Finite Group Databasebeta

← C19⋊C3×Dic39 #22580218

Subgroups — C19⋊C3×Dic39 #22580218

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×C19⋊C3C211yesmaximal, characteristic
2C19×Dic39C311yesmaximal, characteristic, complemented
3Dic13×C19⋊C3—31nomaximal
4C3×C13×C19⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19C2×C311yescharacteristic
6C2×C13×C19⋊C3—21no—
7C2×C13×C19⋊C3D311yescharacteristic
8C19×Dic13—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10C13×C19⋊C3—21no—
11C13×C19⋊C3Dic311yescharacteristic, complemented
12Dic3×C19⋊C3—131nomaximal, Hall
13C2×C13×C19C3×D311yescharacteristic
14C3×Dic39—191nomaximal, Hall
15C2×C3×C19⋊C3D1311yescharacteristic
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C32×C13—191no—
18Dic3×C19—131no—
19C4×C19⋊C3—391no—
20C3×C19⋊C3Dic1311yescharacteristic, complemented, Hall
21Dic39C19⋊C311yescharacteristic, direct product factor
22C3×Dic13—571no—
23C32×C13—191noHall
24C2×C3×C19C3×D1311yescharacteristic
25C2×C19⋊C3—21no—
26C2×C19⋊C3D3911yescharacteristic
27C2×C3×C13—191no—
28C2×C3×C13—381no—
29C2×C3×C13C2×C19⋊C311yescharacteristic
30C4×C19—391noHall
31C3×C19C3×Dic1311yescharacteristic, complemented
32C19⋊C3—21no—
33C19⋊C3Dic3911yescharacteristic, direct product factor
34Dic13—31noHall
35C3×C13—191no—
36C3×C13—381no—
37C3×C13C4×C19⋊C311yescharacteristic, complemented
38C2×C19C3×D3911yescharacteristic
39C3×Dic3—2471noHall
40C2×C13D3×C19⋊C311yescharacteristic
41C19C3×Dic3911yescharacteristic, complemented, Sylow
42C2×C32—191no—
43C13Dic3×C19⋊C311yescharacteristic, complemented, Sylow
44C3×C4—7411no—
45Dic3—131no—
46C32—191noSylow
47C2×C3—191no—
48C2×C3—381no—
49C2×C3D13×C19⋊C311yescharacteristic
50C4—391noSylow
51C3—191no—
52C3—381no—
53C3Dic13×C19⋊C311yescharacteristic, complemented
54C2C19⋊C3×D3911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C19⋊C3×D39
commutator, hypocenterC3×C13×C19C3×C4
Fitting, socleC2×C3×C13×C19C2×C3
LCSG ▷ C3×C13×C19
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C19×Dic39C3semidirect
4. C3×C13×C19⋊C3C4semidirect
9. C3×C13×C19C3×C4semidirect
11. C13×C19⋊C3Dic3semidirect
16. C13×C19C3×Dic3semidirect
20. C3×C19⋊C3Dic13semidirect
21. Dic39C19⋊C3direct (N × H)
31. C3×C19C3×Dic13semidirect
33. C19⋊C3Dic39direct (N × H)
37. C3×C13C4×C19⋊C3semidirect
41. C19C3×Dic39semidirect
43. C13Dic3×C19⋊C3semidirect
53. C3Dic13×C19⋊C3semidirect