Finite Group Databasebeta

← C2×ΓL(1,𝔽8)×C151⋊C5 #44540239

Subgroups — C2×ΓL(1,𝔽8)×C151⋊C5 #44540239

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1ΓL(1,𝔽8)×C151⋊C5C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C151⋊C5C311yesmaximal, characteristic, complemented, Hall
3C2×ΓL(1,𝔽8)×C151C511yesmaximal, characteristic, complemented, Hall
4C7×C151⋊C5C2×C311yescharacteristic, complemented, Hall
5C2×C3×C151⋊C5—71nomaximal, Hall
6ΓL(1,𝔽8)×C151C2×C511yescharacteristic, complemented, Hall
7C3×C151⋊C5—71noHall
8C2×C7×C151C3×C511yescharacteristic, complemented, Hall
9C2×C151⋊C5ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
10C7×C151C2×C3×C511yescharacteristic, complemented, Hall
11C2×C3×C151—71noHall
12C151⋊C5C2×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
13C3×C151—71noHall
14C2×C151C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
15C2×C5×ΓL(1,𝔽8)—1511nomaximal, Hall
16C151C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
17C5×ΓL(1,𝔽8)—1511noHall
18C2×C5×C7—1511noHall
19C2×ΓL(1,𝔽8)C151⋊C511yescharacteristic, direct product factor, Hall
20C5×C7—1511noHall
21C2×C3×C5—10571noHall
22ΓL(1,𝔽8)C2×C151⋊C511yescharacteristic, direct product factor, Hall
23C3×C5—10571noHall
24C2×C7C3×C151⋊C511yescharacteristic, complemented, Hall
25C2×C5—1511noHall
26C7C2×C3×C151⋊C511yescharacteristic, complemented, Sylow
27C2×C3—71noHall
28C5—1511noSylow
29C3—71noSylow
30C2ΓL(1,𝔽8)×C151⋊C511yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×C151⋊C5
commutator, cosocle, hypocenterC7×C151C2×C3×C5
FrattiniC1G
Fitting, socleC2×C7×C151C3×C5
LCSG ▷ C7×C151
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. ΓL(1,𝔽8)×C151⋊C5C2direct (N × H)
2. C2×C7×C151⋊C5C3semidirect
3. C2×ΓL(1,𝔽8)×C151C5semidirect
4. C7×C151⋊C5C2×C3semidirect
6. ΓL(1,𝔽8)×C151C2×C5semidirect
8. C2×C7×C151C3×C5semidirect
9. C2×C151⋊C5ΓL(1,𝔽8)direct (N × H)
10. C7×C151C2×C3×C5semidirect
12. C151⋊C5C2×ΓL(1,𝔽8)direct (N × H)
14. C2×C151C5×ΓL(1,𝔽8)semidirect
16. C151C2×C5×ΓL(1,𝔽8)semidirect
19. C2×ΓL(1,𝔽8)C151⋊C5direct (N × H)
22. ΓL(1,𝔽8)C2×C151⋊C5direct (N × H)
24. C2×C7C3×C151⋊C5semidirect
26. C7C2×C3×C151⋊C5semidirect
30. C2ΓL(1,𝔽8)×C151⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
ΓL(1,𝔽8)×C151⋊C52
C2×C7×C151⋊C53
C2×ΓL(1,𝔽8)×C1515
C2×C3×C151⋊C57
C2×C5×ΓL(1,𝔽8)151