Subgroups — C₉×D₅×D₆₁ #24926698

Order 10980.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₅×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₉×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×D₆₁	C₃	1	1	yes	maximal, characteristic
5	C₅×C₉×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₉×D₆₁	—	5	1	no	maximal, Hall
7	C₃×D₃₀₅	C₂×C₃	1	1	yes	characteristic
8	C₃×D₅×C₆₁	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅×D₆₁	C₂×C₃	1	1	yes	characteristic
10	D₅×D₆₁	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₆₁	—	5	1	no	—
12	C₉×D₆₁	—	5	1	no	—
13	C₉×D₆₁	D₅	1	1	yes	characteristic, direct product factor
14	C₃×C₅×C₆₁	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×D₆₁	—	5	1	no	—
16	D₃₀₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₅×D₆₁	C₂×C₉	1	1	yes	characteristic, complemented
18	D₅×C₆₁	C₂×C₉	1	1	yes	characteristic, complemented
19	C₉×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₆₁	—	5	1	no	—
21	C₃×D₆₁	—	5	1	no	—
22	C₃×D₆₁	C₃×D₅	1	1	yes	characteristic
23	C₅×C₆₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₆₁	—	5	1	no	Hall
25	C₃×C₆₁	C₂×C₃×D₅	1	1	yes	characteristic
26	C₂×C₉×D₅	—	61	1	no	maximal, Hall
27	C₂×C₆₁	—	5	1	no	—
28	D₆₁	—	5	1	no	—
29	D₆₁	C₉×D₅	1	1	yes	characteristic, direct product factor
30	C₂×C₅×C₉	—	61	1	no	—
31	C₉×D₅	—	61	1	no	—
32	C₉×D₅	D₆₁	1	1	yes	characteristic, direct product factor
33	C₆₁	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×D₅	—	61	1	no	—
35	C₅×C₉	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₉	—	305	1	no	Hall
37	C₂×C₃×C₅	—	61	1	no	—
38	C₃×D₅	—	61	1	no	—
39	C₃×D₅	C₃×D₆₁	1	1	yes	characteristic
40	C₂×D₅	—	61	1	no	Hall
41	C₂×C₉	—	5	1	no	—
42	C₂×C₉	—	305	1	no	—
43	C₂×C₉	—	61	1	no	—
44	C₃×C₅	C₂×C₃×D₆₁	1	1	yes	characteristic
45	C₂²×C₃	—	305	1	no	—
46	C₂×C₅	—	61	1	no	—
47	D₅	—	61	1	no	—
48	D₅	C₉×D₆₁	1	1	yes	characteristic, direct product factor
49	C₉	D₅×D₆₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃	—	5	1	no	—
51	C₂×C₃	—	305	1	no	—
52	C₂×C₃	—	61	1	no	—
53	C₅	C₂×C₉×D₆₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	305	1	no	Sylow
55	C₃	C₃×D₅×D₆₁	1	1	yes	characteristic
56	C₂	—	5	1	no	—
57	C₂	—	305	1	no	—
58	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₅×D₆₁
commutator, hypocenter	C₅×C₆₁	C₂²×C₉
Frattini	C₃	C₃×D₅×D₆₁
Fitting	C₅×C₉×C₆₁	C₂²
socle, cosocle	C₃×C₅×C₆₁	C₂²×C₃
prime radical	C₃×D₅×D₆₁	C₃
LCS	G ▷ C₅×C₆₁
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₃₀₅	C₂	semidirect
2. C₉×D₅×C₆₁	C₂	semidirect
3. C₅×C₉×D₆₁	C₂	semidirect
5. C₅×C₉×C₆₁	C₂²	semidirect
10. D₅×D₆₁	C₉	direct (N × H)
13. C₉×D₆₁	D₅	direct (N × H)
16. D₃₀₅	C₂×C₉	semidirect
17. C₅×D₆₁	C₂×C₉	semidirect
18. D₅×C₆₁	C₂×C₉	semidirect
19. C₉×C₆₁	C₂×D₅	semidirect
23. C₅×C₆₁	C₂²×C₉	semidirect
29. D₆₁	C₉×D₅	direct (N × H)
32. C₉×D₅	D₆₁	direct (N × H)
33. C₆₁	C₂×C₉×D₅	semidirect
35. C₅×C₉	C₂×D₆₁	semidirect
48. D₅	C₉×D₆₁	direct (N × H)
49. C₉	D₅×D₆₁	direct (N × H)
53. C₅	C₂×C₉×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₉×D₃₀₅	2
C₉×D₅×C₆₁	2
C₅×C₉×D₆₁	2
C₃×D₅×D₆₁	3
C₂×C₉×D₆₁	5
C₂×C₉×D₅	61

Subgroups — C9×D5×D61 #24926698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₅×D₆₁ #24926698