Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C2×C5×Dic12 | C4 | semidirect |
| 9. C5×#817 | C4 | semidirect |
| 12. #67482 | C5 | direct (N × H) |
| 55. C2×Dic12 | C4×C5 | semidirect |
| 56. #817 | C4×C5 | semidirect |
| 153. C3×C5 | #1340 | semidirect |
| 181. C5 | #67482 | direct (N × H) |
| 191. C3 | C5×#1340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5137 | 2 |
| C3×C5×H(3,ℤ/4) | 2 |
| C5×#4553 | 2 |
| C5×#1340 | 3 |
| #67482 | 5 |