Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10610908 | C2 | semidirect |
| 3. C5×#2140 | C2 | semidirect |
| 4. #10602826 | C2 | semidirect |
| 5. C2×#64734 | C2 | semidirect |
| 6. #10598310 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 16. #65448 | C4 | semidirect |
| 35. C2×C5×D8 | C2×C4 | semidirect |
| 59. C5×#107 | D4 | semidirect |
| 62. #3950 | D4 | semidirect |
| 65. #3949 | C2×C4 | semidirect |
| 74. #2140 | D5 | semidirect |
| 193. C2×D8 | C4×D5 | semidirect |
| 222. #107 | C22⋊D5 | semidirect |
| 345. C5 | #12999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65448 | 2 |
| #10610908 | 2 |
| C5×#2140 | 2 |
| #10602826 | 2 |
| C2×#64734 | 2 |
| #10598310 | 2 |
| #10598217 | 2 |
| #12999 | 5 |