Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10601685 | C2 | semidirect |
| 3. #10599854 | C2 | semidirect |
| 4. #10599370 | C2 | semidirect |
| 5. C5×#1331 | C2 | semidirect |
| 6. #10597994 | C2 | semidirect |
| 7. #10597964 | C2 | semidirect |
| 17. #64988 | C22 | semidirect |
| 20. C4×C5×C16 | C22 | semidirect |
| 21. C5×#335 | C22 | semidirect |
| 24. C4⋊#672 | C22 | semidirect |
| 62. #1331 | D5 | semidirect |
| 118. C4×C16 | C2×D5 | semidirect |
| 119. #335 | C2×D5 | semidirect |
| 145. D20 | SD32 | semidirect |
| 285. C5 | #12320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D20 | 2 |
| #10601685 | 2 |
| #10599854 | 2 |
| #10599370 | 2 |
| C5×#1331 | 2 |
| #10597994 | 2 |
| #10597964 | 2 |
| #12320 | 5 |