Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 94 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. C5×#4683 | C2 | semidirect |
| 3. C3×C5×#364 | C2 | semidirect |
| 5. C5×#4513 | C2 | semidirect |
| 16. #69308 | C5 | direct (N × H) |
| 20. C5×#364 | D3 | semidirect |
| 36. #4683 | C2×C5 | semidirect |
| 37. C3×#364 | C2×C5 | semidirect |
| 39. #4513 | C2×C5 | semidirect |
| 87. #364 | C5×D3 | semidirect |
| 165. C3×C5 | #2231 | semidirect |
| 191. C5 | #69308 | direct (N × H) |
| 199. C3 | C5×#2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4700 | 2 |
| C5×#4683 | 2 |
| C3×C5×#364 | 2 |
| C5×#4518 | 2 |
| C5×#4513 | 2 |
| C5×#2231 | 3 |
| #69308 | 5 |