Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 3. C5×#1515 | C2 | semidirect |
| 4. #10602630 | C2 | semidirect |
| 6. #10598243 | C2 | semidirect |
| 7. #10598124 | C2 | semidirect |
| 12. #65377 | C4 | semidirect |
| 13. #65377 | C4 | semidirect |
| 30. C5×C4⋊Q8 | C2×C4 | semidirect |
| 31. C5×C4⋊Q8 | C2×C4 | semidirect |
| 62. C4×#168 | C2×C4 | semidirect |
| 67. #1515 | D5 | semidirect |
| 171. C4⋊Q8 | C4×D5 | semidirect |
| 172. C4⋊Q8 | C4×D5 | semidirect |
| 308. C5 | #9425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615067 | 2 |
| #10606029 | 2 |
| C5×#1515 | 2 |
| #10602630 | 2 |
| #10601611 | 2 |
| #10598243 | 2 |
| #10598124 | 2 |
| #9425 | 5 |