Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3062 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 3062 conjugacy classes of subgroups — too many to draw. Only its 400 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 |
|---|---|---|
| 2. C2×#65780 | C2 | semidirect |
| 3. C2×C4×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. #10604954 | C2 | semidirect |
| 10. C2×C5×#127 | C4 | semidirect |
| 11. C2×#4086 | C4 | semidirect |
| 12. C2×#4086 | C4 | semidirect |
| 14. C2×#4020 | C4 | semidirect |
| 40. C2×C4⋊AGL(1,𝔽5) | D4 | semidirect |
| 97. C42×C5 | C22⋊C4 | semidirect |
| 98. C4×Dic5 | C22⋊C4 | semidirect |
| 99. C4×Dic5 | C22⋊C4 | semidirect |
| 106. C2×#127 | AGL(1,𝔽5) | semidirect |
| 207. C4×C5 | #390 | semidirect |
| 209. Dic5 | #390 | semidirect |
| 253. C42 | C22⋊AGL(1,𝔽5) | semidirect |
| 302. C5 | #14154 | semidirect |
| 325. C4 | #65780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#127 | 2 |
| C2×#65780 | 2 |
| C2×C4×C4⋊AGL(1,𝔽5) | 2 |
| #10604954 | 2 |
| #14154 | 5 |