Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×#362 | C2 | semidirect |
| 4. C5×#4565 | C2 | semidirect |
| 6. C5×#4513 | C2 | semidirect |
| 7. C5×#4494 | C2 | semidirect |
| 20. #69267 | C5 | direct (N × H) |
| 26. C5×#362 | D3 | semidirect |
| 47. C3×#362 | C2×C5 | semidirect |
| 48. #4565 | C2×C5 | semidirect |
| 50. #4513 | C2×C5 | semidirect |
| 51. #4494 | C2×C5 | semidirect |
| 111. #362 | C5×D3 | semidirect |
| 205. C3×C5 | #2239 | semidirect |
| 234. C5 | #69267 | direct (N × H) |
| 243. C3 | C5×#2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5189 | 2 |
| C5×#4893 | 2 |
| C3×C5×#362 | 2 |
| C5×#4565 | 2 |
| C5×#4514 | 2 |
| C5×#4513 | 2 |
| C5×#4494 | 2 |
| C5×#2239 | 3 |
| #69267 | 5 |