Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
230 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 3. C5×C4⋊C32 | C2 | semidirect |
| 4. #10598081 | C2 | semidirect |
| 5. C4⋊#3926 | C2 | semidirect |
| 37. C4⋊C32 | D5 | direct (N × H) |
| 75. C4×D5 | C32 | semidirect |
| 104. C4×C5 | C2×C32 | semidirect |
| 109. Dic5 | C2×C32 | semidirect |
| 132. D5 | C4⋊C32 | direct (N × H) |
| 149. C5 | C2×C4⋊C32 | semidirect |
| 158. C4 | D5×C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C32 | 2 |
| C4×D5×C16 | 2 |
| C5×C4⋊C32 | 2 |
| #10598081 | 2 |
| C4⋊#3926 | 2 |
| C2×C4⋊C32 | 5 |