Finite Group Databasebeta

← C5×C11×C22⋊(C13⋊C3) #22575179

Subgroups — C5×C11×C22⋊(C13⋊C3) #22575179

Order 8580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C11×C13C311yesmaximal, characteristic, complemented, Hall
2C5×C11×C13⋊C3—41nomaximal, Hall
3C11×C22⋊(C13⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
4C2×C5×C11×C13—31no—
5C5×C22⋊(C13⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
6C5×C11×C13A411yescharacteristic, complemented, Hall
7C5×C11×A4—131nomaximal, Hall
8C22×C11×C13C3×C511yescharacteristic, complemented, Hall
9C11×C13⋊C3—41noHall
10C2×C11×C13—31no—
11C22×C5×C13C3×C1111yescharacteristic, complemented, Hall
12C22×C5×C11C13⋊C311yescharacteristic, complemented, Hall
13C5×C13⋊C3—41noHall
14C3×C5×C11—521noHall
15C22⋊(C13⋊C3)C5×C1111yescharacteristic, direct product factor, Hall
16C11×C13C5×A411yescharacteristic, complemented, Hall
17C11×A4—131noHall
18C2×C5×C13—31no—
19C2×C5×C11—31no—
20C5×C13C11×A411yescharacteristic, complemented, Hall
21C5×A4—131noHall
22C5×C11C22⋊(C13⋊C3)11yescharacteristic, direct product factor, Hall
23C22×C13C3×C5×C1111yescharacteristic, complemented, Hall
24C22×C11C5×C13⋊C311yescharacteristic, complemented, Hall
25C13⋊C3—41noHall
26C3×C11—521noHall
27C2×C13—31no—
28C2×C11—31no—
29C22×C5C11×C13⋊C311yescharacteristic, complemented, Hall
30C3×C5—521noHall
31C13C5×C11×A411yescharacteristic, complemented, Sylow
32A4—131noHall
33C11C5×C22⋊(C13⋊C3)11yescharacteristic, direct product factor, Sylow
34C2×C5—31no—
35C5C11×C22⋊(C13⋊C3)11yescharacteristic, direct product factor, Sylow
36C22C5×C11×C13⋊C311yescharacteristic, complemented, Sylow
37C3—521noSylow
38C2—31no—
subgroupG/H
center, hypercenterC5×C11C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C22×C5×C11×C13C3semidirect
3. C11×C22⋊(C13⋊C3)C5direct (N × H)
5. C5×C22⋊(C13⋊C3)C11direct (N × H)
6. C5×C11×C13A4semidirect
8. C22×C11×C13C3×C5semidirect
11. C22×C5×C13C3×C11semidirect
12. C22×C5×C11C13⋊C3semidirect
15. C22⋊(C13⋊C3)C5×C11direct (N × H)
16. C11×C13C5×A4semidirect
20. C5×C13C11×A4semidirect
22. C5×C11C22⋊(C13⋊C3)direct (N × H)
23. C22×C13C3×C5×C11semidirect
24. C22×C11C5×C13⋊C3semidirect
29. C22×C5C11×C13⋊C3semidirect
31. C13C5×C11×A4semidirect
33. C11C5×C22⋊(C13⋊C3)direct (N × H)
35. C5C11×C22⋊(C13⋊C3)direct (N × H)
36. C22C5×C11×C13⋊C3semidirect