Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 124 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. #11747672 | C2 | semidirect |
| 3. C2×D5×C3⋊C16 | C2 | semidirect |
| 4. #11746383 | C2 | semidirect |
| 5. C5×#4562 | C2 | semidirect |
| 6. #11745898 | C2 | semidirect |
| 7. #11745897 | C2 | semidirect |
| 13. C3×#4058 | C4 | semidirect |
| 59. #4562 | D5 | semidirect |
| 64. #4058 | Dic3 | semidirect |
| 261. C3×C5 | #2138 | semidirect |
| 303. C5 | #72077 | semidirect |
| 317. C3 | #10599981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4058 | 2 |
| #11747672 | 2 |
| C2×D5×C3⋊C16 | 2 |
| #11746383 | 2 |
| C5×#4562 | 2 |
| #11745898 | 2 |
| #11745897 | 2 |
| #10599981 | 3 |
| #72077 | 5 |