Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 227. C5 | #12382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611645 | 2 |
| #10601737 | 2 |
| #10600088 | 2 |
| #10599858 | 2 |
| C5×Q8⋊C16 | 2 |
| #10598052 | 2 |
| #10597996 | 2 |
| #12382 | 5 |