Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 18. #68553 | C5 | direct (N × H) |
| 171. C3×C5 | #1696 | semidirect |
| 198. C5 | #68553 | direct (N × H) |
| 207. C3 | C5×#1696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4850 | 2 |
| C5×#4682 | 2 |
| C5×#4679 | 2 |
| C3×C5×#334 | 2 |
| C5×#4481 | 2 |
| C5×#1696 | 3 |
| #68553 | 5 |