Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×D5×C32 | C2 | semidirect |
| 3. D5×#368 | C2 | semidirect |
| 4. C5×#1417 | C2 | semidirect |
| 5. #10598320 | C2 | semidirect |
| 6. #10598089 | C2 | semidirect |
| 7. #10598076 | C2 | semidirect |
| 20. C2×C5×C32 | C22 | semidirect |
| 21. C5×#368 | C22 | semidirect |
| 22. #64726 | C22 | semidirect |
| 23. C2×#3926 | C22 | semidirect |
| 67. #1417 | D5 | direct (N × H) |
| 118. C2×C32 | C2×D5 | semidirect |
| 121. #368 | C2×D5 | semidirect |
| 237. D5 | #1417 | direct (N × H) |
| 267. C5 | C2×#1417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#508 | 2 |
| C2×D5×C32 | 2 |
| D5×#368 | 2 |
| C5×#1417 | 2 |
| #10598320 | 2 |
| #10598089 | 2 |
| #10598076 | 2 |
| C2×#1417 | 5 |