Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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×#1593 | C2 | semidirect |
| 4. #10598255 | C2 | semidirect |
| 6. #10597955 | C2 | semidirect |
| 7. #10597933 | C2 | semidirect |
| 46. #1593 | D5 | semidirect |
| 189. C5 | #12077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1593 | 2 |
| #10601706 | 2 |
| #10598870 | 2 |
| #10598255 | 2 |
| #10597956 | 2 |
| #10597955 | 2 |
| #10597933 | 2 |
| #12077 | 5 |