Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
848 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 231 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×#498 | C2 | semidirect |
| 3. #11751181 | C2 | semidirect |
| 5. #11750956 | C2 | semidirect |
| 7. #11750781 | C2 | semidirect |
| 27. C5×#498 | D3 | semidirect |
| 51. C8×D15 | Q8 | semidirect |
| 53. C3×#498 | D5 | semidirect |
| 89. C3×C5×C8 | C2×Q8 | semidirect |
| 90. C3⋊#168 | C2×Q8 | semidirect |
| 130. #498 | D15 | direct (N × H) |
| 174. C5×C8 | D3×Q8 | semidirect |
| 194. D15 | #498 | direct (N × H) |
| 208. C3×C8 | Q8×D5 | semidirect |
| 238. C3×C5 | C2×#498 | semidirect |
| 265. C8 | Q8×D15 | semidirect |
| 269. C5 | D3×#498 | semidirect |
| 279. C3 | D5×#498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×C4⋊Q8 | 2 |
| C3×C5×#498 | 2 |
| #11751181 | 2 |
| D15×#106 | 2 |
| #11750956 | 2 |
| C4×C8×D15 | 2 |
| #11750781 | 2 |
| D5×#498 | 3 |
| D3×#498 | 5 |