Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
702 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 280 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 |
|---|---|---|
| 4. C2×ΓL(1,𝔽81) | C2 | direct (N × H) |
| 12. C22×C5×C16 | C4 | semidirect |
| 13. C22×#672 | C4 | semidirect |
| 14. C2×#3930 | C4 | semidirect |
| 16. ΓL(1,𝔽81) | C22 | direct (N × H) |
| 35. C2×C5×C16 | C2×C4 | semidirect |
| 36. C2×#672 | C2×C4 | semidirect |
| 37. #3930 | C2×C4 | semidirect |
| 66. C5×C16 | C22×C4 | semidirect |
| 67. #672 | C22×C4 | semidirect |
| 74. C22×C16 | AGL(1,𝔽5) | semidirect |
| 116. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 121. C22×C5 | #365 | semidirect |
| 156. C16 | C22×AGL(1,𝔽5) | semidirect |
| 157. C2×C5 | C2×#365 | semidirect |
| 181. C5 | C22×#365 | semidirect |
| 186. C22 | ΓL(1,𝔽81) | direct (N × H) |
| 195. C2 | C2×ΓL(1,𝔽81) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3995 | 2 |
| C22×#3993 | 2 |
| C22×#3930 | 2 |
| C2×ΓL(1,𝔽81) | 2 |
| C22×#365 | 5 |