Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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×C5×SD32 | C2 | semidirect |
| 2. #65470 | C2 | semidirect |
| 3. C2×#3960 | C2 | semidirect |
| 5. C2×#3959 | C2 | semidirect |
| 6. C2×#3932 | C2 | semidirect |
| 7. C16×Dic5 | C2 | semidirect |
| 43. C5×C16 | D4 | semidirect |
| 44. #672 | D4 | semidirect |
| 48. C2×SD32 | D5 | semidirect |
| 94. Dic5 | SD32 | semidirect |
| 115. C16 | C22⋊D5 | semidirect |
| 138. C5 | #2248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD32 | 2 |
| #65470 | 2 |
| C2×#3960 | 2 |
| #65440 | 2 |
| C2×#3959 | 2 |
| C2×#3932 | 2 |
| C16×Dic5 | 2 |
| #2248 | 5 |