Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 2. #11746378 | C2 | semidirect |
| 3. C3×#64773 | C2 | semidirect |
| 8. C2×C5×D24 | C4 | semidirect |
| 10. C5×#817 | C4 | semidirect |
| 15. #64773 | D3 | semidirect |
| 56. C2×D24 | Dic5 | semidirect |
| 59. #817 | Dic5 | semidirect |
| 161. C3×C5 | #1339 | semidirect |
| 194. C5 | #67534 | semidirect |
| 206. C3 | #10598269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5135 | 2 |
| #11746378 | 2 |
| C3×#64773 | 2 |
| #10598269 | 3 |
| #67534 | 5 |