Subgroups — C₅×C₁₁×C₁₃×D₉ #27166017

Order 12870.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₁₁×C₁₃	—	3	1	no	maximal
3	C₁₁×C₁₃×D₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₃	D₃	1	1	yes	characteristic
5	C₂×C₅×C₁₁×C₁₃	—	9	1	no	Hall
6	C₉×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₃×D₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×D₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₁₁×C₁₃	—	3	1	no	—
10	C₅×C₁₁×C₁₃	D₉	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₉×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₅×C₉×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁×C₁₃	C₅×D₃	1	1	yes	characteristic
14	C₅×D₃×C₁₃	—	3	1	no	—
15	C₅×D₃×C₁₁	—	3	1	no	—
16	C₂×C₁₁×C₁₃	—	9	1	no	Hall
17	C₁₃×D₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁×D₉	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅×C₁₃	D₃×C₁₁	1	1	yes	characteristic
20	C₃×C₅×C₁₁	D₃×C₁₃	1	1	yes	characteristic
21	C₁₁×C₁₃	C₅×D₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×C₁₃	—	9	1	no	Hall
23	C₉×C₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₁	—	9	1	no	Hall
25	C₉×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₅×D₉	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	D₃×C₁₃	—	3	1	no	—
28	D₃×C₁₁	—	3	1	no	—
29	C₅×C₁₃	C₁₁×D₉	1	1	yes	characteristic, direct product factor, Hall
30	C₅×C₁₁	C₁₃×D₉	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₉	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	C₅×D₃×C₁₁	1	1	yes	characteristic
33	C₃×C₁₁	C₅×D₃×C₁₃	1	1	yes	characteristic
34	C₅×D₃	—	3	1	no	—
35	C₂×C₁₃	—	9	1	no	Hall
36	C₂×C₁₁	—	9	1	no	Hall
37	D₉	C₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	D₃×C₁₁×C₁₃	1	1	yes	characteristic
39	C₁₃	C₅×C₁₁×D₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₁₁	C₅×C₁₃×D₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	9	1	no	Hall
42	C₉	C₂×C₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	3	1	no	—
44	C₅	C₁₁×C₁₃×D₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₃×C₁₁×C₁₃	1	1	yes	characteristic
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁×C₁₃	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₁₁×C₁₃
Frattini	C₃	C₅×D₃×C₁₁×C₁₃
Fitting	C₅×C₉×C₁₁×C₁₃	C₂
socle	C₃×C₅×C₁₁×C₁₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₁₃	C₂	semidirect
3. C₁₁×C₁₃×D₉	C₅	direct (N × H)
6. C₉×C₁₁×C₁₃	C₂×C₅	semidirect
7. C₅×C₁₃×D₉	C₁₁	direct (N × H)
8. C₅×C₁₁×D₉	C₁₃	direct (N × H)
10. C₅×C₁₁×C₁₃	D₉	direct (N × H)
11. C₅×C₉×C₁₃	C₂×C₁₁	semidirect
12. C₅×C₉×C₁₁	C₂×C₁₃	semidirect
17. C₁₃×D₉	C₅×C₁₁	direct (N × H)
18. C₁₁×D₉	C₅×C₁₃	direct (N × H)
21. C₁₁×C₁₃	C₅×D₉	direct (N × H)
23. C₉×C₁₃	C₂×C₅×C₁₁	semidirect
25. C₉×C₁₁	C₂×C₅×C₁₃	semidirect
26. C₅×D₉	C₁₁×C₁₃	direct (N × H)
29. C₅×C₁₃	C₁₁×D₉	direct (N × H)
30. C₅×C₁₁	C₁₃×D₉	direct (N × H)
31. C₅×C₉	C₂×C₁₁×C₁₃	semidirect
37. D₉	C₅×C₁₁×C₁₃	direct (N × H)
39. C₁₃	C₅×C₁₁×D₉	direct (N × H)
40. C₁₁	C₅×C₁₃×D₉	direct (N × H)
42. C₉	C₂×C₅×C₁₁×C₁₃	semidirect
44. C₅	C₁₁×C₁₃×D₉	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×C₁₁×C₁₃	2
C₅×D₃×C₁₁×C₁₃	3
C₁₁×C₁₃×D₉	5
C₅×C₁₃×D₉	11
C₅×C₁₁×D₉	13

Subgroups — C5×C11×C13×D9 #27166017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×C₁₃×D₉ #27166017