Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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. C2×D5×D16 | C2 | semidirect |
| 2. D5×#493 | C2 | semidirect |
| 3. C5×#2246 | C2 | semidirect |
| 4. #10602257 | C2 | semidirect |
| 5. #10602083 | C2 | semidirect |
| 6. #10599853 | C2 | semidirect |
| 7. C4×D5×C16 | C2 | semidirect |
| 11. C2×C5×D16 | C22 | semidirect |
| 12. C5×#493 | C22 | semidirect |
| 14. #65440 | C22 | semidirect |
| 15. C2×#3958 | C22 | semidirect |
| 18. C2×D80 | C22 | semidirect |
| 20. #64984 | C22 | semidirect |
| 22. C4×C5×C16 | C22 | semidirect |
| 23. C16×Dic5 | C22 | semidirect |
| 24. C4×#672 | C22 | semidirect |
| 52. D5×C16 | D4 | semidirect |
| 58. #2246 | D5 | direct (N × H) |
| 87. C5×C16 | C2×D4 | semidirect |
| 88. #672 | C2×D4 | semidirect |
| 95. C2×D16 | C2×D5 | semidirect |
| 101. #493 | C2×D5 | semidirect |
| 105. C4×C16 | C2×D5 | semidirect |
| 123. C4×D5 | D16 | semidirect |
| 165. C4×C5 | C2×D16 | semidirect |
| 169. Dic5 | C2×D16 | semidirect |
| 198. C16 | D4×D5 | semidirect |
| 203. D5 | #2246 | direct (N × H) |
| 228. C5 | C2×#2246 | semidirect |
| 239. C4 | D5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D16 | 2 |
| D5×#493 | 2 |
| C5×#2246 | 2 |
| #10602257 | 2 |
| #10602083 | 2 |
| #10599853 | 2 |
| C4×D5×C16 | 2 |
| C2×#2246 | 5 |