Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#4061 | C2 | semidirect |
| 3. Q8×D20 | C2 | semidirect |
| 4. C5×#460 | C2 | semidirect |
| 5. #65459 | C2 | semidirect |
| 6. #65365 | C2 | semidirect |
| 7. C4×#689 | C2 | semidirect |
| 8. #65138 | C2 | semidirect |
| 9. #65127 | C2 | semidirect |
| 10. #65072 | C2 | semidirect |
| 11. #65069 | C2 | semidirect |
| 67. #689 | D4 | semidirect |
| 89. #460 | D5 | semidirect |
| 166. C4×C5 | #137 | semidirect |
| 250. C5 | #3278 | semidirect |
| 265. C4 | #4061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4061 | 2 |
| #66052 | 2 |
| Q8×D20 | 2 |
| C5×#460 | 2 |
| #65459 | 2 |
| #65365 | 2 |
| C4×#689 | 2 |
| #65138 | 2 |
| #65127 | 2 |
| #65072 | 2 |
| #65069 | 2 |
| #3278 | 5 |