Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #10614786 | C2 | semidirect |
| 4. C2×C5×#330 | C2 | semidirect |
| 6. C2×#64685 | C2 | semidirect |
| 7. #10598150 | C2 | semidirect |
| 82. C2×#330 | D5 | semidirect |
| 351. C5 | #10080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614786 | 2 |
| C2×#65356 | 2 |
| C2×#65002 | 2 |
| C2×C5×#330 | 2 |
| #10600616 | 2 |
| C2×#64685 | 2 |
| #10598150 | 2 |
| #10080 | 5 |