Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 3. #10604118 | C2 | semidirect |
| 4. #10604052 | C2 | semidirect |
| 6. #10598671 | C2 | semidirect |
| 7. #10598605 | C2 | semidirect |
| 27. C5×#360 | C4 | semidirect |
| 28. #64786 | C4 | semidirect |
| 29. #64738 | C4 | semidirect |
| 30. #64708 | C4 | semidirect |
| 72. C5×M32 | C2×C4 | semidirect |
| 73. C5×#106 | C2×C4 | semidirect |
| 74. #3949 | C2×C4 | semidirect |
| 75. #3944 | C2×C4 | semidirect |
| 121. C5×Q16 | C4⋊C4 | semidirect |
| 123. C5×D8 | C4⋊C4 | semidirect |
| 133. Dic20 | C4⋊C4 | semidirect |
| 134. D40 | C4⋊C4 | semidirect |
| 162. #360 | AGL(1,𝔽5) | semidirect |
| 238. M32 | C2×AGL(1,𝔽5) | semidirect |
| 248. #106 | C2×AGL(1,𝔽5) | semidirect |
| 297. Q16 | C4⋊AGL(1,𝔽5) | semidirect |
| 304. D8 | C4⋊AGL(1,𝔽5) | semidirect |
| 385. C5 | #12943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617439 | 2 |
| #10604856 | 2 |
| #10604118 | 2 |
| #10604052 | 2 |
| D5×#360 | 2 |
| #10598671 | 2 |
| #10598605 | 2 |
| #12943 | 5 |