Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10611066 | C2 | semidirect |
| 3. C5×#1555 | C2 | semidirect |
| 4. #10602553 | C2 | semidirect |
| 5. #10601620 | C2 | semidirect |
| 6. #10598241 | C2 | semidirect |
| 7. #10598240 | C2 | semidirect |
| 60. C5×C4⋊C8 | D4 | semidirect |
| 71. C4⋊#168 | D4 | semidirect |
| 77. #1555 | D5 | semidirect |
| 243. C4⋊C8 | C22⋊D5 | semidirect |
| 403. C5 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614919 | 2 |
| #10611066 | 2 |
| C5×#1555 | 2 |
| #10602553 | 2 |
| #10601620 | 2 |
| #10598241 | 2 |
| #10598240 | 2 |
| #9457 | 5 |