Subgroups — C₂²×D₄₀ #66074

Order 320.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₀	C₂	1	12	yes	maximal, direct product factor
4	C₂³×D₅	—	2	2	no	—
5	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×D₂₀	—	2	6	no	—
7	C₂×D₂₀	C₂²	1	12	yes	complemented
8	C₂×C₅×C₈	C₂²	1	6	yes	complemented
9	D₄₀	C₂²	1	16	yes	direct product factor
10	C₂²×D₈	—	5	1	no	maximal, Sylow
11	C₂³×C₅	D₄	1	1	yes	characteristic
12	C₂²×D₅	—	2	12	no	—
13	C₂²×D₅	—	4	8	no	—
14	C₂×C₄×C₅	D₄	1	3	yes	—
15	C₂×C₄×C₅	C₂³	1	3	yes	—
16	D₂₀	—	2	12	no	—
17	D₂₀	C₂³	1	8	yes	complemented
18	C₅×C₈	C₂³	1	4	yes	complemented
19	C₂²×D₄	—	5	2	no	—
20	C₂×D₈	—	5	12	no	—
21	C₂²×C₈	D₅	1	1	yes	characteristic, complemented
22	C₂²×C₅	D₈	1	4	yes	complemented
23	C₂²×C₅	C₂×D₄	1	3	yes	—
24	C₂×D₅	—	2	8	no	—
25	C₂×D₅	—	4	24	no	—
26	C₄×C₅	C₂×D₄	1	3	yes	—
27	C₄×C₅	C₂⁴	1	1	yes	characteristic
28	C₂⁴	—	10	2	no	—
29	C₂×D₄	—	5	12	no	—
30	C₂×D₄	—	10	6	no	—
31	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
32	D₈	—	5	16	no	—
33	C₂×C₈	C₂×D₅	1	6	yes	complemented
34	C₂×C₅	C₂×D₈	1	6	yes	complemented
35	C₂×C₅	C₂²×D₄	1	1	yes	characteristic
36	D₅	—	4	8	no	—
37	C₂³	—	10	12	no	—
38	C₂³	—	20	8	no	—
39	C₂³	D₂₀	1	1	yes	characteristic
40	D₄	—	5	8	no	—
41	D₄	—	10	12	no	—
42	C₂×C₄	D₂₀	1	3	yes	—
43	C₂×C₄	C₂²×D₅	1	3	yes	—
44	C₈	C₂²×D₅	1	4	yes	complemented
45	C₅	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	10	8	no	—
47	C₂²	—	20	24	no	—
48	C₂²	D₄₀	1	4	yes	direct product factor
49	C₂²	C₂×D₂₀	1	3	yes	—
50	C₄	C₂×D₂₀	1	3	yes	—
51	C₄	C₂³×D₅	1	1	yes	characteristic
52	C₂	—	20	8	no	—
53	C₂	C₂×D₄₀	1	6	yes	direct product factor
54	C₂	C₂²×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₀
commutator, cosocle	C₄×C₅	C₂⁴
Frattini	C₄	C₂³×D₅
Fitting	C₂²×C₅×C₈	C₂
socle	C₂³×C₅	D₄
hypercenter	C₂²×C₈	D₅
hypocenter	C₅	C₂²×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×D₂₀	C₂	semidirect
2. C₂²×C₅×C₈	C₂	semidirect
3. C₂×D₄₀	C₂	direct (N × H)
7. C₂×D₂₀	C₂²	semidirect
8. C₂×C₅×C₈	C₂²	semidirect
9. D₄₀	C₂²	direct (N × H)
17. D₂₀	C₂³	semidirect
18. C₅×C₈	C₂³	semidirect
21. C₂²×C₈	D₅	semidirect
22. C₂²×C₅	D₈	semidirect
33. C₂×C₈	C₂×D₅	semidirect
34. C₂×C₅	C₂×D₈	semidirect
44. C₈	C₂²×D₅	semidirect
45. C₅	C₂²×D₈	semidirect
48. C₂²	D₄₀	direct (N × H)
53. C₂	C₂×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
C₂²×D₂₀	2
C₂²×C₅×C₈	2
C₂×D₄₀	2
C₂²×D₈	5

Subgroups — C22×D40 #66074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄₀ #66074