Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 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 |
|---|---|---|
| 4. C5×#3949 | C2 | semidirect |
| 5. C5×#3948 | C2 | semidirect |
| 16. #65010 | C5 | direct (N × H) |
| 36. #3949 | C2×C5 | semidirect |
| 37. #3948 | C2×C5 | semidirect |
| 102. C52 | #483 | semidirect |
| 159. C5 | #65010 | direct (N × H) |
| 160. C5 | C5×#483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊Dic5 | 2 |
| C5×#4070 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3949 | 2 |
| C5×#3948 | 2 |
| C5×#483 | 5 |
| #65010 | 5 |