Finite Group Databasebeta

← C11×ΓL(1,𝔽32)⋊AGL(1,𝔽5) #46802067

Subgroups — C11×ΓL(1,𝔽32)⋊AGL(1,𝔽5) #46802067

Order 34100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C11×ΓL(1,𝔽32)C211yesmaximal, characteristic
2C5×C11×ΓL(1,𝔽32)C411yescharacteristic, complemented, Hall
3C11×C31⋊AGL(1,𝔽5)C511yesmaximal, characteristic, complemented
4C11×Dic31⋊C5—51nomaximal
5D5×C11×C31C2×C511yescharacteristic
6C2×C11×ΓL(1,𝔽32)—51no—
7ΓL(1,𝔽32)⋊AGL(1,𝔽5)C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C31C4×C511yescharacteristic, complemented
9C11×ΓL(1,𝔽32)—41no—
10C11×ΓL(1,𝔽32)AGL(1,𝔽5)11yescharacteristic, complemented
11D5×ΓL(1,𝔽32)C2×C1111yescharacteristic
12C11×Dic31—51noHall
13C5×C11×AGL(1,𝔽5)—311nomaximal, Hall
14C5×ΓL(1,𝔽32)C4×C1111yescharacteristic, complemented, Hall
15C2×C11×C31—51no—
16C31⋊AGL(1,𝔽5)C5×C1111yescharacteristic, complemented
17Dic31⋊C5—51no—
18C5×D5×C11—311no—
19C11×C31C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20D5×C31C2×C5×C1111yescharacteristic
21C2×ΓL(1,𝔽32)—51no—
22C52×C11—311noHall
23C11×AGL(1,𝔽5)—311no—
24C4×C5×C11—1551no—
25C5×C31C4×C5×C1111yescharacteristic, complemented
26ΓL(1,𝔽32)—41no—
27ΓL(1,𝔽32)C11×AGL(1,𝔽5)11yescharacteristic, complemented
28Dic31—51noHall
29C2×C5×C11—1551no—
30D5×C11D31⋊C511yescharacteristic
31C5×AGL(1,𝔽5)—311noHall
32C2×C31—51no—
33C5×C11—311no—
34C5×C11—1241no—
35C5×C11Dic31⋊C511yescharacteristic, complemented
36C5×D5—311no—
37C4×C11—1551noHall
38C31C5×C11×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
39C52—311noSylow
40C2×C11—51no—
41AGL(1,𝔽5)—311no—
42C4×C5—1551no—
43C11ΓL(1,𝔽32)⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
44C2×C5—1551no—
45D5C11×D31⋊C511yescharacteristic
46C5—311no—
47C5—1241no—
48C5C11×Dic31⋊C511yescharacteristic, complemented
49C4—1551noSylow
50C2—51no—
subgroupG/H
center, hypercenterC11ΓL(1,𝔽32)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C31C4×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C31C4×C5
prime radicalD5×C11×ΓL(1,𝔽32)C2
cosocleD5×C31C2×C5×C11
LCSG ▷ C5×C31
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
2. C5×C11×ΓL(1,𝔽32)C4semidirect
3. C11×C31⋊AGL(1,𝔽5)C5semidirect
7. ΓL(1,𝔽32)⋊AGL(1,𝔽5)C11direct (N × H)
8. C5×C11×C31C4×C5semidirect
10. C11×ΓL(1,𝔽32)AGL(1,𝔽5)semidirect
14. C5×ΓL(1,𝔽32)C4×C11semidirect
16. C31⋊AGL(1,𝔽5)C5×C11semidirect
19. C11×C31C5×AGL(1,𝔽5)semidirect
25. C5×C31C4×C5×C11semidirect
27. ΓL(1,𝔽32)C11×AGL(1,𝔽5)semidirect
35. C5×C11Dic31⋊C5semidirect
38. C31C5×C11×AGL(1,𝔽5)semidirect
43. C11ΓL(1,𝔽32)⋊AGL(1,𝔽5)direct (N × H)
48. C5C11×Dic31⋊C5semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D5×C11×ΓL(1,𝔽32)2
C11×C31⋊AGL(1,𝔽5)5
C11×Dic31⋊C55
ΓL(1,𝔽32)⋊AGL(1,𝔽5)11
C5×C11×AGL(1,𝔽5)31