Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4×C5×Q32 | C2 | semidirect |
| 2. C2×#64741 | C2 | semidirect |
| 4. #10598068 | C2 | semidirect |
| 5. C4⋊#3926 | C2 | semidirect |
| 23. C5×Q32 | D4 | semidirect |
| 35. C4×Q32 | D5 | semidirect |
| 87. Q32 | D20 | semidirect |
| 104. C4×C5 | SD64 | semidirect |
| 144. C5 | #13686 | semidirect |
| 152. C4 | #64741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q32 | 2 |
| C2×#64741 | 2 |
| #10599853 | 2 |
| #10598068 | 2 |
| C4⋊#3926 | 2 |
| #13686 | 5 |