Subgroups — C₅×C₉×D₂₂₁ #34091020

Order 19890.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₂₂₁	C₃	1	1	yes	maximal, characteristic
3	C₉×D₂₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₅×D₂₂₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₃×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₉×D₁₇	—	13	1	no	maximal, Hall
8	C₃×D₂₂₁	C₃×C₅	1	1	yes	characteristic
9	C₅×C₉×D₁₃	—	17	1	no	maximal, Hall
10	C₅×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₇	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×C₉×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×D₁₇	—	13	1	no	—
15	D₂₂₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅×D₁₃	—	17	1	no	—
17	C₉×D₁₇	—	13	1	no	Hall
18	C₃×C₅×C₁₇	C₃×D₁₃	1	1	yes	characteristic
19	C₉×D₁₃	—	17	1	no	Hall
20	C₁₃×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	C₃×D₁₇	1	1	yes	characteristic
22	C₅×D₁₇	—	13	1	no	Hall
23	C₉×C₁₇	C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
24	C₅×D₁₃	—	17	1	no	Hall
25	C₉×C₁₃	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
26	C₃×D₁₇	—	13	1	no	—
27	C₂×C₅×C₉	—	221	1	no	Hall
28	C₅×C₁₇	C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₁₃	—	17	1	no	—
30	C₅×C₁₃	C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₇	C₃×C₅×D₁₃	1	1	yes	characteristic
32	C₅×C₉	D₂₂₁	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₁₃	C₃×C₅×D₁₇	1	1	yes	characteristic
34	D₁₇	—	13	1	no	Hall
35	C₂×C₃×C₅	—	221	1	no	—
36	D₁₃	—	17	1	no	Hall
37	C₂×C₉	—	221	1	no	Hall
38	C₁₇	C₅×C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃×D₂₂₁	1	1	yes	characteristic
40	C₁₃	C₅×C₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	221	1	no	Hall
42	C₉	C₅×D₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	221	1	no	—
44	C₅	C₉×D₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×D₂₂₁	1	1	yes	characteristic
46	C₂	—	221	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉	D₂₂₁
commutator, hypocenter	C₁₃×C₁₇	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₂₂₁
Fitting	C₅×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₂₂₁	C₃
cosocle	C₃×C₁₃×C₁₇	C₂×C₃×C₅
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₃×C₁₇	C₂	semidirect
3. C₉×D₂₂₁	C₅	direct (N × H)
5. C₅×D₂₂₁	C₉	direct (N × H)
6. C₉×C₁₃×C₁₇	C₂×C₅	semidirect
10. C₅×C₁₃×C₁₇	C₂×C₉	semidirect
11. C₅×C₉×C₁₇	D₁₃	semidirect
13. C₅×C₉×C₁₃	D₁₇	semidirect
15. D₂₂₁	C₅×C₉	direct (N × H)
20. C₁₃×C₁₇	C₂×C₅×C₉	semidirect
23. C₉×C₁₇	C₅×D₁₃	semidirect
25. C₉×C₁₃	C₅×D₁₇	semidirect
28. C₅×C₁₇	C₉×D₁₃	semidirect
30. C₅×C₁₃	C₉×D₁₇	semidirect
32. C₅×C₉	D₂₂₁	direct (N × H)
38. C₁₇	C₅×C₉×D₁₃	semidirect
40. C₁₃	C₅×C₉×D₁₇	semidirect
42. C₉	C₅×D₂₂₁	direct (N × H)
44. C₅	C₉×D₂₂₁	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×C₉×C₁₃×C₁₇	2
C₃×C₅×D₂₂₁	3
C₉×D₂₂₁	5
C₅×C₉×D₁₇	13
C₅×C₉×D₁₃	17

Subgroups — C5×C9×D221 #34091020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₂₂₁ #34091020