Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
522 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 522 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 |
|---|---|---|
| 1. #10617439 | C2 | semidirect |
| 3. D5⋊#360 | C2 | semidirect |
| 4. #10604803 | C2 | semidirect |
| 5. #10604786 | C2 | semidirect |
| 6. #10598675 | C2 | semidirect |
| 7. #10598671 | C2 | semidirect |
| 21. C5×#509 | C4 | semidirect |
| 22. #65482 | C4 | semidirect |
| 23. #65436 | C4 | semidirect |
| 28. #65197 | C4 | semidirect |
| 47. C2×C5×D8 | C2×C4 | semidirect |
| 61. C2×D40 | C2×C4 | semidirect |
| 77. C5×M32 | C2×C4 | semidirect |
| 82. #3944 | C2×C4 | semidirect |
| 130. C5×Q16 | C22⋊C4 | semidirect |
| 134. C5×D8 | C22⋊C4 | semidirect |
| 143. Dic20 | C22⋊C4 | semidirect |
| 146. D40 | C22⋊C4 | semidirect |
| 163. #509 | AGL(1,𝔽5) | semidirect |
| 243. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 267. M32 | C2×AGL(1,𝔽5) | semidirect |
| 326. Q16 | C22⋊AGL(1,𝔽5) | semidirect |
| 339. D8 | C22⋊AGL(1,𝔽5) | semidirect |
| 417. C5 | #13025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617439 | 2 |
| D5×#509 | 2 |
| D5⋊#360 | 2 |
| #10604803 | 2 |
| #10604786 | 2 |
| #10598675 | 2 |
| #10598671 | 2 |
| #13025 | 5 |