Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#474 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 5. #65296 | C2 | semidirect |
| 6. #65170 | C2 | semidirect |
| 7. #65164 | C2 | semidirect |
| 8. #65140 | C2 | semidirect |
| 9. #65126 | C2 | semidirect |
| 11. #65050 | C2 | semidirect |
| 52. #711 | Q8 | semidirect |
| 90. #474 | D5 | semidirect |
| 98. C5×D4 | C2×Q8 | semidirect |
| 122. Dic10 | C2×Q8 | semidirect |
| 228. D4 | Q8×D5 | semidirect |
| 250. C5 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| C4×#711 | 2 |
| C5×#474 | 2 |
| #65383 | 2 |
| #65296 | 2 |
| #65170 | 2 |
| #65164 | 2 |
| #65140 | 2 |
| #65126 | 2 |
| #65060 | 2 |
| #65050 | 2 |
| #3079 | 5 |