Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
544 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 6. C2×C4×C5×Q8 | C4 | semidirect |
| 8. C5×#391 | C4 | semidirect |
| 11. C5×#382 | C4 | semidirect |
| 13. C43×C5 | C4 | semidirect |
| 56. C2×C5×Q8 | C4⋊C4 | semidirect |
| 89. C42×C5 | C4⋊C4 | semidirect |
| 94. C2×C4×Q8 | Dic5 | semidirect |
| 97. #391 | Dic5 | semidirect |
| 100. #382 | Dic5 | semidirect |
| 103. C43 | Dic5 | semidirect |
| 195. C4×C5 | #354 | semidirect |
| 201. C2×Q8 | C4⋊Dic5 | semidirect |
| 237. C42 | C4⋊Dic5 | semidirect |
| 284. C5 | #12798 | semidirect |
| 307. C4 | #64761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#124 | 2 |
| C2×#64761 | 2 |
| #10602412 | 2 |
| #10598132 | 2 |
| #12798 | 5 |