Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 28. C42×C5 | C16 | semidirect |
| 61. C4×C5 | C4⋊C16 | semidirect |
| 72. C42 | #672 | semidirect |
| 90. C5 | #12898 | semidirect |
| 95. C4 | C4⋊#672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×C8 | 2 |
| C2×C4⋊#672 | 2 |
| #12898 | 5 |