Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. D5×C4⋊Q8 | C2 | semidirect |
| 3. C5×#461 | C2 | semidirect |
| 4. #65464 | C2 | semidirect |
| 5. #65459 | C2 | semidirect |
| 6. #65372 | C2 | semidirect |
| 7. #65308 | C2 | semidirect |
| 8. #65130 | C2 | semidirect |
| 9. #65122 | C2 | semidirect |
| 10. #65095 | C2 | semidirect |
| 11. #65081 | C2 | semidirect |
| 93. #461 | D5 | semidirect |
| 126. C4×D5 | SD16 | semidirect |
| 269. C5 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| #65882 | 2 |
| C5×#461 | 2 |
| #65464 | 2 |
| #65459 | 2 |
| #65372 | 2 |
| #65308 | 2 |
| #65130 | 2 |
| #65122 | 2 |
| #65095 | 2 |
| #65081 | 2 |
| #3206 | 5 |