Finite Group Databasebeta

← C11×C49⋊AGL(1,𝔽5) #24924708

Subgroups — C11×C49⋊AGL(1,𝔽5) #24924708

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C11×C49C211yesmaximal, characteristic
2C5×C11×C49C411yescharacteristic, complemented, Hall
3C11×Dic49—51nomaximal, Hall
4C11×C7⋊AGL(1,𝔽5)—71nomaximal
5C2×C11×C49—51no—
6C49⋊AGL(1,𝔽5)C1111yesmaximal, characteristic, direct product factor, Hall
7C7×D5×C11D711yescharacteristic
8C11×C49AGL(1,𝔽5)11yescharacteristic, complemented, Hall
9D5×C49C2×C1111yescharacteristic
10C5×C7×C11Dic711yescharacteristic
11C11×Dic7—351no—
12C5×C49C4×C1111yescharacteristic, complemented, Hall
13C11×AGL(1,𝔽5)—491noHall
14Dic49—51noHall
15C2×C7×C11—51no—
16C7⋊AGL(1,𝔽5)—71no—
17D5×C11D4911yescharacteristic
18C2×C49—51no—
19C7×C11C7⋊AGL(1,𝔽5)11yescharacteristic
20C7×D5C11×D711yescharacteristic
21C5×C11Dic4911yescharacteristic, complemented, Hall
22C49C11×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
23C4×C11—2451noHall
24C5×C7C11×Dic711yescharacteristic
25Dic7—351no—
26C2×C11—51no—
27AGL(1,𝔽5)—491noHall
28C2×C7—51no—
29C11C49⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
30D5C11×D4911yescharacteristic
31C7C11×C7⋊AGL(1,𝔽5)11yescharacteristic
32C5C11×Dic4911yescharacteristic, complemented, Sylow
33C4—2451noSylow
34C2—51no—
subgroupG/H
center, hypercenterC11C49⋊AGL(1,𝔽5)
commutator, hypocenterC5×C49C4×C11
FrattiniC7C11×C7⋊AGL(1,𝔽5)
FittingC5×C11×C49C4
socleC5×C7×C11Dic7
prime radicalC7×D5×C11D7
cosocleD5×C49C2×C11
LCSG ▷ C5×C49
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
2. C5×C11×C49C4semidirect
6. C49⋊AGL(1,𝔽5)C11direct (N × H)
8. C11×C49AGL(1,𝔽5)semidirect
12. C5×C49C4×C11semidirect
21. C5×C11Dic49semidirect
22. C49C11×AGL(1,𝔽5)semidirect
29. C11C49⋊AGL(1,𝔽5)direct (N × H)
32. C5C11×Dic49semidirect