Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11751241 | C2 | semidirect |
| 3. #11751008 | C2 | semidirect |
| 4. C3×C5×#350 | C2 | semidirect |
| 5. #11746332 | C2 | semidirect |
| 6. #11746329 | C2 | semidirect |
| 7. #11746323 | C2 | semidirect |
| 28. C5×#350 | D3 | semidirect |
| 55. C3×#350 | D5 | semidirect |
| 131. #350 | D15 | semidirect |
| 240. C3×C5 | #2171 | semidirect |
| 273. C5 | #69123 | semidirect |
| 282. C3 | #10599916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751245 | 2 |
| #11751241 | 2 |
| #11751008 | 2 |
| C3×C5×#350 | 2 |
| #11746332 | 2 |
| #11746329 | 2 |
| #11746323 | 2 |
| #10599916 | 3 |
| #69123 | 5 |