Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 13. C5×Dic20 | C4 | direct (N × H) |
| 15. C4×Dic20 | C5 | direct (N × H) |
| 38. C4×C52 | Q16 | semidirect |
| 61. Dic20 | C4×C5 | direct (N × H) |
| 94. C52 | C4×Q16 | semidirect |
| 106. C4×C5 | Dic20 | direct (N × H) |
| 107. C4×C5 | C5×Q16 | semidirect |
| 141. C5 | C4×Dic20 | direct (N × H) |
| 142. C5 | C4×C5×Q16 | semidirect |
| 147. C4 | C5×Dic20 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C4×C5×Dic10 | 2 |
| C4×C52×C8 | 2 |
| C5×#3950 | 2 |
| C5×#3948 | 2 |
| C4×C5×Q16 | 5 |
| C4×Dic20 | 5 |