Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
626 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 172 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. #10598774 | C2 | semidirect |
| 66. C2×C5×C8 | M16 | semidirect |
| 80. C2×#168 | M16 | semidirect |
| 184. C2×C8 | #704 | semidirect |
| 225. C5 | #7919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617473 | 2 |
| C22×#3947 | 2 |
| #10598774 | 2 |
| #7919 | 5 |