Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
440 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 16. #64945 | C5 | direct (N × H) |
| 22. C2×C4×C52 | Q8 | semidirect |
| 30. C2×C5×Dic5 | Q8 | semidirect |
| 102. C2×C4×C5 | Dic10 | semidirect |
| 105. C2×C4×C5 | C5×Q8 | semidirect |
| 113. C2×Dic5 | C5×Q8 | semidirect |
| 120. C52 | #395 | semidirect |
| 185. C2×C4 | C5×Dic10 | semidirect |
| 188. C5 | #64945 | direct (N × H) |
| 189. C5 | C5×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic10 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C5×#683 | 2 |
| C52×#95 | 2 |
| C5×#3963 | 2 |
| C5×#395 | 5 |
| #64945 | 5 |