Finite Group Databasebeta

← C5×C13⋊C3×C11⋊C5 #24924332

Subgroups — C5×C13⋊C3×C11⋊C5 #24924332

Order 10725.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C13×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
2C13⋊C3×C11⋊C5C515yesmaximal, direct product factor
3C5×C11×C13⋊C3C511yesmaximal, characteristic, complemented
4C52×C13⋊C3—111nomaximal, Hall
5C3×C5×C11⋊C5—131nomaximal, Hall
6C5×C11×C13C3×C511yescharacteristic, complemented
7C13×C11⋊C5C3×C515yescomplemented
8C11×C13⋊C3C5211yescharacteristic, complemented, Hall
9C52×C13—111noHall
10C5×C11⋊C5C13⋊C311yescharacteristic, direct product factor, Hall
11C5×C13⋊C3—115no—
12C5×C13⋊C3C11⋊C511yescharacteristic, direct product factor
13C3×C5×C11—131no—
14C3×C11⋊C5—135no—
15C11×C13C3×C5211yescharacteristic, complemented, Hall
16C3×C52—1431noHall
17C5×C13—115no—
18C5×C13C3×C11⋊C511yescharacteristic, complemented
19C5×C11C5×C13⋊C311yescharacteristic, complemented
20C11⋊C5C5×C13⋊C315yesdirect product factor
21C13⋊C3C5×C11⋊C511yescharacteristic, direct product factor, Hall
22C3×C11—131noHall
23C52—111noSylow
24C3×C5—131no—
25C3×C5—1435no—
26C13C3×C5×C11⋊C511yescharacteristic, complemented, Sylow
27C11C52×C13⋊C311yescharacteristic, complemented, Sylow
28C5—115no—
29C5C13⋊C3×C11⋊C511yescharacteristic, direct product factor
30C3—131noSylow
subgroupG/H
center, hypercenterC5C13⋊C3×C11⋊C5
commutator, cosocle, hypocenterC11×C13C3×C52
FrattiniC1G
Fitting, socleC5×C11×C13C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C13×C11⋊C5C3semidirect
2. C13⋊C3×C11⋊C5C5direct (N × H)
3. C5×C11×C13⋊C3C5semidirect
6. C5×C11×C13C3×C5semidirect
7. C13×C11⋊C5C3×C5semidirect
8. C11×C13⋊C3C52semidirect
10. C5×C11⋊C5C13⋊C3direct (N × H)
12. C5×C13⋊C3C11⋊C5direct (N × H)
15. C11×C13C3×C52semidirect
18. C5×C13C3×C11⋊C5semidirect
19. C5×C11C5×C13⋊C3semidirect
20. C11⋊C5C5×C13⋊C3direct (N × H)
21. C13⋊C3C5×C11⋊C5direct (N × H)
26. C13C3×C5×C11⋊C5semidirect
27. C11C52×C13⋊C3semidirect
29. C5C13⋊C3×C11⋊C5direct (N × H)