Finite Group Databasebeta

← C22×C32×C5×C11 #14520495

Subgroups — C22×C32×C5×C11 #14520495

Order 1980.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×C11C213yesmaximal, direct product factor
2C22×C3×C5×C11C314yesmaximal, direct product factor
3C32×C5×C11C2211yescharacteristic, direct product factor, Hall
4C22×C32×C11C511yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C5×C11C2×C3112yesdirect product factor
6C22×C5×C11C3211yescharacteristic, direct product factor, Hall
7C2×C32×C11C2×C513yesdirect product factor
8C22×C32×C5C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C11C22×C314yesdirect product factor
10C22×C3×C11C3×C514yesdirect product factor
11C2×C5×C11C2×C3213yesdirect product factor
12C32×C11C22×C511yescharacteristic, direct product factor, Hall
13C2×C32×C5C2×C1113yesdirect product factor
14C2×C3×C11C2×C3×C5112yesdirect product factor
15C22×C3×C5C3×C1114yesdirect product factor
16C5×C11C22×C3211yescharacteristic, direct product factor, Hall
17C32×C5C22×C1111yescharacteristic, direct product factor, Hall
18C22×C11C32×C511yescharacteristic, direct product factor, Hall
19C22×C32C5×C1111yescharacteristic, direct product factor, Hall
20C3×C11C22×C3×C514yesdirect product factor
21C2×C3×C5C2×C3×C11112yesdirect product factor
22C2×C11C2×C32×C513yesdirect product factor
23C22×C5C32×C1111yescharacteristic, direct product factor, Hall
24C2×C32C2×C5×C1113yesdirect product factor
25C3×C5C22×C3×C1114yesdirect product factor
26C22×C3C3×C5×C1114yesdirect product factor
27C11C22×C32×C511yescharacteristic, direct product factor, Sylow
28C2×C5C2×C32×C1113yesdirect product factor
29C32C22×C5×C1111yescharacteristic, direct product factor, Sylow
30C2×C3C2×C3×C5×C11112yesdirect product factor
31C5C22×C32×C1111yescharacteristic, direct product factor, Sylow
32C22C32×C5×C1111yescharacteristic, direct product factor, Sylow
33C3C22×C3×C5×C1114yesdirect product factor
34C2C2×C32×C5×C1113yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×C11C2direct (N × H)
2. C22×C3×C5×C11C3direct (N × H)
3. C32×C5×C11C22direct (N × H)
4. C22×C32×C11C5direct (N × H)
5. C2×C3×C5×C11C2×C3direct (N × H)
6. C22×C5×C11C32direct (N × H)
7. C2×C32×C11C2×C5direct (N × H)
8. C22×C32×C5C11direct (N × H)
9. C3×C5×C11C22×C3direct (N × H)
10. C22×C3×C11C3×C5direct (N × H)
11. C2×C5×C11C2×C32direct (N × H)
12. C32×C11C22×C5direct (N × H)
13. C2×C32×C5C2×C11direct (N × H)
14. C2×C3×C11C2×C3×C5direct (N × H)
15. C22×C3×C5C3×C11direct (N × H)
16. C5×C11C22×C32direct (N × H)
17. C32×C5C22×C11direct (N × H)
18. C22×C11C32×C5direct (N × H)
19. C22×C32C5×C11direct (N × H)
20. C3×C11C22×C3×C5direct (N × H)
21. C2×C3×C5C2×C3×C11direct (N × H)
22. C2×C11C2×C32×C5direct (N × H)
23. C22×C5C32×C11direct (N × H)
24. C2×C32C2×C5×C11direct (N × H)
25. C3×C5C22×C3×C11direct (N × H)
26. C22×C3C3×C5×C11direct (N × H)
27. C11C22×C32×C5direct (N × H)
28. C2×C5C2×C32×C11direct (N × H)
29. C32C22×C5×C11direct (N × H)
30. C2×C3C2×C3×C5×C11direct (N × H)
31. C5C22×C32×C11direct (N × H)
32. C22C32×C5×C11direct (N × H)
33. C3C22×C3×C5×C11direct (N × H)
34. C2C2×C32×C5×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×C112
C22×C3×C5×C113
C22×C32×C115
C22×C32×C511