Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1532 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1532 conjugacy classes of subgroups — too many to draw. Only its 271 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×C5×#585 | C2 | semidirect |
| 2. #11756587 | C2 | semidirect |
| 3. #11751345 | C2 | semidirect |
| 4. #11751344 | C2 | semidirect |
| 5. #11751341 | C2 | semidirect |
| 12. C22×C4×D15 | C22 | semidirect |
| 15. #91826 | C22 | semidirect |
| 16. #91824 | C22 | semidirect |
| 18. #91815 | C22 | semidirect |
| 19. #91118 | C22 | semidirect |
| 21. C5×#585 | D3 | semidirect |
| 33. C2×C3×C5×Q8 | D4 | semidirect |
| 36. C2×C3×C5×D4 | D4 | semidirect |
| 39. C22×C3×C4×C5 | D4 | semidirect |
| 51. C3×#585 | D5 | semidirect |
| 111. C2×C5×Q8 | #67 | semidirect |
| 114. C2×C5×D4 | #67 | semidirect |
| 117. C22×C4×C5 | #67 | semidirect |
| 129. #585 | D15 | semidirect |
| 154. C2×C3×Q8 | C22⋊D5 | semidirect |
| 157. C2×C3×D4 | C22⋊D5 | semidirect |
| 160. C22×C3×C4 | C22⋊D5 | semidirect |
| 251. C2×Q8 | #1220 | semidirect |
| 255. C2×D4 | #1220 | semidirect |
| 261. C22×C4 | #1220 | semidirect |
| 269. C3×C5 | #3025 | semidirect |
| 312. C5 | #84125 | semidirect |
| 326. C3 | #10615856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#585 | 2 |
| #11756587 | 2 |
| #11751345 | 2 |
| #11751344 | 2 |
| #11751341 | 2 |
| #10615856 | 3 |
| #84125 | 5 |