Subgroups — D₉×D₅₅ #14520403

Order 1980.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₅₅	—	3	1	no	maximal
5	C₅×C₉×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₁₁	—	5	1	no	maximal, Hall
7	D₁₆₅	—	3	1	no	—
8	C₅×D₃×C₁₁	—	3	1	no	—
9	C₃×D₅₅	D₃	1	1	yes	characteristic
10	C₂×D₅₅	—	9	1	no	Hall
11	D₉₉	—	5	1	no	—
12	C₉×D₁₁	—	5	1	no	—
13	C₁₁×D₉	D₅	1	1	yes	characteristic, complemented
14	D₅×D₉	—	11	1	no	maximal, Hall
15	C₃×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
16	D₃×D₁₁	—	15	1	no	—
17	C₂×C₅×C₁₁	—	9	1	no	—
18	D₅₅	—	9	1	no	—
19	D₅₅	D₉	1	1	yes	characteristic, direct product factor
20	C₉×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
21	D₄₅	—	11	1	no	—
22	C₉×D₅	—	11	1	no	—
23	C₅×D₉	D₁₁	1	1	yes	characteristic, complemented
24	D₃₃	—	15	1	no	—
25	C₃×D₁₁	—	5	1	no	—
26	D₃×C₁₁	—	3	1	no	—
27	D₃×D₅	—	33	1	no	—
28	C₅×C₁₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
29	C₅×C₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₂×D₁₁	—	45	1	no	Hall
31	C₂×D₉	—	55	1	no	Hall
32	C₃×C₁₁	D₃×D₅	1	1	yes	characteristic
33	D₁₅	—	33	1	no	—
34	C₃×D₅	—	11	1	no	—
35	C₅×D₃	—	3	1	no	—
36	C₂×C₁₁	—	9	1	no	—
37	D₁₁	—	5	1	no	—
38	D₁₁	—	45	1	no	—
39	C₂×D₅	—	99	1	no	Hall
40	C₂×C₉	—	55	1	no	—
41	D₉	—	55	1	no	—
42	D₉	D₅₅	1	1	yes	characteristic, direct product factor
43	C₃×C₅	D₃×D₁₁	1	1	yes	characteristic
44	C₂×D₃	—	165	1	no	—
45	C₁₁	D₅×D₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₅	—	9	1	no	—
47	D₅	—	11	1	no	—
48	D₅	—	99	1	no	—
49	C₉	C₂×D₅₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	55	1	no	—
51	D₃	—	3	1	no	—
52	D₃	—	165	1	no	—
53	C₅	D₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	495	1	no	Sylow
55	C₃	D₃×D₅₅	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	55	1	no	—
58	C₂	—	495	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₁	C₂²
Frattini	C₃	D₃×D₅₅
socle	C₃×C₅×C₁₁	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₄₉₅	C₂	semidirect
2. C₅×C₁₁×D₉	C₂	semidirect
3. C₉×D₅₅	C₂	semidirect
5. C₅×C₉×C₁₁	C₂²	semidirect
13. C₁₁×D₉	D₅	semidirect
19. D₅₅	D₉	direct (N × H)
20. C₉×C₁₁	C₂×D₅	semidirect
23. C₅×D₉	D₁₁	semidirect
28. C₅×C₁₁	C₂×D₉	semidirect
29. C₅×C₉	C₂×D₁₁	semidirect
42. D₉	D₅₅	direct (N × H)
45. C₁₁	D₅×D₉	semidirect
49. C₉	C₂×D₅₅	semidirect
53. C₅	D₉×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
D₄₉₅	2
C₅×C₁₁×D₉	2
C₉×D₅₅	2
D₃×D₅₅	3
D₉×D₁₁	5
D₅×D₉	11

Subgroups — D9×D55 #14520403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₅₅ #14520403