Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 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 |
|---|---|---|
| 1. C5×#3077 | C2 | semidirect |
| 2. #10615086 | C2 | semidirect |
| 4. #10602628 | C2 | semidirect |
| 5. #10602390 | C2 | semidirect |
| 6. #10601295 | C2 | semidirect |
| 7. #10598206 | C2 | semidirect |
| 39. C5×C4⋊Q8 | D4 | semidirect |
| 40. C5×C4⋊Q8 | D4 | semidirect |
| 68. C5×C4⋊C8 | D4 | semidirect |
| 76. C4⋊#168 | D4 | semidirect |
| 80. #3077 | D5 | semidirect |
| 95. C2×C5×D4 | SD16 | semidirect |
| 226. C4⋊Q8 | C22⋊D5 | semidirect |
| 227. C4⋊Q8 | C22⋊D5 | semidirect |
| 256. C4⋊C8 | C22⋊D5 | semidirect |
| 316. C2×D4 | #688 | semidirect |
| 408. C5 | #10246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3077 | 2 |
| #10615086 | 2 |
| #10614109 | 2 |
| #10602628 | 2 |
| #10602390 | 2 |
| #10601295 | 2 |
| #10598206 | 2 |
| #10246 | 5 |