Finite Group Databasebeta

← D5×ΓL(1,𝔽8)×C151 #44540277

Subgroups — D5×ΓL(1,𝔽8)×C151 #44540277

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×ΓL(1,𝔽8)×C151C211yesmaximal, characteristic, complemented, Hall
2C7×D5×C151C311yesmaximal, characteristic, complemented, Hall
3C2×ΓL(1,𝔽8)×C151—51nomaximal, Hall
4C5×C7×C151C2×C311yescharacteristic, complemented, Hall
5C3×D5×C151—71nomaximal, Hall
6ΓL(1,𝔽8)×C151D511yescharacteristic, direct product factor, Hall
7C3×C5×C151—71noHall
8C2×C7×C151—51noHall
9D5×C151ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
10C7×C151C3×D511yescharacteristic, complemented, Hall
11C2×C3×C151—351noHall
12C5×C151C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
13C3×C151—71noHall
14C2×C151—51noHall
15D5×ΓL(1,𝔽8)C15111yesmaximal, characteristic, direct product factor, Hall
16C151D5×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
17C5×ΓL(1,𝔽8)C2×C15111yescharacteristic, complemented, Hall
18C7×D5C3×C15111yescharacteristic, complemented, Hall
19C2×ΓL(1,𝔽8)—51noHall
20C5×C7C2×C3×C15111yescharacteristic, complemented, Hall
21C3×D5—71noHall
22ΓL(1,𝔽8)D5×C15111yescharacteristic, direct product factor, Hall
23C3×C5—71noHall
24C2×C7—51noHall
25D5ΓL(1,𝔽8)×C15111yescharacteristic, direct product factor, Hall
26C7C3×D5×C15111yescharacteristic, complemented, Sylow
27C2×C3—351noHall
28C5C2×ΓL(1,𝔽8)×C15111yescharacteristic, complemented, Sylow
29C3—71noSylow
30C2—51noSylow
subgroupG/H
center, hypercenterC151D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C151
FrattiniC1G
Fitting, socleC5×C7×C151C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C151

Complements

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

NH ≅ G/Ntype
1. C5×ΓL(1,𝔽8)×C151C2semidirect
2. C7×D5×C151C3semidirect
4. C5×C7×C151C2×C3semidirect
6. ΓL(1,𝔽8)×C151D5direct (N × H)
9. D5×C151ΓL(1,𝔽8)direct (N × H)
10. C7×C151C3×D5semidirect
12. C5×C151C2×ΓL(1,𝔽8)semidirect
15. D5×ΓL(1,𝔽8)C151direct (N × H)
16. C151D5×ΓL(1,𝔽8)direct (N × H)
17. C5×ΓL(1,𝔽8)C2×C151semidirect
18. C7×D5C3×C151semidirect
20. C5×C7C2×C3×C151semidirect
22. ΓL(1,𝔽8)D5×C151direct (N × H)
25. D5ΓL(1,𝔽8)×C151direct (N × H)
26. C7C3×D5×C151semidirect
28. C5C2×ΓL(1,𝔽8)×C151semidirect

Maximal subgroups

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

subgroupindex
C5×ΓL(1,𝔽8)×C1512
C7×D5×C1513
C2×ΓL(1,𝔽8)×C1515
C3×D5×C1517
D5×ΓL(1,𝔽8)151