Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11751297 | C2 | semidirect |
| 3. #11746388 | C2 | semidirect |
| 4. #11746327 | C2 | semidirect |
| 5. #11746323 | C2 | semidirect |
| 9. C3×C5×Q32 | C4 | semidirect |
| 10. C3×C5×SD32 | C4 | semidirect |
| 11. C3×C5×D16 | C4 | semidirect |
| 43. C5×Q32 | Dic3 | semidirect |
| 44. C5×SD32 | Dic3 | semidirect |
| 45. C5×D16 | Dic3 | semidirect |
| 64. C3×Q32 | Dic5 | semidirect |
| 65. C3×SD32 | Dic5 | semidirect |
| 66. C3×D16 | Dic5 | semidirect |
| 121. Q32 | Dic15 | semidirect |
| 122. SD32 | Dic15 | semidirect |
| 123. D16 | Dic15 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #71512 | semidirect |
| 191. C3 | #10602305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| #11751297 | 2 |
| #11746388 | 2 |
| #11746327 | 2 |
| #11746323 | 2 |
| #10602305 | 3 |
| #71512 | 5 |