Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
476 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 3. C5×#4541 | C2 | semidirect |
| 6. C22×C3×C5×Q8 | C4 | semidirect |
| 7. C3×C5×C4⋊Q8 | C4 | semidirect |
| 11. C3×C5×#117 | C4 | semidirect |
| 15. #71871 | C5 | direct (N × H) |
| 39. #4541 | C2×C5 | semidirect |
| 41. C22×C5×Q8 | Dic3 | semidirect |
| 42. C5×C4⋊Q8 | Dic3 | semidirect |
| 47. C5×#117 | Dic3 | semidirect |
| 69. C22×C3×Q8 | C4×C5 | semidirect |
| 70. C3×C4⋊Q8 | C4×C5 | semidirect |
| 74. C3×#117 | C4×C5 | semidirect |
| 146. C22×Q8 | C5×Dic3 | semidirect |
| 147. C4⋊Q8 | C5×Dic3 | semidirect |
| 152. #117 | C5×Dic3 | semidirect |
| 205. C3×C5 | #2129 | semidirect |
| 242. C5 | #71871 | direct (N × H) |
| 254. C3 | C5×#2129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#536 | 2 |
| C5×#5240 | 2 |
| C5×#4541 | 2 |
| C5×#2129 | 3 |
| #71871 | 5 |