Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10598279 | C2 | direct (N × H) |
| 5. C2×C5×C4⋊Q8 | C4 | semidirect |
| 8. C5×#492 | C4 | semidirect |
| 10. C2×C4×C5×C8 | C4 | semidirect |
| 25. C5×C4⋊Q8 | C2×C4 | semidirect |
| 34. C4×C5×C8 | C2×C4 | semidirect |
| 71. C2×C4⋊Q8 | Dic5 | semidirect |
| 74. #492 | Dic5 | semidirect |
| 77. C2×C4×C8 | Dic5 | semidirect |
| 117. C4⋊Q8 | C2×Dic5 | semidirect |
| 128. C4×C8 | C2×Dic5 | semidirect |
| 179. C2×C5 | #1409 | semidirect |
| 208. C5 | C2×#1409 | semidirect |
| 229. C2 | #10598279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#492 | 2 |
| C2×#64765 | 2 |
| #10598279 | 2 |
| C2×#1409 | 5 |