Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
362 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10603828 | C2 | semidirect |
| 3. D5⋊(C4⋊C16) | C2 | semidirect |
| 4. Q8⋊#674 | C2 | semidirect |
| 5. #10598579 | C2 | semidirect |
| 63. #713 | C16 | semidirect |
| 120. C5×Q8 | C2×C16 | semidirect |
| 132. D20 | C2×C16 | semidirect |
| 246. Q8 | D5⋊C16 | semidirect |
| 275. C5 | #11621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#713 | 2 |
| #10603828 | 2 |
| D5⋊(C4⋊C16) | 2 |
| Q8⋊#674 | 2 |
| #10598579 | 2 |
| #11621 | 5 |