Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1214 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10602923 | C2 | semidirect |
| 3. C2×#64765 | C2 | semidirect |
| 4. C2×#64761 | C2 | semidirect |
| 5. C22×C5×#41 | C4 | semidirect |
| 9. C2×C5×#127 | C4 | semidirect |
| 11. C2×C5×#124 | C4 | semidirect |
| 15. C2×C5×#117 | C4 | semidirect |
| 81. C2×C5×Q8 | C22⋊C4 | semidirect |
| 103. C2×C5×D4 | C22⋊C4 | semidirect |
| 125. C42×C5 | C22⋊C4 | semidirect |
| 126. C42×C5 | C22⋊C4 | semidirect |
| 130. C22×#41 | Dic5 | semidirect |
| 134. C2×#127 | Dic5 | semidirect |
| 136. C2×#124 | Dic5 | semidirect |
| 140. C2×#117 | Dic5 | semidirect |
| 282. C2×Q8 | C22⋊Dic5 | semidirect |
| 304. C2×D4 | C22⋊Dic5 | semidirect |
| 329. C42 | C22⋊Dic5 | semidirect |
| 330. C42 | C22⋊Dic5 | semidirect |
| 392. C5 | #12696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#535 | 2 |
| #10602923 | 2 |
| C2×#64765 | 2 |
| C2×#64761 | 2 |
| #12696 | 5 |