Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #10604117 | C2 | semidirect |
| 4. C2×ΓL(1,𝔽81) | C2 | semidirect |
| 6. #10598675 | C2 | semidirect |
| 7. #10598666 | C2 | semidirect |
| 25. C5×#350 | C4 | semidirect |
| 26. #64781 | C4 | semidirect |
| 27. #64735 | C4 | semidirect |
| 28. #64728 | C4 | semidirect |
| 63. C5×M32 | C2×C4 | semidirect |
| 64. C2×C5×C16 | C2×C4 | semidirect |
| 65. #3944 | C2×C4 | semidirect |
| 66. C2×#672 | C2×C4 | semidirect |
| 147. #350 | AGL(1,𝔽5) | semidirect |
| 209. M32 | C2×AGL(1,𝔽5) | semidirect |
| 212. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 335. C5 | #12934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617416 | 2 |
| #10604779 | 2 |
| #10604117 | 2 |
| C2×ΓL(1,𝔽81) | 2 |
| #10599918 | 2 |
| #10598675 | 2 |
| #10598666 | 2 |
| #12934 | 5 |