Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#64723 | C2 | semidirect |
| 5. #10601447 | C2 | semidirect |
| 6. C5×#1382 | C2 | semidirect |
| 7. #10598223 | C2 | semidirect |
| 20. #65185 | C4 | semidirect |
| 44. C2×Dic20 | C2×C4 | semidirect |
| 61. C5×#108 | C2×C4 | semidirect |
| 79. #1382 | D5 | semidirect |
| 221. #108 | C4×D5 | semidirect |
| 339. C5 | #12997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65185 | 2 |
| #10610910 | 2 |
| C2×#64723 | 2 |
| C2×#64728 | 2 |
| #10601447 | 2 |
| C5×#1382 | 2 |
| #10598223 | 2 |
| #12997 | 5 |