Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
840 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10613814 | C2 | semidirect |
| 3. #10602466 | C2 | semidirect |
| 4. #10602332 | C2 | semidirect |
| 5. #10598109 | C2 | semidirect |
| 11. C5×#399 | C4 | semidirect |
| 12. C5×#392 | C4 | semidirect |
| 25. C22×C5×D4 | C2×C4 | semidirect |
| 34. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 50. C5×#95 | C2×C4 | semidirect |
| 52. #3963 | D4 | semidirect |
| 113. #399 | Dic5 | semidirect |
| 114. #392 | Dic5 | semidirect |
| 174. C22×D4 | C2×Dic5 | semidirect |
| 184. C2×C4⋊C4 | C2×Dic5 | semidirect |
| 203. #95 | C2×Dic5 | semidirect |
| 338. C5 | #9409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2539 | 2 |
| #10613814 | 2 |
| #10602466 | 2 |
| #10602332 | 2 |
| #10598109 | 2 |
| #9409 | 5 |