Finite Group Databasebeta

← C19×C3⋊(Dic13⋊C3) #22580205

Subgroups — C19×C3⋊(Dic13⋊C3) #22580205

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19×C13⋊C3C211yesmaximal, characteristic
2C19×Dic39C311yesmaximal, characteristic, complemented
3C19×Dic13⋊C3—31nomaximal
4C3×C19×C13⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19C2×C311yescharacteristic
6C2×C19×C13⋊C3—21no—
7C2×C19×C13⋊C3D311yescharacteristic
8C19×Dic13—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10C19×C13⋊C3—21no—
11C19×C13⋊C3Dic311yescharacteristic, complemented
12C3×Dic3×C19—131nomaximal, Hall
13C2×C13×C19C3×D311yescharacteristic
14C3⋊(Dic13⋊C3)C1911yesmaximal, characteristic, direct product factor, Hall
15C2×C32×C19—131no—
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C3×C13⋊C3C2×C1911yescharacteristic
18C3×C4×C19—391no—
19Dic3×C19—131no—
20C32×C19—131noHall
21Dic39C3×C1911yescharacteristic, complemented
22Dic13⋊C3—31no—
23C3×C13⋊C3C4×C1911yescharacteristic, complemented, Hall
24C2×C3×C19—131no—
25C2×C3×C19—261no—
26C2×C3×C19D13⋊C311yescharacteristic
27C2×C3×C13C2×C3×C1911yescharacteristic
28C2×C13⋊C3—21no—
29C2×C13⋊C3D3×C1911yescharacteristic
30C4×C19—391noHall
31C3×C19—131no—
32C3×C19—261no—
33C3×C19Dic13⋊C311yescharacteristic, complemented
34Dic13—31noHall
35C3×C13C3×C4×C1911yescharacteristic, complemented
36C13⋊C3—21no—
37C13⋊C3Dic3×C1911yescharacteristic, complemented
38C2×C19C3⋊(D13⋊C3)11yescharacteristic
39C3×Dic3—131noHall
40C2×C13C3×D3×C1911yescharacteristic
41C19C3⋊(Dic13⋊C3)11yescharacteristic, direct product factor, Sylow
42C2×C32—131no—
43C13C3×Dic3×C1911yescharacteristic, complemented, Sylow
44C3×C4—391no—
45Dic3—131no—
46C32—131noSylow
47C2×C3—131no—
48C2×C3—261no—
49C2×C3C19×D13⋊C311yescharacteristic
50C4—391noSylow
51C3—131no—
52C3—261no—
53C3C19×Dic13⋊C311yescharacteristic, complemented
54C2C19×C3⋊(D13⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C19C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C19
FrattiniC2C19×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C19C2×C3
LCSG ▷ C3×C13
UCSC1 ◁ C2×C19

Complements

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

NH ≅ G/Ntype
2. C19×Dic39C3semidirect
4. C3×C19×C13⋊C3C4semidirect
9. C3×C13×C19C3×C4semidirect
11. C19×C13⋊C3Dic3semidirect
14. C3⋊(Dic13⋊C3)C19direct (N × H)
16. C13×C19C3×Dic3semidirect
21. Dic39C3×C19semidirect
23. C3×C13⋊C3C4×C19semidirect
33. C3×C19Dic13⋊C3semidirect
35. C3×C13C3×C4×C19semidirect
37. C13⋊C3Dic3×C19semidirect
41. C19C3⋊(Dic13⋊C3)direct (N × H)
43. C13C3×Dic3×C19semidirect
53. C3C19×Dic13⋊C3semidirect