Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
280 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 24. #68515 | C5 | direct (N × H) |
| 230. C3×C5 | #1704 | semidirect |
| 264. C5 | #68515 | direct (N × H) |
| 275. C3 | C5×#1704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5093 | 2 |
| C5×#5091 | 2 |
| C5×#4851 | 2 |
| C5×#4831 | 2 |
| C3×C5×#333 | 2 |
| C5×#4482 | 2 |
| C5×#4480 | 2 |
| C5×#1704 | 3 |
| #68515 | 5 |