Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 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×D5×#106 | C2 | semidirect |
| 3. C2×C5×#360 | C2 | semidirect |
| 4. C2×#64786 | C2 | semidirect |
| 5. #10602224 | C2 | semidirect |
| 6. #10598310 | C2 | semidirect |
| 7. #10598212 | C2 | semidirect |
| 15. #65477 | C4 | semidirect |
| 17. #65446 | C4 | semidirect |
| 35. C2×C5×Q16 | C2×C4 | semidirect |
| 37. C2×C5×D8 | C2×C4 | semidirect |
| 61. C5×#106 | D4 | semidirect |
| 64. #3950 | C2×C4 | semidirect |
| 67. #3949 | D4 | semidirect |
| 75. C2×#360 | D5 | semidirect |
| 199. C2×Q16 | C4×D5 | semidirect |
| 201. C2×D8 | C4×D5 | semidirect |
| 233. #106 | C22⋊D5 | semidirect |
| 246. C2×D5 | #360 | semidirect |
| 356. C5 | #13001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615645 | 2 |
| C2×D5×#106 | 2 |
| C2×C5×#360 | 2 |
| C2×#64786 | 2 |
| #10602224 | 2 |
| #10598310 | 2 |
| #10598212 | 2 |
| #13001 | 5 |