Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1470 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 744 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. #10604190 | C2 | direct (N × H) |
| 18. C2×C42×C5 | C8 | semidirect |
| 44. C42×C5 | C2×C8 | semidirect |
| 61. C2×C4×C5 | C4⋊C8 | semidirect |
| 85. C2×C42 | #170 | semidirect |
| 94. C4×C5 | C2×C4⋊C8 | semidirect |
| 117. C42 | C2×#170 | semidirect |
| 118. C2×C5 | #1842 | semidirect |
| 134. C2×C4 | C4⋊#170 | semidirect |
| 139. C5 | C2×#1842 | semidirect |
| 150. C4 | C2×C4⋊#170 | semidirect |
| 151. C2 | #10604190 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#170 | 2 |
| C2×C42×Dic5 | 2 |
| #10604190 | 2 |
| C2×#1842 | 5 |