Subgroups — C₅×C₉×C₁₁×D₁₃ #27166010

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	C₃×C₅×C₁₁×D₁₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₁×D₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₁×D₁₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₉×D₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₉×C₁₁	—	13	1	no	maximal, Hall
9	C₃×C₁₁×D₁₃	C₃×C₅	1	1	yes	characteristic
10	C₅×C₁₁×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₅×C₉×C₁₁	D₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
14	C₃×C₅×D₁₃	C₃×C₁₁	1	1	yes	characteristic
15	C₂×C₃×C₅×C₁₁	—	13	1	no	—
16	C₁₁×D₁₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₉×D₁₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₉×C₁₁	—	13	1	no	Hall
19	C₃×C₅×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
20	C₃×C₅×C₁₁	C₃×D₁₃	1	1	yes	characteristic
21	C₁₁×C₁₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
22	C₅×D₁₃	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₉×C₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₁	—	13	1	no	Hall
25	C₉×C₁₁	C₅×D₁₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₉	—	13	1	no	Hall
27	C₃×D₁₃	C₃×C₅×C₁₁	1	1	yes	characteristic
28	C₂×C₃×C₁₁	—	13	1	no	—
29	C₅×C₁₃	C₂×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₅×C₁₁	C₉×D₁₃	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₉	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₃	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
33	C₃×C₁₁	C₃×C₅×D₁₃	1	1	yes	characteristic
34	C₂×C₃×C₅	—	13	1	no	—
35	D₁₃	C₅×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₁₁	—	13	1	no	Hall
37	C₂×C₉	—	13	1	no	Hall
38	C₃×C₅	C₃×C₁₁×D₁₃	1	1	yes	characteristic
39	C₁₃	C₂×C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₁₁	C₅×C₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	13	1	no	Hall
42	C₉	C₅×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₅	C₉×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×C₁₁×D₁₃	1	1	yes	characteristic
46	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉×C₁₁	D₁₃
commutator, hypocenter	C₁₃	C₂×C₅×C₉×C₁₁
Frattini	C₃	C₃×C₅×C₁₁×D₁₃
Fitting	C₅×C₉×C₁₁×C₁₃	C₂
socle	C₃×C₅×C₁₁×C₁₃	C₂×C₃
prime radical	C₃×C₅×C₁₁×D₁₃	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₅×C₁₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₉×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₁₃	C₂	semidirect
3. C₉×C₁₁×D₁₃	C₅	direct (N × H)
5. C₅×C₁₁×D₁₃	C₉	direct (N × H)
6. C₉×C₁₁×C₁₃	C₂×C₅	semidirect
7. C₅×C₉×D₁₃	C₁₁	direct (N × H)
10. C₅×C₁₁×C₁₃	C₂×C₉	semidirect
11. C₅×C₉×C₁₃	C₂×C₁₁	semidirect
12. C₅×C₉×C₁₁	D₁₃	direct (N × H)
16. C₁₁×D₁₃	C₅×C₉	direct (N × H)
17. C₉×D₁₃	C₅×C₁₁	direct (N × H)
21. C₁₁×C₁₃	C₂×C₅×C₉	semidirect
22. C₅×D₁₃	C₉×C₁₁	direct (N × H)
23. C₉×C₁₃	C₂×C₅×C₁₁	semidirect
25. C₉×C₁₁	C₅×D₁₃	direct (N × H)
29. C₅×C₁₃	C₂×C₉×C₁₁	semidirect
30. C₅×C₁₁	C₉×D₁₃	direct (N × H)
31. C₅×C₉	C₁₁×D₁₃	direct (N × H)
35. D₁₃	C₅×C₉×C₁₁	direct (N × H)
39. C₁₃	C₂×C₅×C₉×C₁₁	semidirect
40. C₁₁	C₅×C₉×D₁₃	direct (N × H)
42. C₉	C₅×C₁₁×D₁₃	direct (N × H)
44. C₅	C₉×C₁₁×D₁₃	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
C₃×C₅×C₁₁×D₁₃	3
C₉×C₁₁×D₁₃	5
C₅×C₉×D₁₃	11
C₂×C₅×C₉×C₁₁	13

Subgroups — C5×C9×C11×D13 #27166010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₁×D₁₃ #27166010