Finite Group Databasebeta

← AGL(1,𝔽5)×ΓL(1,𝔽8)×C31 #27189151

Subgroups — AGL(1,𝔽5)×ΓL(1,𝔽8)×C31 #27189151

Order 13020.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×ΓL(1,𝔽8)×C31C211yesmaximal, characteristic
2C7×AGL(1,𝔽5)×C31C311yesmaximal, characteristic, complemented, Hall
3C5×ΓL(1,𝔽8)×C31C411yescharacteristic, complemented, Hall
4C4×ΓL(1,𝔽8)×C31—51nomaximal, Hall
5C7×D5×C31C2×C311yescharacteristic
6C3×AGL(1,𝔽5)×C31—71nomaximal, Hall
7C2×ΓL(1,𝔽8)×C31—51no—
8C5×C7×C31C3×C411yescharacteristic, complemented, Hall
9C3×D5×C31—71no—
10C4×C7×C31—51noHall
11ΓL(1,𝔽8)×C31AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
12AGL(1,𝔽5)×C31ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
13C3×C5×C31—71noHall
14C2×C7×C31—51no—
15AGL(1,𝔽5)×ΓL(1,𝔽8)C3111yesmaximal, characteristic, direct product factor, Hall
16C3×C4×C31—351noHall
17D5×C31C2×ΓL(1,𝔽8)11yescharacteristic
18C7×C31C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
19D5×ΓL(1,𝔽8)C2×C3111yescharacteristic
20C2×C3×C31—351no—
21C5×C31C4×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
22C7×AGL(1,𝔽5)C3×C3111yescharacteristic, complemented, Hall
23C4×C31—51noHall
24C5×ΓL(1,𝔽8)C4×C3111yescharacteristic, complemented, Hall
25C3×C31—71noHall
26C4×ΓL(1,𝔽8)—51noHall
27C7×D5C2×C3×C3111yescharacteristic
28C2×C31—51no—
29C3×AGL(1,𝔽5)—71noHall
30C2×ΓL(1,𝔽8)—51no—
31C5×C7C3×C4×C3111yescharacteristic, complemented, Hall
32C31AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
33C3×D5—71no—
34C4×C7—51noHall
35ΓL(1,𝔽8)AGL(1,𝔽5)×C3111yescharacteristic, direct product factor, Hall
36AGL(1,𝔽5)ΓL(1,𝔽8)×C3111yescharacteristic, direct product factor, Hall
37C3×C5—71noHall
38C2×C7—51no—
39C3×C4—351noHall
40D5C2×ΓL(1,𝔽8)×C3111yescharacteristic
41C7C3×AGL(1,𝔽5)×C3111yescharacteristic, complemented, Sylow
42C2×C3—351no—
43C5C4×ΓL(1,𝔽8)×C3111yescharacteristic, complemented, Sylow
44C4—51noSylow
45C3—71noSylow
46C2—51no—
subgroupG/H
center, hypercenterC31AGL(1,𝔽5)×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C31
FrattiniC1G
Fitting, socleC5×C7×C31C3×C4
prime radicalD5×ΓL(1,𝔽8)×C31C2
cosocleC7×D5C2×C3×C31
LCSG ▷ C5×C7
UCSC1 ◁ C31

Complements

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

NH ≅ G/Ntype
2. C7×AGL(1,𝔽5)×C31C3semidirect
3. C5×ΓL(1,𝔽8)×C31C4semidirect
8. C5×C7×C31C3×C4semidirect
11. ΓL(1,𝔽8)×C31AGL(1,𝔽5)direct (N × H)
12. AGL(1,𝔽5)×C31ΓL(1,𝔽8)direct (N × H)
15. AGL(1,𝔽5)×ΓL(1,𝔽8)C31direct (N × H)
18. C7×C31C3×AGL(1,𝔽5)semidirect
21. C5×C31C4×ΓL(1,𝔽8)semidirect
22. C7×AGL(1,𝔽5)C3×C31semidirect
24. C5×ΓL(1,𝔽8)C4×C31semidirect
31. C5×C7C3×C4×C31semidirect
32. C31AGL(1,𝔽5)×ΓL(1,𝔽8)direct (N × H)
35. ΓL(1,𝔽8)AGL(1,𝔽5)×C31direct (N × H)
36. AGL(1,𝔽5)ΓL(1,𝔽8)×C31direct (N × H)
41. C7C3×AGL(1,𝔽5)×C31semidirect
43. C5C4×ΓL(1,𝔽8)×C31semidirect

Maximal subgroups

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

subgroupindex
D5×ΓL(1,𝔽8)×C312
C7×AGL(1,𝔽5)×C313
C4×ΓL(1,𝔽8)×C315
C3×AGL(1,𝔽5)×C317
AGL(1,𝔽5)×ΓL(1,𝔽8)31