Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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. #10611475 | C2 | semidirect |
| 2. #10601707 | C2 | semidirect |
| 3. #10599873 | C2 | semidirect |
| 5. C5×#1334 | C2 | semidirect |
| 6. #10598006 | C2 | semidirect |
| 7. #10597959 | C2 | semidirect |
| 67. #1334 | D5 | semidirect |
| 271. C5 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611475 | 2 |
| #10601707 | 2 |
| #10599873 | 2 |
| #10599333 | 2 |
| C5×#1334 | 2 |
| #10598006 | 2 |
| #10597959 | 2 |
| #12349 | 5 |