Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. C3×#66087 | C2 | semidirect |
| 2. C5×#5142 | C2 | semidirect |
| 3. C2×#90941 | C2 | semidirect |
| 4. #11747540 | C2 | semidirect |
| 5. #11746382 | C2 | semidirect |
| 6. #11745921 | C2 | semidirect |
| 7. #11745903 | C2 | semidirect |
| 27. #66087 | D3 | semidirect |
| 64. #5142 | D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #72124 | semidirect |
| 357. C3 | #10601888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66087 | 2 |
| C5×#5142 | 2 |
| C2×#90941 | 2 |
| #11747540 | 2 |
| #11746382 | 2 |
| #11745921 | 2 |
| #11745903 | 2 |
| #10601888 | 3 |
| #72124 | 5 |