Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. C3×C5×#362 | C2 | semidirect |
| 4. C3×#64785 | C2 | semidirect |
| 6. C3×#64733 | C2 | semidirect |
| 7. C3×#64714 | C2 | semidirect |
| 8. #10600060 | C3 | direct (N × H) |
| 23. C5×#362 | C2×C3 | semidirect |
| 24. #64785 | C2×C3 | semidirect |
| 26. #64733 | C2×C3 | semidirect |
| 27. #64714 | C2×C3 | semidirect |
| 50. C3×#362 | D5 | semidirect |
| 111. #362 | C3×D5 | semidirect |
| 205. C3×C5 | #2239 | semidirect |
| 234. C5 | C3×#2239 | semidirect |
| 243. C3 | #10600060 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65478 | 2 |
| C3×#65182 | 2 |
| C3×C5×#362 | 2 |
| C3×#64785 | 2 |
| C3×#64734 | 2 |
| C3×#64733 | 2 |
| C3×#64714 | 2 |
| #10600060 | 3 |
| C3×#2239 | 5 |