Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 77 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. C3×C5×#510 | C2 | semidirect |
| 3. #11751293 | C2 | semidirect |
| 4. C2×#91112 | C2 | semidirect |
| 5. #11746388 | C2 | semidirect |
| 6. #11746337 | C2 | semidirect |
| 7. #11746336 | C2 | semidirect |
| 11. C2×C3×C5×Q16 | C22 | semidirect |
| 21. C3×C5×M32 | C22 | semidirect |
| 24. #91103 | C22 | semidirect |
| 25. C2×C3⋊#672 | C22 | semidirect |
| 28. C5×#510 | D3 | semidirect |
| 62. C3×#510 | D5 | semidirect |
| 70. C2×C5×Q16 | C2×D3 | semidirect |
| 80. C5×M32 | C2×D3 | semidirect |
| 111. C2×C3×Q16 | C2×D5 | semidirect |
| 121. C3×M32 | C2×D5 | semidirect |
| 154. #510 | D15 | semidirect |
| 227. C2×Q16 | C2×D15 | semidirect |
| 234. M32 | C2×D15 | semidirect |
| 304. C3×C5 | #2194 | semidirect |
| 349. C5 | #71523 | semidirect |
| 361. C3 | #10602316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756528 | 2 |
| C3×C5×#510 | 2 |
| #11751293 | 2 |
| C2×#91112 | 2 |
| #11746388 | 2 |
| #11746337 | 2 |
| #11746336 | 2 |
| #10602316 | 3 |
| #71523 | 5 |