Subgroups — C₅×C₉×D₈ #10623617

Order 720.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₅×C₉	D₄
commutator	C₄	C₂²×C₅×C₉
Frattini, cosocle	C₃×C₄	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₃×D₄
prime radical	C₃×C₅×D₈	C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₉ ◁ C₄×C₅×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×C₉	C₂	semidirect
2. C₅×C₈×C₉	C₂	semidirect
6. C₉×D₈	C₅	direct (N × H)
11. C₅×D₈	C₉	direct (N × H)
12. D₄×C₉	C₂×C₅	semidirect
13. C₈×C₉	C₂×C₅	semidirect
17. C₅×C₉	D₈	direct (N × H)
18. C₅×D₄	C₂×C₉	semidirect
19. C₅×C₈	C₂×C₉	semidirect
30. D₈	C₅×C₉	direct (N × H)
36. C₉	C₅×D₈	direct (N × H)
37. D₄	C₂×C₅×C₉	semidirect
38. C₈	C₂×C₅×C₉	semidirect
41. C₅	C₉×D₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₄×C₉	2
C₅×C₈×C₉	2
C₃×C₅×D₈	3
C₉×D₈	5

Subgroups — C5×C9×D8 #10623617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₈ #10623617