Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #10602412 | C2 | semidirect |
| 3. #10602393 | C2 | semidirect |
| 4. #10598136 | C2 | semidirect |
| 6. C2×C5×#127 | C4 | semidirect |
| 10. C5×#392 | C4 | semidirect |
| 13. C4×C5×C4⋊C4 | C4 | semidirect |
| 108. C2×#127 | Dic5 | semidirect |
| 114. #392 | Dic5 | semidirect |
| 118. C4×C4⋊C4 | Dic5 | semidirect |
| 347. C5 | #11877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2541 | 2 |
| #10602412 | 2 |
| #10602393 | 2 |
| #10598136 | 2 |
| #11877 | 5 |