Finite Group Databasebeta

← C2×C3×C5×C7×C151 #44540232

Subgroups — C2×C3×C5×C7×C151 #44540232

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C7×C151C211yesmaximal, characteristic, direct product factor, Hall
2C2×C5×C7×C151C311yesmaximal, characteristic, direct product factor, Hall
3C2×C3×C7×C151C511yesmaximal, characteristic, direct product factor, Hall
4C5×C7×C151C2×C311yescharacteristic, direct product factor, Hall
5C2×C3×C5×C151C711yesmaximal, characteristic, direct product factor, Hall
6C3×C7×C151C2×C511yescharacteristic, direct product factor, Hall
7C3×C5×C151C2×C711yescharacteristic, direct product factor, Hall
8C2×C7×C151C3×C511yescharacteristic, direct product factor, Hall
9C2×C5×C151C3×C711yescharacteristic, direct product factor, Hall
10C7×C151C2×C3×C511yescharacteristic, direct product factor, Hall
11C2×C3×C151C5×C711yescharacteristic, direct product factor, Hall
12C5×C151C2×C3×C711yescharacteristic, direct product factor, Hall
13C3×C151C2×C5×C711yescharacteristic, direct product factor, Hall
14C2×C151C3×C5×C711yescharacteristic, direct product factor, Hall
15C2×C3×C5×C7C15111yesmaximal, characteristic, direct product factor, Hall
16C151C2×C3×C5×C711yescharacteristic, direct product factor, Sylow
17C3×C5×C7C2×C15111yescharacteristic, direct product factor, Hall
18C2×C5×C7C3×C15111yescharacteristic, direct product factor, Hall
19C2×C3×C7C5×C15111yescharacteristic, direct product factor, Hall
20C5×C7C2×C3×C15111yescharacteristic, direct product factor, Hall
21C2×C3×C5C7×C15111yescharacteristic, direct product factor, Hall
22C3×C7C2×C5×C15111yescharacteristic, direct product factor, Hall
23C3×C5C2×C7×C15111yescharacteristic, direct product factor, Hall
24C2×C7C3×C5×C15111yescharacteristic, direct product factor, Hall
25C2×C5C3×C7×C15111yescharacteristic, direct product factor, Hall
26C7C2×C3×C5×C15111yescharacteristic, direct product factor, Sylow
27C2×C3C5×C7×C15111yescharacteristic, direct product factor, Hall
28C5C2×C3×C7×C15111yescharacteristic, direct product factor, Sylow
29C3C2×C5×C7×C15111yescharacteristic, direct product factor, Sylow
30C2C3×C5×C7×C15111yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×C151C2direct (N × H)
2. C2×C5×C7×C151C3direct (N × H)
3. C2×C3×C7×C151C5direct (N × H)
4. C5×C7×C151C2×C3direct (N × H)
5. C2×C3×C5×C151C7direct (N × H)
6. C3×C7×C151C2×C5direct (N × H)
7. C3×C5×C151C2×C7direct (N × H)
8. C2×C7×C151C3×C5direct (N × H)
9. C2×C5×C151C3×C7direct (N × H)
10. C7×C151C2×C3×C5direct (N × H)
11. C2×C3×C151C5×C7direct (N × H)
12. C5×C151C2×C3×C7direct (N × H)
13. C3×C151C2×C5×C7direct (N × H)
14. C2×C151C3×C5×C7direct (N × H)
15. C2×C3×C5×C7C151direct (N × H)
16. C151C2×C3×C5×C7direct (N × H)
17. C3×C5×C7C2×C151direct (N × H)
18. C2×C5×C7C3×C151direct (N × H)
19. C2×C3×C7C5×C151direct (N × H)
20. C5×C7C2×C3×C151direct (N × H)
21. C2×C3×C5C7×C151direct (N × H)
22. C3×C7C2×C5×C151direct (N × H)
23. C3×C5C2×C7×C151direct (N × H)
24. C2×C7C3×C5×C151direct (N × H)
25. C2×C5C3×C7×C151direct (N × H)
26. C7C2×C3×C5×C151direct (N × H)
27. C2×C3C5×C7×C151direct (N × H)
28. C5C2×C3×C7×C151direct (N × H)
29. C3C2×C5×C7×C151direct (N × H)
30. C2C3×C5×C7×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×C1512
C2×C5×C7×C1513
C2×C3×C7×C1515
C2×C3×C5×C1517
C2×C3×C5×C7151