Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. C5×#803 | C4 | semidirect |
| 13. C3×C4⋊#168 | C4 | semidirect |
| 42. C4⋊#168 | Dic3 | semidirect |
| 68. #803 | Dic5 | semidirect |
| 175. C3×C5 | #1300 | semidirect |
| 210. C5 | #67748 | semidirect |
| 222. C3 | #10598156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751033 | 2 |
| C4×C5×#208 | 2 |
| C3×#65215 | 2 |
| #10598156 | 3 |
| #67748 | 5 |