Finite Group Databasebeta

← C13×C3⋊((C19⋊C3)⋊C4) #22580203

Subgroups — C13×C3⋊((C19⋊C3)⋊C4) #22580203

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×C19⋊C3C211yesmaximal, characteristic
2C13×Dic57C311yesmaximal, characteristic, complemented
3C13×(C19⋊C3)⋊C4—31nomaximal
4C3×C13×C19⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19C2×C311yescharacteristic
6C2×C13×C19⋊C3—21no—
7C2×C13×C19⋊C3D311yescharacteristic
8C13×Dic19—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10C13×C19⋊C3—21no—
11C13×C19⋊C3Dic311yescharacteristic, complemented
12C3⋊((C19⋊C3)⋊C4)C1311yesmaximal, characteristic, direct product factor, Hall
13C2×C13×C19C3×D311yescharacteristic
14C3×Dic3×C13—191nomaximal, Hall
15C2×C3×C19⋊C3C2×C1311yescharacteristic
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C32×C13—191no—
18Dic57C3×C1311yescharacteristic, complemented
19(C19⋊C3)⋊C4—31no—
20C3×C19⋊C3C4×C1311yescharacteristic, complemented, Hall
21C3×C4×C13—571no—
22Dic3×C13—191no—
23C32×C13—191noHall
24C2×C3×C19C2×C3×C1311yescharacteristic
25C2×C19⋊C3—21no—
26C2×C19⋊C3D3×C1311yescharacteristic
27C2×C3×C13—191no—
28C2×C3×C13—381no—
29C2×C3×C13D19⋊C311yescharacteristic
30Dic19—31noHall
31C3×C19C3×C4×C1311yescharacteristic, complemented
32C19⋊C3—21no—
33C19⋊C3Dic3×C1311yescharacteristic, complemented
34C4×C13—571noHall
35C3×C13—191no—
36C3×C13—381no—
37C3×C13(C19⋊C3)⋊C411yescharacteristic, complemented
38C2×C19C3×D3×C1311yescharacteristic
39C3×Dic3—191noHall
40C2×C13C3⋊(D19⋊C3)11yescharacteristic
41C19C3×Dic3×C1311yescharacteristic, complemented, Sylow
42C2×C32—191no—
43C13C3⋊((C19⋊C3)⋊C4)11yescharacteristic, direct product factor, Sylow
44C3×C4—571no—
45Dic3—191no—
46C32—191noSylow
47C2×C3—191no—
48C2×C3—381no—
49C2×C3C13×D19⋊C311yescharacteristic
50C4—571noSylow
51C3—191no—
52C3—381no—
53C3C13×(C19⋊C3)⋊C411yescharacteristic, complemented
54C2C13×C3⋊(D19⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C13C3⋊(D19⋊C3)
commutator, hypocenterC3×C19C3×C4×C13
FrattiniC2C13×C3⋊(D19⋊C3)
Fitting, socleC2×C3×C13×C19C2×C3
LCSG ▷ C3×C19
UCSC1 ◁ C2×C13

Complements

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

NH ≅ G/Ntype
2. C13×Dic57C3semidirect
4. C3×C13×C19⋊C3C4semidirect
9. C3×C13×C19C3×C4semidirect
11. C13×C19⋊C3Dic3semidirect
12. C3⋊((C19⋊C3)⋊C4)C13direct (N × H)
16. C13×C19C3×Dic3semidirect
18. Dic57C3×C13semidirect
20. C3×C19⋊C3C4×C13semidirect
31. C3×C19C3×C4×C13semidirect
33. C19⋊C3Dic3×C13semidirect
37. C3×C13(C19⋊C3)⋊C4semidirect
41. C19C3×Dic3×C13semidirect
43. C13C3⋊((C19⋊C3)⋊C4)direct (N × H)
53. C3C13×(C19⋊C3)⋊C4semidirect