Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×C5×SD32 | C2 | semidirect |
| 2. #65481 | C2 | semidirect |
| 4. #65190 | C2 | semidirect |
| 5. #64785 | C2 | semidirect |
| 6. #64783 | C2 | semidirect |
| 7. #64726 | C2 | semidirect |
| 44. C2×SD32 | D5 | semidirect |
| 130. C5 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD32 | 2 |
| #65481 | 2 |
| #65449 | 2 |
| #65190 | 2 |
| #64785 | 2 |
| #64783 | 2 |
| #64726 | 2 |
| #2223 | 5 |