Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
496 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 81 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. D5×#349 | C2 | semidirect |
| 3. D5×H(3,ℤ/4) | C2 | semidirect |
| 4. C5×#1339 | C2 | semidirect |
| 5. #10598269 | C2 | semidirect |
| 6. #10598025 | C2 | semidirect |
| 7. #10597972 | C2 | semidirect |
| 8. C2×D5×D8 | C4 | semidirect |
| 13. #65448 | C4 | semidirect |
| 17. #65154 | C4 | semidirect |
| 18. D5×#106 | C4 | semidirect |
| 21. C5×#349 | C22 | semidirect |
| 22. C5×H(3,ℤ/4) | C22 | semidirect |
| 23. #64777 | C22 | semidirect |
| 24. #64773 | C22 | semidirect |
| 31. C2×C5×D8 | C2×C4 | semidirect |
| 45. C2×D40 | C2×C4 | semidirect |
| 61. C5×#106 | C2×C4 | semidirect |
| 65. #3949 | C2×C4 | semidirect |
| 77. #1339 | D5 | direct (N × H) |
| 152. #349 | C2×D5 | semidirect |
| 155. H(3,ℤ/4) | C2×D5 | semidirect |
| 213. C2×D8 | C4×D5 | semidirect |
| 244. #106 | C4×D5 | semidirect |
| 343. D5 | #1339 | direct (N × H) |
| 394. C5 | C2×#1339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#469 | 2 |
| D5×#349 | 2 |
| D5×H(3,ℤ/4) | 2 |
| C5×#1339 | 2 |
| #10598269 | 2 |
| #10598025 | 2 |
| #10597972 | 2 |
| C2×#1339 | 5 |