Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. C5×D4×Q16 | C2 | semidirect |
| 2. #10602106 | C2 | semidirect |
| 3. #10601707 | C2 | semidirect |
| 5. #10598284 | C2 | semidirect |
| 6. #10598256 | C2 | semidirect |
| 7. D4⋊#672 | C2 | semidirect |
| 57. D4×Q16 | D5 | semidirect |
| 80. C5×Q16 | D8 | semidirect |
| 128. C5×D4 | SD32 | semidirect |
| 212. Q16 | #686 | semidirect |
| 253. D4 | #3960 | semidirect |
| 269. C5 | #12318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Q16 | 2 |
| #10602106 | 2 |
| #10601707 | 2 |
| #10601640 | 2 |
| #10598284 | 2 |
| #10598256 | 2 |
| D4⋊#672 | 2 |
| #12318 | 5 |