Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#64732 | C2 | semidirect |
| 4. C5×#1375 | C2 | semidirect |
| 5. #10598154 | C2 | semidirect |
| 17. #64727 | C4 | semidirect |
| 39. C2×C5×C16 | C2×C4 | semidirect |
| 45. C2×#672 | C2×C4 | semidirect |
| 51. #1375 | D5 | semidirect |
| 151. C2×C16 | C4×D5 | semidirect |
| 164. C2×D5 | #347 | semidirect |
| 241. C5 | #12605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#97 | 2 |
| #10602224 | 2 |
| C2×#64732 | 2 |
| C5×#1375 | 2 |
| #10598154 | 2 |
| #12605 | 5 |