Finite Group Databasebeta

← C3⋊((C19⋊C3)⋊Dic13) #22580217

Subgroups — C3⋊((C19⋊C3)⋊Dic13) #22580217

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×C19⋊C3C211yesmaximal, characteristic
2Dic741C311yesmaximal, characteristic, complemented
3(C19⋊C3)⋊Dic13—31nomaximal
4C3×C13×C19⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19C2×C311yescharacteristic
6C2×C13×C19⋊C3—21no—
7C2×C13×C19⋊C3D311yescharacteristic
8Dic247—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10C13×C19⋊C3—21no—
11C13×C19⋊C3Dic311yescharacteristic, complemented
12C3⋊((C19⋊C3)⋊C4)—131nomaximal, Hall
13C2×C13×C19C3×D311yescharacteristic
14C3×Dic39—191nomaximal, Hall
15C2×C3×C19⋊C3D1311yescharacteristic
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C32×C13—191no—
18Dic57—131no—
19(C19⋊C3)⋊C4—391no—
20C3×C19⋊C3Dic1311yescharacteristic, complemented, Hall
21Dic39—191no—
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×C13D19⋊C311yescharacteristic
30Dic19—391noHall
31C3×C19C3×Dic1311yescharacteristic, complemented
32C19⋊C3—21no—
33C19⋊C3Dic3911yescharacteristic, complemented
34Dic13—571noHall
35C3×C13—191no—
36C3×C13—381no—
37C3×C13(C19⋊C3)⋊C411yescharacteristic, complemented
38C2×C19C3×D3911yescharacteristic
39C3×Dic3—2471noHall
40C2×C13C3⋊(D19⋊C3)11yescharacteristic
41C19C3×Dic3911yescharacteristic, complemented, Sylow
42C2×C32—191no—
43C13C3⋊((C19⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
44C3×C4—7411no—
45Dic3—2471no—
46C32—191noSylow
47C2×C3—191no—
48C2×C3—381no—
49C2×C3(C19⋊C3)⋊D1311yescharacteristic
50C4—7411noSylow
51C3—191no—
52C3—381no—
53C3(C19⋊C3)⋊Dic1311yescharacteristic, complemented
54C2C3⋊((C19⋊C3)⋊D13)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊((C19⋊C3)⋊D13)
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. Dic741C3semidirect
4. C3×C13×C19⋊C3C4semidirect
9. C3×C13×C19C3×C4semidirect
11. C13×C19⋊C3Dic3semidirect
16. C13×C19C3×Dic3semidirect
20. C3×C19⋊C3Dic13semidirect
31. C3×C19C3×Dic13semidirect
33. C19⋊C3Dic39semidirect
37. C3×C13(C19⋊C3)⋊C4semidirect
41. C19C3×Dic39semidirect
43. C13C3⋊((C19⋊C3)⋊C4)semidirect
53. C3(C19⋊C3)⋊Dic13semidirect