Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 2. C5×#4893 | C2 | semidirect |
| 3. C3×C5×#361 | C2 | semidirect |
| 4. C5×#4563 | C2 | semidirect |
| 5. C5×#4514 | C2 | semidirect |
| 6. C5×#4513 | C2 | semidirect |
| 7. C5×#4494 | C2 | semidirect |
| 20. #69257 | C5 | direct (N × H) |
| 26. C5×#361 | D3 | semidirect |
| 46. #4893 | C2×C5 | semidirect |
| 47. C3×#361 | C2×C5 | semidirect |
| 48. #4563 | C2×C5 | semidirect |
| 49. #4514 | C2×C5 | semidirect |
| 50. #4513 | C2×C5 | semidirect |
| 51. #4494 | C2×C5 | semidirect |
| 112. #361 | C5×D3 | semidirect |
| 213. C3×C5 | #2238 | semidirect |
| 247. C5 | #69257 | direct (N × H) |
| 258. C3 | C5×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5159 | 2 |
| C5×#4893 | 2 |
| C3×C5×#361 | 2 |
| C5×#4563 | 2 |
| C5×#4514 | 2 |
| C5×#4513 | 2 |
| C5×#4494 | 2 |
| C5×#2238 | 3 |
| #69257 | 5 |