Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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×#65183 | C2 | semidirect |
| 3. C2×#64715 | C2 | semidirect |
| 4. #10601369 | C2 | semidirect |
| 5. C2×#64708 | C2 | semidirect |
| 6. C5×#1383 | C2 | semidirect |
| 7. #10598302 | C2 | semidirect |
| 21. C2×#3932 | C4 | semidirect |
| 22. C2×D80 | C4 | semidirect |
| 74. #1383 | D5 | semidirect |
| 112. Dic20 | C22⋊C4 | semidirect |
| 118. D40 | C22⋊C4 | semidirect |
| 330. C5 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65197 | 2 |
| C2×#65183 | 2 |
| C2×#64715 | 2 |
| #10601369 | 2 |
| C2×#64708 | 2 |
| C5×#1383 | 2 |
| #10598302 | 2 |
| #13040 | 5 |