Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. #10604738 | C2 | semidirect |
| 4. #10604185 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598696 | C2 | semidirect |
| 99. C5×M16 | M16 | semidirect |
| 106. C42×C5 | M16 | semidirect |
| 267. M16 | #700 | semidirect |
| 297. C42 | #700 | semidirect |
| 346. C5 | #8842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617122 | 2 |
| #10604738 | 2 |
| #10604360 | 2 |
| #10604185 | 2 |
| #10599521 | 2 |
| #10598793 | 2 |
| #10598696 | 2 |
| #8842 | 5 |