Finite Group Databasebeta

← C3⋊((C19⋊C3)⋊#261) #22580293

Subgroups — C3⋊((C19⋊C3)⋊#261) #22580293

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D13×C19⋊C3C211yesmaximal, characteristic
2C3⋊(C19⋊#261)C311yesmaximal, characteristic, complemented
3(C19⋊C3)⋊#261—31nomaximal
4C3×C13×C19⋊C3C411yescharacteristic, complemented, Hall
5C3×C19×D13C2×C311yescharacteristic
6D13×C19⋊C3—21no—
7D13×C19⋊C3D311yescharacteristic
8C19⋊#261—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10C13×C19⋊C3—21no—
11C13×C19⋊C3Dic311yescharacteristic, complemented
12C3⋊((C19⋊C3)⋊C4)—131nomaximal, Hall
13C19×D13C3×D311yescharacteristic
14C3×C3⋊#261—191nomaximal, Hall
15C2×C3×C19⋊C3—131no—
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C32×D13—191no—
18Dic57—131no—
19(C19⋊C3)⋊C4—391no—
20C3×C19⋊C3#26111yescharacteristic, complemented, Hall
21C3⋊#261—191no—
22C3×#261—571no—
23C32×C13—191noHall
24C2×C3×C19—131no—
25C2×C19⋊C3—131no—
26C2×C19⋊C3—261no—
27C3×D13—191no—
28C3×D13—381no—
29C3×D13D19⋊C311yescharacteristic
30Dic19—391noHall
31C3×C19C3×#26111yescharacteristic, complemented
32C19⋊C3—21no—
33C19⋊C3C3⋊#26111yescharacteristic, complemented
34#261—571noHall
35C3×C13—191no—
36C3×C13—381no—
37C3×C13(C19⋊C3)⋊C411yescharacteristic, complemented
38C2×C19—131no—
39C3×Dic3—2471noHall
40D13C3⋊(D19⋊C3)11yescharacteristic
41C19C3×C3⋊#26111yescharacteristic, complemented, Sylow
42C2×C32—2471no—
43C13C3⋊((C19⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
44C3×C4—7411no—
45Dic3—2471no—
46C32—191noSylow
47C2×C3—131no—
48C2×C3—4941no—
49C2×C3—2471no—
50C4—7411noSylow
51C3—191no—
52C3—381no—
53C3(C19⋊C3)⋊#26111yescharacteristic, complemented
54C2—131no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C13×C19C3×C4
LCSG ▷ C3×C13×C19
UCSC1

Complements

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

NH ≅ G/Ntype
2. C3⋊(C19⋊#261)C3semidirect
4. C3×C13×C19⋊C3C4semidirect
9. C3×C13×C19C3×C4semidirect
11. C13×C19⋊C3Dic3semidirect
16. C13×C19C3×Dic3semidirect
20. C3×C19⋊C3#261semidirect
31. C3×C19C3×#261semidirect
33. C19⋊C3C3⋊#261semidirect
37. C3×C13(C19⋊C3)⋊C4semidirect
41. C19C3×C3⋊#261semidirect
43. C13C3⋊((C19⋊C3)⋊C4)semidirect
53. C3(C19⋊C3)⋊#261semidirect