Subgroups — D₉×D₃₀₅ #24926709

Order 10980.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₇₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₃₀₅	—	3	1	no	maximal
5	C₅×C₉×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₆₁	—	5	1	no	maximal, Hall
7	D₉₁₅	—	3	1	no	—
8	C₅×D₃×C₆₁	—	3	1	no	—
9	C₃×D₃₀₅	D₃	1	1	yes	characteristic
10	C₂×D₃₀₅	—	9	1	no	Hall
11	D₅₄₉	—	5	1	no	—
12	C₉×D₆₁	—	5	1	no	—
13	D₉×C₆₁	D₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₆₁	C₂×D₃	1	1	yes	characteristic
15	D₃×D₆₁	—	15	1	no	—
16	C₂×C₅×C₆₁	—	9	1	no	—
17	D₃₀₅	—	9	1	no	—
18	D₃₀₅	D₉	1	1	yes	characteristic, direct product factor
19	C₉×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₁₈₃	—	15	1	no	—
21	C₃×D₆₁	—	5	1	no	—
22	D₃×C₆₁	—	3	1	no	—
23	C₅×C₆₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₆₁	—	45	1	no	Hall
25	C₃×C₆₁	D₃×D₅	1	1	yes	characteristic
26	D₅×D₉	—	61	1	no	maximal, Hall
27	C₂×C₆₁	—	9	1	no	—
28	D₆₁	—	5	1	no	—
29	D₆₁	—	45	1	no	—
30	D₄₅	—	61	1	no	—
31	C₉×D₅	—	61	1	no	—
32	C₅×D₉	D₆₁	1	1	yes	characteristic, complemented
33	C₆₁	D₅×D₉	1	1	yes	characteristic, complemented, Sylow
34	D₃×D₅	—	183	1	no	—
35	C₅×C₉	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
36	C₂×D₉	—	305	1	no	Hall
37	D₁₅	—	183	1	no	—
38	C₃×D₅	—	61	1	no	—
39	C₅×D₃	—	3	1	no	—
40	C₂×D₅	—	549	1	no	Hall
41	C₂×C₉	—	305	1	no	—
42	D₉	—	305	1	no	—
43	D₉	D₃₀₅	1	1	yes	characteristic, direct product factor
44	C₃×C₅	D₃×D₆₁	1	1	yes	characteristic
45	C₂×D₃	—	915	1	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	549	1	no	—
48	D₅	—	61	1	no	—
49	C₉	C₂×D₃₀₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	305	1	no	—
51	D₃	—	3	1	no	—
52	D₃	—	915	1	no	—
53	C₅	D₉×D₆₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	2745	1	no	Sylow
55	C₃	D₃×D₃₀₅	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	305	1	no	—
58	C₂	—	2745	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₆₁	C₂²
Frattini	C₃	D₃×D₃₀₅
socle	C₃×C₅×C₆₁	C₂×D₃
LCS	G ▷ C₅×C₉×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₇₄₅	C₂	semidirect
2. C₅×D₉×C₆₁	C₂	semidirect
3. C₉×D₃₀₅	C₂	semidirect
5. C₅×C₉×C₆₁	C₂²	semidirect
13. D₉×C₆₁	D₅	semidirect
18. D₃₀₅	D₉	direct (N × H)
19. C₉×C₆₁	C₂×D₅	semidirect
23. C₅×C₆₁	C₂×D₉	semidirect
32. C₅×D₉	D₆₁	semidirect
33. C₆₁	D₅×D₉	semidirect
35. C₅×C₉	C₂×D₆₁	semidirect
43. D₉	D₃₀₅	direct (N × H)
49. C₉	C₂×D₃₀₅	semidirect
53. C₅	D₉×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
D₂₇₄₅	2
C₅×D₉×C₆₁	2
C₉×D₃₀₅	2
D₃×D₃₀₅	3
D₉×D₆₁	5
D₅×D₉	61

Subgroups — D9×D305 #24926709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₃₀₅ #24926709