Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×#536 | C2 | semidirect |
| 3. C2×#4093 | C2 | semidirect |
| 4. C2×#3969 | C2 | semidirect |
| 5. C2×#3968 | C2 | semidirect |
| 6. #65290 | C2 | semidirect |
| 7. #64752 | C2 | semidirect |
| 71. #536 | D5 | semidirect |
| 236. C5 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#536 | 2 |
| C2×#4095 | 2 |
| C2×#4093 | 2 |
| C2×#3969 | 2 |
| C2×#3968 | 2 |
| #65290 | 2 |
| #64752 | 2 |
| #2003 | 5 |