Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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×#1338 | C2 | semidirect |
| 5. #10598260 | C2 | semidirect |
| 6. #10598050 | C2 | semidirect |
| 7. #10598009 | C2 | semidirect |
| 69. #1338 | D5 | direct (N × H) |
| 245. D5 | #1338 | direct (N × H) |
| 273. C5 | C2×#1338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#446 | 2 |
| D5×C4⋊C16 | 2 |
| D5×#346 | 2 |
| C5×#1338 | 2 |
| #10598260 | 2 |
| #10598050 | 2 |
| #10598009 | 2 |
| C2×#1338 | 5 |