Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×C5×C8 | C2 | semidirect |
| 3. C2×#3953 | C2 | semidirect |
| 4. #65224 | C2 | semidirect |
| 12. #4020 | C4 | semidirect |
| 29. C2×C5×C8 | D4 | semidirect |
| 36. C2×C4×C8 | D5 | semidirect |
| 77. C4×C5 | #102 | semidirect |
| 94. C2×C8 | D20 | semidirect |
| 124. C5 | #1957 | semidirect |
| 136. C4 | #3953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4020 | 2 |
| C2×C4×C5×C8 | 2 |
| C2×#3953 | 2 |
| #65224 | 2 |
| #1957 | 5 |