Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 2. C2×C22⋊#674 | C2 | semidirect |
| 3. #10598781 | C2 | direct (N × H) |
| 13. C22⋊#674 | C22 | semidirect |
| 212. C2×C5 | #1315 | semidirect |
| 251. C5 | C2×#1315 | semidirect |
| 272. C2 | #10598781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65418 | 2 |
| C2×C22⋊#674 | 2 |
| #10598781 | 2 |
| C2×#1315 | 5 |