Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
200 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. #64882 | C2 | direct (N × H) |
| 18. C2×C5×C8 | C8 | semidirect |
| 42. C5×C8 | C2×C8 | semidirect |
| 71. C2×C8 | #170 | semidirect |
| 77. C2×C5 | #335 | semidirect |
| 95. C8 | C2×#170 | semidirect |
| 96. C5 | C2×#335 | semidirect |
| 109. C2 | #64882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#170 | 2 |
| C2×C8×Dic5 | 2 |
| #64882 | 2 |
| C2×#335 | 5 |