Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
946 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 192 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. #10617428 | C2 | semidirect |
| 3. #10604828 | C2 | semidirect |
| 4. #10604670 | C2 | semidirect |
| 6. #10603851 | C2 | semidirect |
| 21. C5×#492 | C4 | semidirect |
| 22. #65464 | C4 | semidirect |
| 23. #65374 | C4 | semidirect |
| 24. #65365 | C4 | semidirect |
| 25. #64982 | C4 | semidirect |
| 38. C2×C5×SD16 | C2×C4 | semidirect |
| 39. C5×C4⋊Q8 | C2×C4 | semidirect |
| 41. #4090 | C2×C4 | semidirect |
| 42. C2×#688 | C2×C4 | semidirect |
| 45. C2×#687 | C2×C4 | semidirect |
| 50. C2×#677 | C2×C4 | semidirect |
| 56. #4015 | C2×C4 | semidirect |
| 63. #3994 | D4 | semidirect |
| 64. #3993 | D4 | semidirect |
| 67. C4×C5×C8 | C2×C4 | semidirect |
| 68. C8×Dic5 | C2×C4 | semidirect |
| 69. C4×#168 | C2×C4 | semidirect |
| 133. #492 | AGL(1,𝔽5) | semidirect |
| 188. C2×SD16 | C2×AGL(1,𝔽5) | semidirect |
| 194. C4⋊Q8 | C2×AGL(1,𝔽5) | semidirect |
| 218. C4×C8 | C2×AGL(1,𝔽5) | semidirect |
| 323. C5 | #23198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617428 | 2 |
| D5×#492 | 2 |
| #10604828 | 2 |
| #10604670 | 2 |
| #10604614 | 2 |
| #10603851 | 2 |
| #23198 | 5 |