Finite Group Databasebeta

← C13⋊C3×Dic57 #22580216

Subgroups — C13⋊C3×Dic57 #22580216

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19×C13⋊C3C211yesmaximal, characteristic
2C13×Dic57C311yesmaximal, characteristic, complemented
3C13⋊C3×Dic19—31nomaximal
4C3×C19×C13⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19C2×C311yescharacteristic
6C2×C19×C13⋊C3—21no—
7C2×C19×C13⋊C3D311yescharacteristic
8C13×Dic19—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10C19×C13⋊C3—21no—
11C19×C13⋊C3Dic311yescharacteristic, complemented
12C3×Dic57—131nomaximal, Hall
13C2×C13×C19C3×D311yescharacteristic
14Dic3×C13⋊C3—191nomaximal, Hall
15C2×C32×C19—131no—
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C3×C13⋊C3D1911yescharacteristic
18Dic57C13⋊C311yescharacteristic, direct product factor
19C3×Dic19—391no—
20C32×C19—131noHall
21Dic3×C13—191no—
22C4×C13⋊C3—571no—
23C3×C13⋊C3Dic1911yescharacteristic, complemented, Hall
24C2×C3×C19—131no—
25C2×C3×C19—261no—
26C2×C3×C19C2×C13⋊C311yescharacteristic
27C2×C3×C13C3×D1911yescharacteristic
28C2×C13⋊C3—21no—
29C2×C13⋊C3D5711yescharacteristic
30Dic19—31noHall
31C3×C19—131no—
32C3×C19—261no—
33C3×C19C4×C13⋊C311yescharacteristic, complemented
34C4×C13—571noHall
35C3×C13C3×Dic1911yescharacteristic, complemented
36C13⋊C3—21no—
37C13⋊C3Dic5711yescharacteristic, direct product factor
38C2×C19D3×C13⋊C311yescharacteristic
39C3×Dic3—2471noHall
40C2×C13C3×D5711yescharacteristic
41C19Dic3×C13⋊C311yescharacteristic, complemented, Sylow
42C2×C32—131no—
43C13C3×Dic5711yescharacteristic, complemented, Sylow
44C3×C4—7411no—
45Dic3—191no—
46C32—131noSylow
47C2×C3—131no—
48C2×C3—261no—
49C2×C3D19×C13⋊C311yescharacteristic
50C4—571noSylow
51C3—131no—
52C3—261no—
53C3C13⋊C3×Dic1911yescharacteristic, complemented
54C2C13⋊C3×D5711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×D57
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. C13×Dic57C3semidirect
4. C3×C19×C13⋊C3C4semidirect
9. C3×C13×C19C3×C4semidirect
11. C19×C13⋊C3Dic3semidirect
16. C13×C19C3×Dic3semidirect
18. Dic57C13⋊C3direct (N × H)
23. C3×C13⋊C3Dic19semidirect
33. C3×C19C4×C13⋊C3semidirect
35. C3×C13C3×Dic19semidirect
37. C13⋊C3Dic57direct (N × H)
41. C19Dic3×C13⋊C3semidirect
43. C13C3×Dic57semidirect
53. C3C13⋊C3×Dic19semidirect