Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 84 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×#64849 | C2 | semidirect |
| 4. #10604088 | C2 | semidirect |
| 6. #10598662 | C2 | semidirect |
| 7. #10598629 | 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 |
| 146. #359 | AGL(1,𝔽5) | semidirect |
| 214. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 217. #108 | C2×AGL(1,𝔽5) | semidirect |
| 342. C5 | #12945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617440 | 2 |
| #10604856 | 2 |
| C2×#64849 | 2 |
| #10604088 | 2 |
| D5×#359 | 2 |
| #10598662 | 2 |
| #10598629 | 2 |
| #12945 | 5 |