Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
698 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#65440 | C2 | semidirect |
| 2. C22×#3958 | C2 | semidirect |
| 3. C22×D80 | C2 | semidirect |
| 4. C2×C5×#357 | C2 | semidirect |
| 5. #10601421 | C2 | semidirect |
| 6. C2×#64711 | C2 | semidirect |
| 7. #10598295 | C2 | semidirect |
| 61. C2×D40 | D4 | semidirect |
| 64. C2×C5×C16 | D4 | semidirect |
| 72. C2×#672 | D4 | semidirect |
| 79. C2×#357 | D5 | semidirect |
| 190. C2×Dic5 | D16 | semidirect |
| 243. C2×C16 | C22⋊D5 | semidirect |
| 384. C5 | #13325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65440 | 2 |
| C22×#3958 | 2 |
| C22×D80 | 2 |
| C2×C5×#357 | 2 |
| #10601421 | 2 |
| C2×#64711 | 2 |
| #10598295 | 2 |
| #13325 | 5 |