Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. C5×#2245 | C2 | semidirect |
| 4. #10602146 | C2 | semidirect |
| 5. #10602104 | C2 | semidirect |
| 7. #10600008 | C2 | semidirect |
| 8. #10599876 | C2 | semidirect |
| 77. #2245 | D5 | semidirect |
| 275. C5 | #33705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613647 | 2 |
| D5×#494 | 2 |
| C5×#2245 | 2 |
| #10602146 | 2 |
| #10602104 | 2 |
| #10600015 | 2 |
| #10600008 | 2 |
| #10599876 | 2 |
| #10599864 | 2 |
| #33705 | 5 |