Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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. C5×#2216 | C2 | semidirect |
| 3. C2×#64741 | C2 | semidirect |
| 4. C22⋊#3926 | C2 | semidirect |
| 5. #10598068 | C2 | semidirect |
| 7. C2×C5×Q32 | C22 | semidirect |
| 13. C5×#366 | C22 | semidirect |
| 16. C2×#3926 | C22 | semidirect |
| 38. #2216 | D5 | semidirect |
| 63. C2×Q32 | C2×D5 | semidirect |
| 71. #366 | C2×D5 | semidirect |
| 112. C22×C5 | SD64 | semidirect |
| 168. C5 | #13664 | semidirect |
| 175. C22 | #64741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D80 | 2 |
| C5×#2216 | 2 |
| C2×#64741 | 2 |
| C22⋊#3926 | 2 |
| #10598068 | 2 |
| #13664 | 5 |