Order 1280.
7630 conjugacy classes of subgroups.
The subgroup lattice has 344 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#4072 | C2 | semidirect |
| 4. #10615758 | C2 | direct (N × H) |
| 5. C2×#65500 | C2 | semidirect |
| 6. C2×#65501 | C2 | semidirect |
| 7. C2×C4×C22⋊Dic5 | C2 | semidirect |
| 10. C24×C4×C5 | C4 | semidirect |
| 19. C2×#4072 | C22 | semidirect |
| 20. C22×C4⋊Dic5 | C22 | semidirect |
| 21. C22×C4×Dic5 | C22 | semidirect |
| 23. #65501 | C22 | semidirect |
| 24. #65500 | C22 | semidirect |
| 25. C4×C22⋊Dic5 | C22 | semidirect |
| 26. C2×#3963 | C22 | semidirect |
| 43. C23×C4×C5 | C2×C4 | semidirect |
| 59. C2×C4⋊Dic5 | C23 | semidirect |
| 61. C2×C4×Dic5 | C23 | semidirect |
| 62. #3963 | C23 | semidirect |
| 94. C22×C4×C5 | C22⋊C4 | semidirect |
| 117. C24×C4 | Dic5 | semidirect |
| 147. C23×C5 | #117 | semidirect |
| 163. C2×C4×C5 | C2×C22⋊C4 | semidirect |
| 188. C23×C4 | C2×Dic5 | semidirect |
| 218. C22×C5 | C2×#117 | semidirect |
| 254. C22×C4 | C22⋊Dic5 | semidirect |
| 274. C2×C5 | #2280 | semidirect |
| 290. C23 | #4072 | semidirect |
| 310. C2×C4 | C2×C22⋊Dic5 | semidirect |
| 316. C5 | C2×#2280 | semidirect |
| 326. C22 | C2×#4072 | semidirect |
| 339. C2 | #10615758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C5 | 2 |
| C22×#4072 | 2 |
| C2×#65536 | 2 |
| #10615758 | 2 |
| C2×#65500 | 2 |
| C2×#65501 | 2 |
| C2×C4×C22⋊Dic5 | 2 |
| C2×#2280 | 5 |