Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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×#64850 | C2 | semidirect |
| 4. #10604075 | C2 | semidirect |
| 6. (C2×AGL(1,𝔽5))⋊C16 | C2 | semidirect |
| 7. #10598619 | C2 | semidirect |
| 23. C5×#357 | C4 | semidirect |
| 24. #64782 | C4 | semidirect |
| 25. #64729 | C4 | semidirect |
| 26. #64711 | C4 | semidirect |
| 58. C2×C5×C16 | C2×C4 | semidirect |
| 59. C5×#107 | C2×C4 | semidirect |
| 60. #3950 | C2×C4 | semidirect |
| 61. C2×#672 | C2×C4 | semidirect |
| 101. C5×D8 | C4⋊C4 | semidirect |
| 110. D40 | C4⋊C4 | semidirect |
| 135. #357 | AGL(1,𝔽5) | semidirect |
| 205. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 212. #107 | C2×AGL(1,𝔽5) | semidirect |
| 266. D8 | C4⋊AGL(1,𝔽5) | semidirect |
| 342. C5 | #12937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×AGL(1,𝔽5) | 2 |
| C2×#64904 | 2 |
| C2×#64850 | 2 |
| #10604075 | 2 |
| D5×#357 | 2 |
| (C2×AGL(1,𝔽5))⋊C16 | 2 |
| #10598619 | 2 |
| #12937 | 5 |