Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
670 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 670 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. C2×#64746 | C2 | semidirect |
| 3. C2×#64745 | C2 | semidirect |
| 4. #10598140 | C2 | semidirect |
| 5. #10598136 | C2 | semidirect |
| 6. C2×C5×#121 | C4 | semidirect |
| 10. C5×#397 | C4 | semidirect |
| 14. C5×#392 | C4 | semidirect |
| 17. C5×#380 | C4 | semidirect |
| 28. C22×C5×D4 | C2×C4 | semidirect |
| 37. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 57. C5×#95 | C2×C4 | semidirect |
| 58. C5×#95 | C2×C4 | semidirect |
| 125. C2×#121 | Dic5 | semidirect |
| 130. #397 | Dic5 | semidirect |
| 134. #392 | Dic5 | semidirect |
| 137. #380 | Dic5 | semidirect |
| 214. C22×D4 | C2×Dic5 | semidirect |
| 224. C2×C4⋊C4 | C2×Dic5 | semidirect |
| 245. #95 | C2×Dic5 | semidirect |
| 246. #95 | C2×Dic5 | semidirect |
| 429. C5 | #11692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2617 | 2 |
| C2×#64746 | 2 |
| C2×#64745 | 2 |
| #10598140 | 2 |
| #10598136 | 2 |
| #11692 | 5 |