Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #168 | Q16 | semidirect |
| 127. C5 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#462 | 2 |
| #65368 | 2 |
| #65313 | 2 |
| #65310 | 2 |
| #64767 | 2 |
| #64701 | 2 |
| #64699 | 2 |
| #1692 | 5 |