Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10610908 | C2 | semidirect |
| 3. #10602243 | C2 | semidirect |
| 4. C2×#64734 | C2 | semidirect |
| 5. #10601449 | C2 | semidirect |
| 6. C5×#1384 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 21. #65157 | C4 | semidirect |
| 22. #65154 | C4 | semidirect |
| 35. C2×Dic20 | C2×C4 | semidirect |
| 40. C2×D40 | C2×C4 | semidirect |
| 64. C5×#106 | C2×C4 | semidirect |
| 65. C5×#106 | D4 | semidirect |
| 67. #3949 | D4 | semidirect |
| 81. #1384 | D5 | semidirect |
| 237. #106 | C4×D5 | semidirect |
| 238. #106 | D20 | semidirect |
| 359. C5 | #13008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610912 | 2 |
| #10610908 | 2 |
| #10602243 | 2 |
| C2×#64734 | 2 |
| #10601449 | 2 |
| C5×#1384 | 2 |
| #10598216 | 2 |
| #13008 | 5 |