Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
168 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 6. C5×#870 | C4 | semidirect |
| 10. C4×C5×C3⋊C8 | C4 | semidirect |
| 47. #870 | Dic5 | semidirect |
| 52. C4×C3⋊C8 | Dic5 | semidirect |
| 129. C3×C5 | #1414 | semidirect |
| 154. C5 | #67543 | semidirect |
| 163. C3 | #10598273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5056 | 2 |
| #11746363 | 2 |
| C3×#64761 | 2 |
| #10598273 | 3 |
| #67543 | 5 |