Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C5×#3061 | C2 | semidirect |
| 2. C2×#65482 | C2 | semidirect |
| 3. C2×#65431 | C2 | semidirect |
| 4. C2×#64787 | C2 | semidirect |
| 5. C2×#64781 | C2 | semidirect |
| 6. C2×#64711 | C2 | semidirect |
| 7. #10598214 | C2 | semidirect |
| 66. C2×D40 | D4 | semidirect |
| 75. #3951 | D4 | semidirect |
| 77. #3944 | D4 | semidirect |
| 84. #3061 | D5 | semidirect |
| 405. C5 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3061 | 2 |
| C2×#65482 | 2 |
| C2×#65431 | 2 |
| C2×#64787 | 2 |
| C2×#64781 | 2 |
| C2×#64711 | 2 |
| #10598214 | 2 |
| #13307 | 5 |