Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 22. #65471 | C5 | direct (N × H) |
| 61. C5×Dic5 | Q16 | semidirect |
| 141. C52 | #462 | semidirect |
| 164. Dic5 | C5×Q16 | semidirect |
| 203. C5 | #65471 | direct (N × H) |
| 204. C5 | C5×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C5×Q8×Dic5 | 2 |
| C5×#4090 | 2 |
| C2×C5×#689 | 2 |
| C5×#3967 | 2 |
| C5×#3948 | 2 |
| C5×#3946 | 2 |
| C5×#462 | 5 |
| #65471 | 5 |