Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#4064 | C2 | semidirect |
| 2. C2×#4061 | C2 | semidirect |
| 3. D5×C4⋊Q8 | C2 | semidirect |
| 5. C5×#497 | C2 | semidirect |
| 6. #65470 | C2 | semidirect |
| 7. #65464 | C2 | semidirect |
| 8. #65375 | C2 | semidirect |
| 9. #65349 | C2 | semidirect |
| 10. #65004 | C2 | semidirect |
| 11. #64996 | C2 | semidirect |
| 80. #676 | D4 | semidirect |
| 88. #497 | D5 | semidirect |
| 165. Dic5 | #137 | semidirect |
| 240. C5 | #3152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4064 | 2 |
| C2×#4061 | 2 |
| D5×C4⋊Q8 | 2 |
| #66002 | 2 |
| C5×#497 | 2 |
| #65470 | 2 |
| #65464 | 2 |
| #65375 | 2 |
| #65349 | 2 |
| #65004 | 2 |
| #64996 | 2 |
| #3152 | 5 |