Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 114 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×C16×AGL(1,𝔽5) | C2 | semidirect |
| 4. AGL(1,𝔽5)×#108 | C2 | semidirect |
| 6. #10598665 | C2 | semidirect |
| 7. #10598626 | C2 | semidirect |
| 21. #64909 | C4 | semidirect |
| 22. #64905 | C4 | semidirect |
| 25. C5×#359 | C4 | semidirect |
| 26. #64787 | C4 | semidirect |
| 27. #64730 | C4 | semidirect |
| 28. #64717 | C4 | semidirect |
| 54. #3996 | C2×C4 | semidirect |
| 63. D5⋊C16 | C2×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) | direct (N × H) |
| 213. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 218. #108 | C2×AGL(1,𝔽5) | semidirect |
| 236. AGL(1,𝔽5) | #359 | direct (N × H) |
| 336. C5 | C4×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×#135 | 2 |
| D5⋊#359 | 2 |
| C2×C16×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×#108 | 2 |
| D5×#359 | 2 |
| #10598665 | 2 |
| #10598626 | 2 |
| C4×#359 | 5 |