Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C5×#1368 | C2 | semidirect |
| 5. #10598004 | C2 | semidirect |
| 6. #10597955 | C2 | semidirect |
| 7. #10597955 | C2 | semidirect |
| 51. #1368 | D5 | semidirect |
| 72. C5×C16 | M16 | semidirect |
| 74. #672 | M16 | semidirect |
| 164. C16 | #676 | semidirect |
| 189. C5 | #12019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#346 | 2 |
| #10599323 | 2 |
| #10599322 | 2 |
| C5×#1368 | 2 |
| #10598004 | 2 |
| #10597955 | 2 |
| #12019 | 5 |