Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3798 conjugacy classes of subgroups; only the 824 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 824 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. C2×#65779 | C2 | semidirect |
| 3. #10617370 | C2 | direct (N × H) |
| 4. C2×#65690 | C2 | semidirect |
| 8. C2×C5×#127 | C4 | semidirect |
| 9. C2×#4086 | C4 | semidirect |
| 10. D5×#127 | C4 | semidirect |
| 12. C2×#4020 | C4 | semidirect |
| 14. #65779 | C22 | semidirect |
| 16. #65690 | C22 | semidirect |
| 22. C22×C5×D4 | C2×C4 | semidirect |
| 23. C22×C22⋊D5 | C2×C4 | semidirect |
| 26. C2×D4×D5 | C2×C4 | semidirect |
| 28. C22×D20 | C2×C4 | semidirect |
| 32. C5×#127 | C2×C4 | semidirect |
| 33. C2×C42×C5 | C2×C4 | semidirect |
| 34. #4086 | C2×C4 | semidirect |
| 35. C2×C4×Dic5 | C2×C4 | semidirect |
| 36. #4020 | C2×C4 | semidirect |
| 37. C42×D5 | C2×C4 | semidirect |
| 56. C2×C5×D4 | C22×C4 | semidirect |
| 59. C2×C22⋊D5 | C22×C4 | semidirect |
| 65. C2×D20 | C22×C4 | semidirect |
| 70. C42×C5 | C22×C4 | semidirect |
| 71. C4×Dic5 | C22×C4 | semidirect |
| 78. C2×#127 | AGL(1,𝔽5) | semidirect |
| 116. C22×D4 | C2×AGL(1,𝔽5) | semidirect |
| 123. #127 | C2×AGL(1,𝔽5) | semidirect |
| 129. C2×C42 | C2×AGL(1,𝔽5) | semidirect |
| 161. C2×D4 | C22×AGL(1,𝔽5) | semidirect |
| 173. C42 | C22×AGL(1,𝔽5) | semidirect |
| 175. C2×C5 | #2380 | semidirect |
| 178. D5 | #2380 | semidirect |
| 205. C5 | C2×#2380 | semidirect |
| 225. C2 | #10617370 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#127 | 2 |
| C2×#65779 | 2 |
| #10617370 | 2 |
| C2×#65690 | 2 |
| C2×#2380 | 5 |