Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
342 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 121 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×D5×C32 | C2 | semidirect |
| 3. C5×C22⋊C32 | C2 | semidirect |
| 4. C22⋊#3926 | C2 | semidirect |
| 5. #10598085 | C2 | semidirect |
| 14. C2×C5×C32 | C22 | semidirect |
| 15. C2×#3926 | C22 | semidirect |
| 43. C22⋊C32 | D5 | direct (N × H) |
| 80. C2×C32 | C2×D5 | semidirect |
| 84. C22×D5 | C32 | semidirect |
| 128. C22×C5 | C2×C32 | semidirect |
| 135. C2×D5 | C2×C32 | semidirect |
| 173. D5 | C22⋊C32 | direct (N × H) |
| 198. C5 | C2×C22⋊C32 | semidirect |
| 208. C22 | D5×C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×C16 | 2 |
| C2×D5×C32 | 2 |
| C5×C22⋊C32 | 2 |
| C22⋊#3926 | 2 |
| #10598085 | 2 |
| C2×C22⋊C32 | 5 |