Subgroups — C₂×C₉×D₅₀₅ #32911413

Order 18180.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅₀₅	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₁₀₁	—	5	1	no	maximal, Hall
6	C₃×D₅₀₅	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₀₁	C₂×C₃	1	1	yes	characteristic
8	C₂×D₅₀₅	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₉×C₁₀₁	D₅	1	1	yes	characteristic, complemented
10	C₉×D₁₀₁	—	5	2	no	—
11	C₃×C₅×C₁₀₁	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×D₁₀₁	—	5	1	no	—
13	C₂×C₅×C₁₀₁	C₂×C₉	1	1	yes	characteristic, complemented
14	D₅₀₅	C₂×C₉	1	2	yes	direct product factor
15	C₉×C₁₀₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₀₁	C₃×D₅	1	1	yes	characteristic
17	C₃×D₁₀₁	—	5	2	no	—
18	C₅×C₁₀₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₀₁	—	5	1	no	Hall
20	C₃×C₁₀₁	C₂×C₃×D₅	1	1	yes	characteristic
21	C₂×C₁₀₁	C₉×D₅	1	1	yes	characteristic, complemented
22	D₁₀₁	—	5	2	no	—
23	C₂×C₉×D₅	—	101	1	no	maximal, Hall
24	C₁₀₁	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅×C₉	D₁₀₁	1	1	yes	characteristic, complemented
26	C₉×D₅	—	101	2	no	—
27	C₂×C₃×D₅	—	101	1	no	—
28	C₅×C₉	C₂×D₁₀₁	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₉	—	505	1	no	Hall
30	C₂×C₃×C₅	C₃×D₁₀₁	1	1	yes	characteristic
31	C₃×D₅	—	101	2	no	—
32	C₂×D₅	—	101	1	no	Hall
33	C₂×C₉	—	505	2	no	—
34	C₂×C₉	D₅₀₅	1	1	yes	characteristic, direct product factor
35	C₃×C₅	C₂×C₃×D₁₀₁	1	1	yes	characteristic
36	C₂²×C₃	—	505	1	no	—
37	C₂×C₅	C₉×D₁₀₁	1	1	yes	characteristic, complemented
38	D₅	—	101	2	no	—
39	C₉	C₂×D₅₀₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	505	2	no	—
41	C₂×C₃	C₃×D₅₀₅	1	1	yes	characteristic
42	C₅	C₂×C₉×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	505	1	no	Sylow
44	C₃	C₂×C₃×D₅₀₅	1	1	yes	characteristic
45	C₂	—	505	2	no	—
46	C₂	C₉×D₅₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	D₅₀₅
commutator, hypocenter	C₅×C₁₀₁	C₂²×C₉
Frattini	C₃	C₂×C₃×D₅₀₅
Fitting	C₂×C₅×C₉×C₁₀₁	C₂
socle	C₂×C₃×C₅×C₁₀₁	C₂×C₃
prime radical	C₂×C₃×D₅₀₅	C₃
cosocle	C₃×C₅×C₁₀₁	C₂²×C₃
LCS	G ▷ C₅×C₁₀₁
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₅₀₅	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₀₁	C₂	semidirect
4. C₅×C₉×C₁₀₁	C₂²	semidirect
8. C₂×D₅₀₅	C₉	direct (N × H)
9. C₂×C₉×C₁₀₁	D₅	semidirect
13. C₂×C₅×C₁₀₁	C₂×C₉	semidirect
14. D₅₀₅	C₂×C₉	direct (N × H)
15. C₉×C₁₀₁	C₂×D₅	semidirect
18. C₅×C₁₀₁	C₂²×C₉	semidirect
21. C₂×C₁₀₁	C₉×D₅	semidirect
24. C₁₀₁	C₂×C₉×D₅	semidirect
25. C₂×C₅×C₉	D₁₀₁	semidirect
28. C₅×C₉	C₂×D₁₀₁	semidirect
34. C₂×C₉	D₅₀₅	direct (N × H)
37. C₂×C₅	C₉×D₁₀₁	semidirect
39. C₉	C₂×D₅₀₅	direct (N × H)
42. C₅	C₂×C₉×D₁₀₁	semidirect
46. C₂	C₉×D₅₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₅₀₅	2
C₂×C₅×C₉×C₁₀₁	2
C₂×C₃×D₅₀₅	3
C₂×C₉×D₁₀₁	5
C₂×C₉×D₅	101

Subgroups — C2×C9×D505 #32911413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₅₀₅ #32911413