Subgroups — C₉×D₄₀ #10623567

Order 720.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄₀	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×D₅	—	2	2	no	—
5	C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₉×D₈	—	5	1	no	maximal, Hall
7	C₃×D₂₀	C₂×C₃	1	2	yes	—
8	C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂×C₅×C₉	D₄	1	1	yes	characteristic
10	C₉×D₅	—	4	2	no	—
11	D₄₀	C₉	1	1	yes	characteristic, direct product factor, Hall
12	D₄×C₉	—	5	2	no	—
13	C₈×C₉	D₅	1	1	yes	characteristic, complemented
14	C₂×C₃×D₅	—	2	2	no	—
15	C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
16	C₃×D₈	—	5	1	no	—
17	C₅×C₉	D₈	1	1	yes	characteristic, complemented, Hall
18	D₂₀	C₂×C₉	1	2	yes	complemented
19	C₅×C₈	C₂×C₉	1	1	yes	characteristic, complemented
20	C₂²×C₉	—	10	2	no	—
21	C₄×C₉	C₂×D₅	1	1	yes	characteristic
22	C₂×C₃×C₅	C₃×D₄	1	1	yes	characteristic
23	C₃×D₅	—	4	2	no	—
24	C₃×D₄	—	5	2	no	—
25	C₃×C₈	C₃×D₅	1	1	yes	characteristic
26	C₂×D₅	—	2	2	no	—
27	C₄×C₅	C₂²×C₉	1	1	yes	characteristic
28	C₂×C₉	—	20	2	no	—
29	C₂×C₉	D₂₀	1	1	yes	characteristic
30	D₈	—	5	1	no	Sylow
31	C₃×C₅	C₃×D₈	1	1	yes	characteristic
32	C₂²×C₃	—	10	2	no	—
33	C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
34	C₂×C₅	D₄×C₉	1	1	yes	characteristic
35	D₅	—	4	2	no	—
36	C₉	D₄₀	1	1	yes	characteristic, direct product factor, Sylow
37	D₄	—	5	2	no	—
38	C₈	C₉×D₅	1	1	yes	characteristic, complemented
39	C₂×C₃	—	20	2	no	—
40	C₂×C₃	C₃×D₂₀	1	1	yes	characteristic
41	C₅	C₉×D₈	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	10	2	no	—
43	C₄	C₂×C₉×D₅	1	1	yes	characteristic
44	C₃	C₃×D₄₀	1	1	yes	characteristic
45	C₂	—	20	2	no	—
46	C₂	C₉×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	D₂₀
commutator	C₄×C₅	C₂²×C₉
Frattini	C₃×C₄	C₂×C₃×D₅
Fitting	C₅×C₈×C₉	C₂
socle	C₂×C₃×C₅	C₃×D₄
prime radical	C₃×D₄₀	C₃
cosocle	C₃×C₄×C₅	C₂²×C₃
hypercenter	C₈×C₉	D₅
hypocenter	C₅	C₉×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉ ◁ C₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₂₀	C₂	semidirect
2. C₅×C₈×C₉	C₂	semidirect
11. D₄₀	C₉	direct (N × H)
13. C₈×C₉	D₅	semidirect
17. C₅×C₉	D₈	semidirect
18. D₂₀	C₂×C₉	semidirect
19. C₅×C₈	C₂×C₉	semidirect
36. C₉	D₄₀	direct (N × H)
38. C₈	C₉×D₅	semidirect
41. C₅	C₉×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₉×D₂₀	2
C₅×C₈×C₉	2
C₃×D₄₀	3
C₉×D₈	5

Subgroups — C9×D40 #10623567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₄₀ #10623567