Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
7902 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7902 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C22×#3999 | C2 | direct (N × H) |
| 4. C25×D5 | C4 | semidirect |
| 7. C24×C4×C5 | C4 | semidirect |
| 10. C23×D20 | C4 | semidirect |
| 13. C22×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 14. C2×#3999 | C22 | direct (N × H) |
| 22. C24×D5 | C2×C4 | semidirect |
| 30. C23×C4×C5 | C2×C4 | semidirect |
| 35. C22×D20 | C2×C4 | semidirect |
| 38. C2×C22⋊AGL(1,𝔽5) | C23 | semidirect |
| 39. #3999 | C23 | direct (N × H) |
| 59. C23×D5 | C22×C4 | semidirect |
| 67. C22×C4×C5 | C22×C4 | semidirect |
| 72. C2×D20 | C22×C4 | semidirect |
| 75. C22⋊AGL(1,𝔽5) | C24 | semidirect |
| 83. C24×C4 | AGL(1,𝔽5) | semidirect |
| 89. C23×C5 | #99 | semidirect |
| 107. C22×D5 | C23×C4 | semidirect |
| 115. C2×C4×C5 | C23×C4 | semidirect |
| 138. C23×C4 | C2×AGL(1,𝔽5) | semidirect |
| 144. C22×C5 | C2×#99 | semidirect |
| 192. C22×C4 | C22×AGL(1,𝔽5) | semidirect |
| 197. C2×C5 | C22×#99 | semidirect |
| 222. C23 | #3999 | direct (N × H) |
| 232. C2×C4 | C23×AGL(1,𝔽5) | semidirect |
| 233. C5 | C23×#99 | semidirect |
| 248. C22 | C2×#3999 | direct (N × H) |
| 259. C2 | C22×#3999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D20 | 2 |
| C23×C22⋊AGL(1,𝔽5) | 2 |
| C22×#3999 | 2 |
| C23×#99 | 5 |