Finite Group Databasebeta

← C3⋊(C11⋊#63120) #22575154

Subgroups — C3⋊(C11⋊#63120) #22575154

Order 8580.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C11×C13C211yesmaximal, characteristic
2C11⋊#63120—31nomaximal, Hall
3C3×C5×C11×C13C411yescharacteristic, complemented, Hall
4Dic429—51nomaximal, Hall
5D5×C11×C13D311yescharacteristic
6C2×C3×C11×C13—51no—
7C3⋊#63120—111nomaximal, Hall
8C5×C11×C13Dic311yescharacteristic, complemented, Hall
9C3⋊(C11⋊AGL(1,𝔽5))—131nomaximal, Hall
10Dic143—151noHall
11C3×C11×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
12C3×D5×C13D1111yescharacteristic
13C3×D5×C11D1311yescharacteristic
14C2×C11×C13—51no—
15#63120—331noHall
16C11⋊AGL(1,𝔽5)—391noHall
17C3×C5×C13Dic1111yescharacteristic, complemented, Hall
18C3×C5×C11Dic1311yescharacteristic, complemented, Hall
19Dic39—551noHall
20C11×C13ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
21Dic33—651noHall
22D5×C13D3311yescharacteristic
23D5×C11D3911yescharacteristic
24C2×C3×C13—51no—
25C2×C3×C11—51no—
26C5×C13Dic3311yescharacteristic, complemented, Hall
27ΓL(1,𝔽16)—1431noHall
28C5×C11Dic3911yescharacteristic, complemented, Hall
29Dic13—1651noHall
30Dic11—1951noHall
31C3×C13C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
32C3×C11#6312011yescharacteristic, complemented, Hall
33C3×D5D14311yescharacteristic
34C2×C13—51no—
35C2×C11—51no—
36AGL(1,𝔽5)—4291noHall
37C3×C5Dic14311yescharacteristic, complemented, Hall
38C13C3⋊(C11⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
39Dic3—7151noHall
40C11C3⋊#6312011yescharacteristic, complemented, Sylow
41D5D42911yescharacteristic
42C2×C3—51no—
43C5Dic42911yescharacteristic, complemented, Sylow
44C4—21451noSylow
45C3C11⋊#6312011yescharacteristic, complemented, Sylow
46C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C13C4
LCSG ▷ C3×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×C5×C11×C13C4semidirect
8. C5×C11×C13Dic3semidirect
11. C3×C11×C13AGL(1,𝔽5)semidirect
17. C3×C5×C13Dic11semidirect
18. C3×C5×C11Dic13semidirect
20. C11×C13ΓL(1,𝔽16)semidirect
26. C5×C13Dic33semidirect
28. C5×C11Dic39semidirect
31. C3×C13C11⋊AGL(1,𝔽5)semidirect
32. C3×C11#63120semidirect
37. C3×C5Dic143semidirect
38. C13C3⋊(C11⋊AGL(1,𝔽5))semidirect
40. C11C3⋊#63120semidirect
43. C5Dic429semidirect
45. C3C11⋊#63120semidirect