Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×ΓL(1,𝔽81) | C2 | semidirect |
| 4. #10604091 | C2 | semidirect |
| 6. #10598661 | C2 | semidirect |
| 7. #10598627 | C2 | semidirect |
| 25. C5×#359 | C4 | semidirect |
| 26. #64787 | C4 | semidirect |
| 27. #64730 | C4 | semidirect |
| 28. #64717 | C4 | semidirect |
| 64. C2×C5×C16 | C2×C4 | semidirect |
| 65. C5×#108 | C2×C4 | semidirect |
| 67. #3951 | C2×C4 | semidirect |
| 68. C2×#672 | C2×C4 | semidirect |
| 147. #359 | AGL(1,𝔽5) | semidirect |
| 211. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 218. #108 | C2×AGL(1,𝔽5) | semidirect |
| 332. C5 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617441 | 2 |
| #10604860 | 2 |
| C2×ΓL(1,𝔽81) | 2 |
| #10604091 | 2 |
| #10600034 | 2 |
| #10598661 | 2 |
| #10598627 | 2 |
| #12949 | 5 |