Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 23. #64698 | C4 | direct (N × H) |
| 224. C4×C5 | #356 | semidirect |
| 319. C5 | C4×#356 | semidirect |
| 337. C4 | #64698 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4090 | 2 |
| C4×C5×#101 | 2 |
| C4×#3968 | 2 |
| C2×#64698 | 2 |
| #10598190 | 2 |
| C4×#356 | 5 |