Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10600077 | C2 | semidirect |
| 3. #10599864 | C2 | semidirect |
| 4. C5×#1330 | C2 | semidirect |
| 5. #10598252 | C2 | semidirect |
| 6. #10598048 | C2 | semidirect |
| 7. #10598006 | C2 | semidirect |
| 21. C5×C4⋊C16 | C22 | semidirect |
| 22. C5×#346 | C22 | semidirect |
| 25. C4⋊#672 | C22 | semidirect |
| 26. #64681 | C22 | semidirect |
| 71. #1330 | D5 | semidirect |
| 133. C4⋊C16 | C2×D5 | semidirect |
| 135. #346 | C2×D5 | semidirect |
| 316. C5 | #11587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#436 | 2 |
| #10600077 | 2 |
| #10599864 | 2 |
| C5×#1330 | 2 |
| #10598252 | 2 |
| #10598048 | 2 |
| #10598006 | 2 |
| #11587 | 5 |