Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
280 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 83 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×#2252 | C2 | semidirect |
| 2. #10602175 | C2 | semidirect |
| 4. #10602153 | C2 | semidirect |
| 7. #10597989 | C2 | semidirect |
| 46. #2252 | D5 | semidirect |
| 75. C5×C16 | SD16 | semidirect |
| 167. C16 | #688 | semidirect |
| 191. C5 | #12508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2252 | 2 |
| #10602175 | 2 |
| #10602174 | 2 |
| #10602153 | 2 |
| #10602152 | 2 |
| #10599854 | 2 |
| #10597989 | 2 |
| #12508 | 5 |