Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 64. C4×C5 | Q32 | semidirect |
| 101. C5 | #2209 | semidirect |
| 107. C4 | #3961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#494 | 2 |
| C2×#3961 | 2 |
| C4×Dic20 | 2 |
| #64784 | 2 |
| C4⋊#672 | 2 |
| #2209 | 5 |