Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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. #10601674 | C2 | semidirect |
| 3. #10599356 | C2 | semidirect |
| 4. C5×#1331 | C2 | semidirect |
| 5. #10597995 | C2 | semidirect |
| 6. #10597989 | C2 | semidirect |
| 7. #10597961 | C2 | semidirect |
| 50. #1331 | D5 | semidirect |
| 76. #672 | M16 | semidirect |
| 203. C5 | #12086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3958 | 2 |
| #10601674 | 2 |
| #10599356 | 2 |
| C5×#1331 | 2 |
| #10597995 | 2 |
| #10597989 | 2 |
| #10597961 | 2 |
| #12086 | 5 |