Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. C2×#3930 | C2 | semidirect |
| 3. D5×#107 | C2 | semidirect |
| 4. C5×#358 | C2 | semidirect |
| 5. #64784 | C2 | semidirect |
| 6. #64729 | C2 | semidirect |
| 7. #64711 | C2 | semidirect |
| 12. #4065 | C4 | semidirect |
| 32. C5×Q16 | C2×C4 | semidirect |
| 40. D40 | C2×C4 | semidirect |
| 49. #358 | D5 | semidirect |
| 107. Q16 | C4×D5 | semidirect |
| 144. C5 | #2139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4065 | 2 |
| C2×#3930 | 2 |
| D5×#107 | 2 |
| C5×#358 | 2 |
| #64784 | 2 |
| #64729 | 2 |
| #64711 | 2 |
| #2139 | 5 |