Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 138 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. C3×C5×#367 | C2 | semidirect |
| 4. C5×#4505 | C2 | semidirect |
| 5. C5×#4489 | C2 | semidirect |
| 14. C5×D3×C16 | C4 | semidirect |
| 15. #69345 | C5 | direct (N × H) |
| 19. C5×#367 | D3 | semidirect |
| 34. C3×#367 | C2×C5 | semidirect |
| 35. #4505 | C2×C5 | semidirect |
| 36. #4489 | C2×C5 | semidirect |
| 63. D3×C16 | C4×C5 | semidirect |
| 78. #367 | C5×D3 | semidirect |
| 149. C3×C5 | #2158 | semidirect |
| 174. C5 | #69345 | direct (N × H) |
| 183. C3 | C5×#2158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×C16 | 2 |
| C5×#4880 | 2 |
| C3×C5×#367 | 2 |
| C5×#4505 | 2 |
| C5×#4489 | 2 |
| C5×#2158 | 3 |
| #69345 | 5 |