Finite Group Databasebeta

← C3×C5×C13×C11⋊C5 #24924333

Subgroups — C3×C5×C13×C11⋊C5 #24924333

Order 10725.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C13×C11⋊C5C311yesmaximal, characteristic, direct product factor, Hall
2C3×C13×C11⋊C5C515yesmaximal, direct product factor
3C3×C5×C11×C13C511yesmaximal, characteristic, complemented
4C3×C52×C13—111nomaximal, Hall
5C3×C5×C11⋊C5C1311yesmaximal, characteristic, direct product factor, Hall
6C5×C11×C13C3×C511yescharacteristic, complemented
7C13×C11⋊C5C3×C515yesdirect product factor
8C3×C11×C13C5211yescharacteristic, complemented, Hall
9C52×C13—111noHall
10C5×C11⋊C5C3×C1311yescharacteristic, direct product factor, Hall
11C3×C5×C13—115no—
12C3×C5×C13C11⋊C511yescharacteristic, direct product factor
13C3×C5×C11C5×C1311yescharacteristic, complemented
14C3×C11⋊C5C5×C1315yesdirect product factor
15C11×C13C3×C5211yescharacteristic, complemented, Hall
16C3×C52—111noHall
17C5×C13—115no—
18C5×C13C3×C11⋊C511yescharacteristic, direct product factor
19C5×C11C3×C5×C1311yescharacteristic, complemented
20C11⋊C5C3×C5×C1315yesdirect product factor
21C3×C13C5×C11⋊C511yescharacteristic, direct product factor, Hall
22C3×C11C52×C1311yescharacteristic, complemented, Hall
23C52—111noSylow
24C3×C5—115no—
25C3×C5C13×C11⋊C511yescharacteristic, direct product factor
26C13C3×C5×C11⋊C511yescharacteristic, direct product factor, Sylow
27C11C3×C52×C1311yescharacteristic, complemented, Sylow
28C5—115no—
29C5C3×C13×C11⋊C511yescharacteristic, direct product factor
30C3C5×C13×C11⋊C511yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC3×C5×C13C11⋊C5
commutator, cosocle, hypocenterC11C3×C52×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C5
LCSG ▷ C11
UCSC1 ◁ C3×C5×C13

Complements

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

NH ≅ G/Ntype
1. C5×C13×C11⋊C5C3direct (N × H)
2. C3×C13×C11⋊C5C5direct (N × H)
3. C3×C5×C11×C13C5semidirect
5. C3×C5×C11⋊C5C13direct (N × H)
6. C5×C11×C13C3×C5semidirect
7. C13×C11⋊C5C3×C5direct (N × H)
8. C3×C11×C13C52semidirect
10. C5×C11⋊C5C3×C13direct (N × H)
12. C3×C5×C13C11⋊C5direct (N × H)
13. C3×C5×C11C5×C13semidirect
14. C3×C11⋊C5C5×C13direct (N × H)
15. C11×C13C3×C52semidirect
18. C5×C13C3×C11⋊C5direct (N × H)
19. C5×C11C3×C5×C13semidirect
20. C11⋊C5C3×C5×C13direct (N × H)
21. C3×C13C5×C11⋊C5direct (N × H)
22. C3×C11C52×C13semidirect
25. C3×C5C13×C11⋊C5direct (N × H)
26. C13C3×C5×C11⋊C5direct (N × H)
27. C11C3×C52×C13semidirect
29. C5C3×C13×C11⋊C5direct (N × H)
30. C3C5×C13×C11⋊C5direct (N × H)