Finite Group Databasebeta

← C5×(C151⋊C3)⋊D7 #44540272

Subgroups — C5×(C151⋊C3)⋊D7 #44540272

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C7×C151⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5×D1057C311yesmaximal, characteristic, complemented, Hall
3(C151⋊C3)⋊D7C511yesmaximal, characteristic, direct product factor, Hall
4C5×C7×C151C2×C311yescharacteristic, complemented, Hall
5C5×D151⋊C3—71nomaximal, Hall
6C7×C151⋊C3C2×C511yescharacteristic, complemented, Hall
7C5×C151⋊C3D711yescharacteristic, complemented, Hall
8D1057C3×C511yescharacteristic, complemented, Hall
9C5×D151—71noHall
10C7×C151C2×C3×C511yescharacteristic, complemented, Hall
11D151⋊C3—71noHall
12C5×C151C3×D711yescharacteristic, complemented, Hall
13C151⋊C3C5×D711yescharacteristic, complemented, Hall
14D151—71noHall
15C3×C5×D7—1511nomaximal, Hall
16C151C3×C5×D711yescharacteristic, complemented, Sylow
17C3×C5×C7—1511noHall
18C5×D7—1511noHall
19C3×D7—1511noHall
20C5×C7D151⋊C311yescharacteristic, complemented, Hall
21C2×C3×C5—10571noHall
22C3×C7—1511noHall
23C3×C5—1511noHall
24D7—1511noHall
25C2×C5—10571noHall
26C7C5×D151⋊C311yescharacteristic, complemented, Sylow
27C2×C3—10571noHall
28C5(C151⋊C3)⋊D711yescharacteristic, direct product factor, Sylow
29C3—1511noSylow
30C2—10571noSylow
subgroupG/H
center, hypercenterC5(C151⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C151C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C151C2×C3
LCSG ▷ C7×C151
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C7×C151⋊C3C2semidirect
2. C5×D1057C3semidirect
3. (C151⋊C3)⋊D7C5direct (N × H)
4. C5×C7×C151C2×C3semidirect
6. C7×C151⋊C3C2×C5semidirect
7. C5×C151⋊C3D7semidirect
8. D1057C3×C5semidirect
10. C7×C151C2×C3×C5semidirect
12. C5×C151C3×D7semidirect
13. C151⋊C3C5×D7semidirect
16. C151C3×C5×D7semidirect
20. C5×C7D151⋊C3semidirect
26. C7C5×D151⋊C3semidirect
28. C5(C151⋊C3)⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×C151⋊C32
C5×D10573
(C151⋊C3)⋊D75
C5×D151⋊C37
C3×C5×D7151