Subgroups — C₅×C₉×D₉ #11717607

Order 810.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₉	—	3	1	no	maximal
3	C₃×C₅×D₉	C₃	1	1	yes	maximal, characteristic
4	C₉×D₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₉	—	2	1	no	—
6	C₃×C₅×C₉	D₃	1	1	yes	characteristic
7	C₃×C₅×C₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₅×D₃	—	3	1	no	—
9	C₂×C₅×C₉	—	9	1	no	—
10	C₅×D₉	C₉	1	1	yes	characteristic, direct product factor
11	C₉²	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
12	D₃×C₉	—	3	1	no	—
13	C₃×D₉	C₃×C₅	1	1	yes	characteristic
14	C₃²×C₅	C₃×D₃	1	1	yes	characteristic
15	C₅×C₉	—	2	3	no	—
16	C₅×C₉	—	2	1	no	—
17	C₅×C₉	—	2	1	no	—
18	C₅×C₉	D₉	1	1	yes	characteristic, direct product factor
19	C₅×C₉	C₂×C₉	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅	—	9	1	no	—
21	C₅×D₃	—	3	1	no	—
22	C₃×C₉	—	2	1	no	—
23	C₃×C₉	C₅×D₃	1	1	yes	characteristic
24	C₃×C₉	C₂×C₃×C₅	1	1	yes	characteristic
25	C₃×D₃	—	3	1	no	—
26	C₂×C₉	—	9	1	no	—
27	D₉	C₅×C₉	1	1	yes	characteristic, direct product factor
28	C₃×C₅	—	2	1	no	—
29	C₃×C₅	C₃×D₉	1	1	yes	characteristic
30	C₃×C₅	D₃×C₉	1	1	yes	characteristic
31	C₂×C₅	—	9	1	no	Hall
32	C₃²	C₃×C₅×D₃	1	1	yes	characteristic
33	C₉	—	2	3	no	—
34	C₉	—	2	1	no	—
35	C₉	—	2	1	no	—
36	C₉	C₅×D₉	1	1	yes	characteristic, direct product factor
37	C₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
38	C₂×C₃	—	9	1	no	—
39	D₃	—	3	1	no	—
40	C₅	C₉×D₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₃	—	2	1	no	—
42	C₃	C₃×C₅×D₉	1	1	yes	characteristic
43	C₃	C₅×D₃×C₉	1	1	yes	characteristic
44	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉	D₉
commutator, hypocenter	C₉	C₂×C₅×C₉
Frattini	C₃²	C₃×C₅×D₃
Fitting	C₅×C₉²	C₂
socle	C₃²×C₅	C₃×D₃
prime radical	C₃×C₅×D₉	C₃
cosocle	C₃×C₉	C₂×C₃×C₅
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉²	C₂	semidirect
4. C₉×D₉	C₅	direct (N × H)
10. C₅×D₉	C₉	direct (N × H)
11. C₉²	C₂×C₅	semidirect
18. C₅×C₉	D₉	direct (N × H)
19. C₅×C₉	C₂×C₉	semidirect
27. D₉	C₅×C₉	direct (N × H)
36. C₉	C₅×D₉	direct (N × H)
37. C₉	C₂×C₅×C₉	semidirect
40. C₅	C₉×D₉	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×C₉²	2
C₅×D₃×C₉	3
C₃×C₅×D₉	3
C₉×D₉	5

Subgroups — C5×C9×D9 #11717607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₉ #11717607