Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 86 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×#64847 | C2 | semidirect |
| 4. #10604076 | C2 | semidirect |
| 6. #10598660 | C2 | semidirect |
| 7. #10598622 | C2 | semidirect |
| 23. C5×#358 | C4 | semidirect |
| 24. #64784 | C4 | semidirect |
| 25. #64729 | C4 | semidirect |
| 26. #64711 | C4 | semidirect |
| 98. C5×Q16 | C4⋊C4 | semidirect |
| 107. D40 | C4⋊C4 | semidirect |
| 130. #358 | AGL(1,𝔽5) | semidirect |
| 234. Q16 | C4⋊AGL(1,𝔽5) | semidirect |
| 303. C5 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65741 | 2 |
| C2×#64907 | 2 |
| C2×#64847 | 2 |
| #10604076 | 2 |
| #10600014 | 2 |
| #10598660 | 2 |
| #10598622 | 2 |
| #12955 | 5 |