Finite Group Databasebeta

← C11⋊C5×Dic49 #24924690

Subgroups — C11⋊C5×Dic49 #24924690

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C49×C11⋊C5C211yesmaximal, characteristic
2C49×C11⋊C5C411yescharacteristic, complemented, Hall
3C11×Dic49C511yesmaximal, characteristic, complemented, Hall
4Dic7×C11⋊C5—71nomaximal
5C2×C11×C49C2×C511yescharacteristic
6C5×Dic49—111nomaximal, Hall
7C2×C7×C11⋊C5D711yescharacteristic
8C11×C49C4×C511yescharacteristic, complemented, Hall
9C2×C5×C49—111no—
10C7×C11⋊C5Dic711yescharacteristic
11C11×Dic7—71no—
12C5×C49—111noHall
13C4×C11⋊C5—491noHall
14Dic49C11⋊C511yescharacteristic, direct product factor, Hall
15C2×C7×C11C5×D711yescharacteristic
16C5×Dic7—771no—
17C2×C11⋊C5D4911yescharacteristic
18C2×C49C2×C11⋊C511yescharacteristic
19C7×C11C5×Dic711yescharacteristic
20C2×C5×C7—111no—
21C11⋊C5Dic4911yescharacteristic, direct product factor, Hall
22C49C4×C11⋊C511yescharacteristic, complemented, Sylow
23C4×C11—491noHall
24C5×C7—111no—
25Dic7—71no—
26C2×C11C5×D4911yescharacteristic
27C4×C5—5391noHall
28C2×C7D7×C11⋊C511yescharacteristic
29C11C5×Dic4911yescharacteristic, complemented, Sylow
30C2×C5—111no—
31C7Dic7×C11⋊C511yescharacteristic
32C5—111noSylow
33C4—491noSylow
34C2C11⋊C5×D4911yescharacteristic
subgroupG/H
center, hypercenterC2C11⋊C5×D49
commutator, hypocenterC11×C49C4×C5
FrattiniC2×C7D7×C11⋊C5
Fitting, cosocleC2×C11×C49C2×C5
socleC2×C7×C11C5×D7
prime radicalC2×C7×C11⋊C5D7
LCSG ▷ C11×C49
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C49×C11⋊C5C4semidirect
3. C11×Dic49C5semidirect
8. C11×C49C4×C5semidirect
14. Dic49C11⋊C5direct (N × H)
21. C11⋊C5Dic49direct (N × H)
22. C49C4×C11⋊C5semidirect
29. C11C5×Dic49semidirect