Finite Group Databasebeta

← C22×C72×C11⋊C5 #24924755

Subgroups — C22×C72×C11⋊C5 #24924755

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C72×C11⋊C5C213yesmaximal, direct product factor
2C72×C11⋊C5C2211yescharacteristic, direct product factor, Hall
3C22×C72×C11C511yesmaximal, characteristic, complemented, Hall
4C22×C7×C11⋊C5C718yesmaximal, direct product factor
5C2×C72×C11C2×C513yescomplemented
6C22×C5×C72—111nomaximal, Hall
7C2×C7×C11⋊C5C2×C7124yesdirect product factor
8C72×C11C22×C511yescharacteristic, complemented, Hall
9C2×C5×C72—113no—
10C7×C11⋊C5C22×C718yesdirect product factor
11C22×C7×C11C5×C718yescomplemented
12C5×C72—111noHall
13C22×C11⋊C5C7211yescharacteristic, direct product factor, Hall
14C22×C72C11⋊C511yescharacteristic, direct product factor, Hall
15C2×C7×C11C2×C5×C7124yescomplemented
16C22×C5×C7—118no—
17C2×C11⋊C5C2×C7213yesdirect product factor
18C2×C72C2×C11⋊C513yesdirect product factor
19C7×C11C22×C5×C718yescomplemented
20C2×C5×C7—1124no—
21C11⋊C5C22×C7211yescharacteristic, direct product factor, Hall
22C72C22×C11⋊C511yescharacteristic, direct product factor, Sylow
23C22×C11C5×C7211yescharacteristic, complemented, Hall
24C5×C7—118no—
25C22×C7C7×C11⋊C518yesdirect product factor
26C2×C11C2×C5×C7213yescomplemented
27C22×C5—111noHall
28C2×C7C2×C7×C11⋊C5124yesdirect product factor
29C11C22×C5×C7211yescharacteristic, complemented, Sylow
30C2×C5—113no—
31C7C22×C7×C11⋊C518yesdirect product factor
32C5—111noSylow
33C22C72×C11⋊C511yescharacteristic, direct product factor, Sylow
34C2C2×C72×C11⋊C513yesdirect product factor
subgroupG/H
center, hypercenterC22×C72C11⋊C5
commutator, cosocle, hypocenterC11C22×C5×C72
FrattiniC1G
Fitting, socleC22×C72×C11C5
LCSG ▷ C11
UCSC1 ◁ C22×C72

Complements

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

NH ≅ G/Ntype
1. C2×C72×C11⋊C5C2direct (N × H)
2. C72×C11⋊C5C22direct (N × H)
3. C22×C72×C11C5semidirect
4. C22×C7×C11⋊C5C7direct (N × H)
5. C2×C72×C11C2×C5semidirect
7. C2×C7×C11⋊C5C2×C7direct (N × H)
8. C72×C11C22×C5semidirect
10. C7×C11⋊C5C22×C7direct (N × H)
11. C22×C7×C11C5×C7semidirect
13. C22×C11⋊C5C72direct (N × H)
14. C22×C72C11⋊C5direct (N × H)
15. C2×C7×C11C2×C5×C7semidirect
17. C2×C11⋊C5C2×C72direct (N × H)
18. C2×C72C2×C11⋊C5direct (N × H)
19. C7×C11C22×C5×C7semidirect
21. C11⋊C5C22×C72direct (N × H)
22. C72C22×C11⋊C5direct (N × H)
23. C22×C11C5×C72semidirect
25. C22×C7C7×C11⋊C5direct (N × H)
26. C2×C11C2×C5×C72semidirect
28. C2×C7C2×C7×C11⋊C5direct (N × H)
29. C11C22×C5×C72semidirect
31. C7C22×C7×C11⋊C5direct (N × H)
33. C22C72×C11⋊C5direct (N × H)
34. C2C2×C72×C11⋊C5direct (N × H)