Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 160 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. #11746367 | C2 | semidirect |
| 4. C5×#4546 | C2 | semidirect |
| 5. #11745861 | C2 | semidirect |
| 44. #4546 | D5 | direct (N × H) |
| 160. C3×D5 | #333 | semidirect |
| 203. C3×C5 | C2×#333 | semidirect |
| 216. D5 | #4546 | direct (N × H) |
| 236. C5 | C2×#4546 | semidirect |
| 247. C3 | D5×#333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×C4⋊Q8 | 2 |
| D5×C4⋊(C3⋊C8) | 2 |
| #11746367 | 2 |
| C5×#4546 | 2 |
| #11745861 | 2 |
| D5×#333 | 3 |
| C2×#4546 | 5 |