Subgroups — C₉×Dic₂₀ #10623568

Order 720.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×Dic₁₀	C₂	1	2	yes	maximal
2	C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₂₀	C₃	1	1	yes	maximal, characteristic
4	C₄×C₅×C₉	C₂²	1	1	yes	characteristic
5	C₉×Dic₅	—	2	2	no	—
6	C₉×Q₁₆	—	5	1	no	maximal, Hall
7	C₃×Dic₁₀	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	Dic₂₀	C₉	1	1	yes	characteristic, direct product factor, Hall
11	Q₈×C₉	—	5	2	no	—
12	C₈×C₉	D₅	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
14	C₃×Dic₅	—	2	2	no	—
15	C₃×Q₁₆	—	5	1	no	—
16	C₅×C₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
17	Dic₁₀	C₂×C₉	1	2	yes	—
18	C₅×C₈	C₂×C₉	1	1	yes	characteristic
19	C₄×C₉	—	10	2	no	—
20	C₄×C₉	C₂×D₅	1	1	yes	characteristic
21	C₂×C₃×C₅	C₃×D₄	1	1	yes	characteristic
22	C₃×Q₈	—	5	2	no	—
23	C₃×C₈	C₃×D₅	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₉	1	1	yes	characteristic
25	Dic₅	—	2	2	no	—
26	C₂×C₉	D₂₀	1	1	yes	characteristic
27	Q₁₆	—	5	1	no	Sylow
28	C₃×C₅	C₃×Q₁₆	1	1	yes	characteristic
29	C₃×C₄	—	10	2	no	—
30	C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
31	C₂×C₅	D₄×C₉	1	1	yes	characteristic
32	C₉	Dic₂₀	1	1	yes	characteristic, direct product factor, Sylow
33	Q₈	—	5	2	no	—
34	C₈	C₉×D₅	1	1	yes	characteristic
35	C₂×C₃	C₃×D₂₀	1	1	yes	characteristic
36	C₅	C₉×Q₁₆	1	1	yes	characteristic, complemented, Sylow
37	C₄	—	10	2	no	—
38	C₄	C₂×C₉×D₅	1	1	yes	characteristic
39	C₃	C₃×Dic₂₀	1	1	yes	characteristic
40	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, prime radical	C₂×C₃×C₅	C₃×D₄
cosocle	C₃×C₄×C₅	C₂²×C₃
hypercenter	C₈×C₉	D₅
hypocenter	C₅	C₉×Q₁₆
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
10. Dic₂₀	C₉	direct (N × H)
16. C₅×C₉	Q₁₆	semidirect
32. C₉	Dic₂₀	direct (N × H)
36. C₅	C₉×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₉×Dic₁₀	2
C₅×C₈×C₉	2
C₃×Dic₂₀	3
C₉×Q₁₆	5

Subgroups — C9×Dic20 #10623568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₂₀ #10623568