Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 3. C5×#3950 | C2 | semidirect |
| 4. C5×#3949 | C2 | semidirect |
| 6. C2×C52×C8 | C4 | semidirect |
| 13. #65395 | C5 | direct (N × H) |
| 29. #3950 | C2×C5 | semidirect |
| 30. #3949 | C2×C5 | semidirect |
| 44. C2×C5×C8 | Dic5 | semidirect |
| 45. C2×C5×C8 | C4×C5 | semidirect |
| 87. C52 | #427 | semidirect |
| 109. C2×C8 | C5×Dic5 | semidirect |
| 133. C5 | #65395 | direct (N × H) |
| 134. C5 | C5×#427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| C5×#4072 | 2 |
| C5×#3950 | 2 |
| C5×#3949 | 2 |
| C5×#427 | 5 |
| #65395 | 5 |