
67	C₃	C₂×D₄₀	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	20	4	no	—
69	C₂	C₃×D₄₀	1	2	yes	direct product factor
70	C₂	C₂×C₃×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₂₀
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₃×C₈	D₅
hypocenter	C₅	C₂×C₃×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₂₀	C₂	semidirect
2. C₂×C₃×C₅×C₈	C₂	semidirect
3. C₃×D₄₀	C₂	direct (N × H)
4. C₂×D₄₀	C₃	direct (N × H)
8. C₃×D₂₀	C₂²	semidirect
9. C₃×C₅×C₈	C₂²	semidirect
11. C₂×D₂₀	C₂×C₃	semidirect
12. C₂×C₅×C₈	C₂×C₃	semidirect
13. D₄₀	C₂×C₃	direct (N × H)
21. C₂×C₃×C₈	D₅	semidirect
25. D₂₀	C₂²×C₃	semidirect
26. C₅×C₈	C₂²×C₃	semidirect
28. C₂×C₃×C₅	D₈	semidirect
35. C₃×C₈	C₂×D₅	semidirect
43. C₂×C₈	C₃×D₅	semidirect
44. C₃×C₅	C₂×D₈	semidirect
50. C₂×C₅	C₃×D₈	semidirect
57. C₈	C₂×C₃×D₅	semidirect
59. C₂×C₃	D₄₀	direct (N × H)
61. C₅	C₂×C₃×D₈	semidirect
67. C₃	C₂×D₄₀	direct (N × H)
69. C₂	C₃×D₄₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₂₀	2
C₂×C₃×C₅×C₈	2
C₃×D₄₀	2
C₂×D₄₀	3
C₂×C₃×D₈	5

Subgroups — C2×C3×D40 #91620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄₀ #91620