Finite Group Databasebeta

← C22×C49×C11⋊C5 #24924705

Subgroups — C22×C49×C11⋊C5 #24924705

Order 10780.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C49×C11⋊C5C213yesmaximal, direct product factor
2C49×C11⋊C5C2211yescharacteristic, direct product factor, Hall
3C22×C11×C49C511yesmaximal, characteristic, complemented, Hall
4C22×C7×C11⋊C5C711yesmaximal, characteristic
5C2×C11×C49C2×C513yescomplemented
6C22×C5×C49—111nomaximal, Hall
7C2×C7×C11⋊C5C2×C713yes—
8C11×C49C22×C511yescharacteristic, complemented, Hall
9C2×C5×C49—113no—
10C7×C11⋊C5C22×C711yescharacteristic
11C22×C7×C11C5×C711yescharacteristic
12C5×C49—111noHall
13C22×C11⋊C5C4911yescharacteristic, direct product factor, Hall
14C22×C49C11⋊C511yescharacteristic, direct product factor, Hall
15C2×C7×C11C2×C5×C713yes—
16C22×C5×C7—111no—
17C2×C11⋊C5C2×C4913yesdirect product factor
18C2×C49C2×C11⋊C513yesdirect product factor
19C7×C11C22×C5×C711yescharacteristic
20C2×C5×C7—113no—
21C11⋊C5C22×C4911yescharacteristic, direct product factor, Hall
22C49C22×C11⋊C511yescharacteristic, direct product factor, Sylow
23C22×C11C5×C4911yescharacteristic, complemented, Hall
24C5×C7—111no—
25C22×C7C7×C11⋊C511yescharacteristic
26C2×C11C2×C5×C4913yescomplemented
27C22×C5—111noHall
28C2×C7C2×C7×C11⋊C513yes—
29C11C22×C5×C4911yescharacteristic, complemented, Sylow
30C2×C5—113no—
31C7C22×C7×C11⋊C511yescharacteristic
32C5—111noSylow
33C22C49×C11⋊C511yescharacteristic, direct product factor, Sylow
34C2C2×C49×C11⋊C513yesdirect product factor
subgroupG/H
center, hypercenterC22×C49C11⋊C5
commutator, hypocenterC11C22×C5×C49
FrattiniC7C22×C7×C11⋊C5
FittingC22×C11×C49C5
socleC22×C7×C11C5×C7
prime radicalC22×C7×C11⋊C5C7
cosocleC7×C11C22×C5×C7
LCSG ▷ C11
UCSC1 ◁ C22×C49

Complements

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

NH ≅ G/Ntype
1. C2×C49×C11⋊C5C2direct (N × H)
2. C49×C11⋊C5C22direct (N × H)
3. C22×C11×C49C5semidirect
5. C2×C11×C49C2×C5semidirect
8. C11×C49C22×C5semidirect
13. C22×C11⋊C5C49direct (N × H)
14. C22×C49C11⋊C5direct (N × H)
17. C2×C11⋊C5C2×C49direct (N × H)
18. C2×C49C2×C11⋊C5direct (N × H)
21. C11⋊C5C22×C49direct (N × H)
22. C49C22×C11⋊C5direct (N × H)
23. C22×C11C5×C49semidirect
26. C2×C11C2×C5×C49semidirect
29. C11C22×C5×C49semidirect
33. C22C49×C11⋊C5direct (N × H)
34. C2C2×C49×C11⋊C5direct (N × H)