Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×Dic20 | C2 | semidirect |
| 4. C5×#1312 | C2 | semidirect |
| 5. #10597996 | C2 | semidirect |
| 7. #10597991 | C2 | semidirect |
| 51. #1312 | D5 | semidirect |
| 69. Dic20 | M16 | semidirect |
| 194. C5 | #12075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3932 | 2 |
| C8×Dic20 | 2 |
| #10598845 | 2 |
| C5×#1312 | 2 |
| #10597996 | 2 |
| #10597995 | 2 |
| #10597991 | 2 |
| #12075 | 5 |