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 |
|---|---|---|
| 8. #10599308 | C3 | direct (N × H) |
| 230. C3×C5 | #1704 | semidirect |
| 264. C5 | C3×#1704 | semidirect |
| 275. C3 | #10599308 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65382 | 2 |
| C3×#65380 | 2 |
| C3×#65140 | 2 |
| C3×#65120 | 2 |
| C3×C5×#333 | 2 |
| C3×#64702 | 2 |
| C3×#64700 | 2 |
| #10599308 | 3 |
| C3×#1704 | 5 |