Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 91. C5×M16 | Q16 | semidirect |
| 249. M16 | #689 | semidirect |
| 315. C5 | #10505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614953 | 2 |
| C5×#1997 | 2 |
| #10602571 | 2 |
| #10601302 | 2 |
| #10600661 | 2 |
| #10600643 | 2 |
| #10598206 | 2 |
| #10505 | 5 |