Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
680 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 3. #10602412 | C2 | semidirect |
| 4. #10598132 | C2 | semidirect |
| 7. C2×C4×C5×D4 | C4 | semidirect |
| 10. C5×#390 | C4 | semidirect |
| 12. C5×#384 | C4 | semidirect |
| 13. C43×C5 | C4 | semidirect |
| 64. C2×C5×D4 | C4⋊C4 | semidirect |
| 95. C42×C5 | C4⋊C4 | semidirect |
| 101. C2×C4×D4 | Dic5 | semidirect |
| 105. #390 | Dic5 | semidirect |
| 107. #384 | Dic5 | semidirect |
| 109. C43 | Dic5 | semidirect |
| 212. C4×C5 | #353 | semidirect |
| 225. C2×D4 | C4⋊Dic5 | semidirect |
| 259. C42 | C4⋊Dic5 | semidirect |
| 313. C5 | #12797 | semidirect |
| 340. C4 | #64765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#127 | 2 |
| C2×#64765 | 2 |
| #10602412 | 2 |
| #10598132 | 2 |
| #12797 | 5 |