Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 146 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×#5237 | C2 | semidirect |
| 3. C5×#4542 | C2 | semidirect |
| 13. C5×#836 | C22 | semidirect |
| 15. #71862 | C5 | direct (N × H) |
| 38. #5237 | C2×C5 | semidirect |
| 39. #4542 | C2×C5 | semidirect |
| 78. #836 | C22×C5 | semidirect |
| 214. C3×C5 | #2134 | semidirect |
| 256. C5 | #71862 | direct (N × H) |
| 269. C3 | C5×#2134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#535 | 2 |
| C5×#5237 | 2 |
| C5×#4542 | 2 |
| C5×#2134 | 3 |
| #71862 | 5 |