Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. C5×#2178 | C2 | semidirect |
| 2. #10602302 | C2 | semidirect |
| 3. #10599853 | C2 | semidirect |
| 4. #10598074 | C2 | semidirect |
| 5. #10598001 | C2 | semidirect |
| 23. C5×Q32 | D4 | semidirect |
| 25. C5×D16 | D4 | semidirect |
| 37. #2178 | D5 | semidirect |
| 90. Q32 | D20 | semidirect |
| 95. D16 | D20 | semidirect |
| 148. C5 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2178 | 2 |
| #10602302 | 2 |
| #10599853 | 2 |
| #10598074 | 2 |
| #10598001 | 2 |
| #13692 | 5 |