Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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. #65470 | C5 | direct (N × H) |
| 43. C5×Dic5 | Q16 | semidirect |
| 98. C52 | #494 | semidirect |
| 114. Dic5 | C5×Q16 | semidirect |
| 141. C5 | #65470 | direct (N × H) |
| 142. C5 | C5×#494 | 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×#4090 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×Dic20 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#494 | 5 |
| #65470 | 5 |