Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
680 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #10600821 | C2 | semidirect |
| 5. #10598186 | C2 | semidirect |
| 8. C2×D4×Dic5 | C4 | semidirect |
| 12. #65510 | C4 | semidirect |
| 16. #65224 | C4 | semidirect |
| 17. C42×Dic5 | C4 | semidirect |
| 71. C2×C5×D4 | C4⋊C4 | semidirect |
| 93. C42×C5 | C4⋊C4 | semidirect |
| 232. Dic5 | #353 | semidirect |
| 244. C2×D4 | #683 | semidirect |
| 281. C42 | #683 | semidirect |
| 338. C5 | #12797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×#127 | 2 |
| C2×C5×#353 | 2 |
| C2×#64765 | 2 |
| #10600821 | 2 |
| #10598186 | 2 |
| #12797 | 5 |