Finite Group Databasebeta

← C2×C7×(C151⋊C3)⋊C5 #44540238

Subgroups — C2×C7×(C151⋊C3)⋊C5 #44540238

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×(C151⋊C3)⋊C5C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C151⋊C5C311yesmaximal, characteristic, complemented, Hall
3C2×C7×C151⋊C3C511yesmaximal, characteristic, complemented, Hall
4C7×C151⋊C5C2×C311yescharacteristic, complemented, Hall
5C2×(C151⋊C3)⋊C5C711yesmaximal, characteristic, direct product factor, Hall
6C7×C151⋊C3C2×C511yescharacteristic, complemented, Hall
7(C151⋊C3)⋊C5C2×C711yescharacteristic, direct product factor, Hall
8C2×C7×C151C3×C511yescharacteristic, complemented, Hall
9C2×C151⋊C5C3×C711yescharacteristic, complemented, Hall
10C7×C151C2×C3×C511yescharacteristic, complemented, Hall
11C2×C151⋊C3C5×C711yescharacteristic, complemented, Hall
12C151⋊C5C2×C3×C711yescharacteristic, complemented, Hall
13C151⋊C3C2×C5×C711yescharacteristic, complemented, Hall
14C2×C151C3×C5×C711yescharacteristic, complemented, Hall
15C2×C3×C5×C7—1511nomaximal, Hall
16C151C2×C3×C5×C711yescharacteristic, complemented, Sylow
17C3×C5×C7—1511noHall
18C2×C5×C7—1511noHall
19C2×C3×C7—1511noHall
20C5×C7—1511noHall
21C2×C3×C5—1511noHall
22C3×C7—1511noHall
23C3×C5—1511noHall
24C2×C7(C151⋊C3)⋊C511yescharacteristic, direct product factor, Hall
25C2×C5—1511noHall
26C7C2×(C151⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
27C2×C3—1511noHall
28C5—1511noSylow
29C3—1511noSylow
30C2C7×(C151⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C7(C151⋊C3)⋊C5
commutator, cosocle, hypocenterC151C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C7×C151C3×C5
LCSG ▷ C151
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×(C151⋊C3)⋊C5C2direct (N × H)
2. C2×C7×C151⋊C5C3semidirect
3. C2×C7×C151⋊C3C5semidirect
4. C7×C151⋊C5C2×C3semidirect
5. C2×(C151⋊C3)⋊C5C7direct (N × H)
6. C7×C151⋊C3C2×C5semidirect
7. (C151⋊C3)⋊C5C2×C7direct (N × H)
8. C2×C7×C151C3×C5semidirect
9. C2×C151⋊C5C3×C7semidirect
10. C7×C151C2×C3×C5semidirect
11. C2×C151⋊C3C5×C7semidirect
12. C151⋊C5C2×C3×C7semidirect
13. C151⋊C3C2×C5×C7semidirect
14. C2×C151C3×C5×C7semidirect
16. C151C2×C3×C5×C7semidirect
24. C2×C7(C151⋊C3)⋊C5direct (N × H)
26. C7C2×(C151⋊C3)⋊C5direct (N × H)
30. C2C7×(C151⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C7×(C151⋊C3)⋊C52
C2×C7×C151⋊C53
C2×C7×C151⋊C35
C2×(C151⋊C3)⋊C57
C2×C3×C5×C7151