Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 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. C5×#1953 | C2 | semidirect |
| 5. C2×#64714 | C2 | semidirect |
| 6. #10598221 | C2 | semidirect |
| 7. #10598163 | C2 | semidirect |
| 22. #64717 | C4 | semidirect |
| 50. C5×#108 | C2×C4 | semidirect |
| 62. C2×#672 | C2×C4 | semidirect |
| 67. #1953 | D5 | semidirect |
| 187. #108 | C4×D5 | semidirect |
| 283. C5 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610305 | 2 |
| C5×#1953 | 2 |
| #10601483 | 2 |
| #10601480 | 2 |
| C2×#64714 | 2 |
| #10598221 | 2 |
| #10598163 | 2 |
| #12949 | 5 |