Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
444 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×#64890 | C2 | semidirect |
| 4. C2×#64890 | C2 | semidirect |
| 5. #10598729 | C2 | semidirect |
| 19. #64898 | C4 | semidirect |
| 48. #3998 | C2×C4 | semidirect |
| 50. C2×#674 | C2×C4 | semidirect |
| 275. C5 | #12609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610281 | 2 |
| #10604745 | 2 |
| C2×#64890 | 2 |
| #10598729 | 2 |
| #12609 | 5 |