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 |
|---|---|---|
| 4. C5×#3950 | C2 | semidirect |
| 5. C5×#3949 | C2 | semidirect |
| 8. C52×M16 | C4 | semidirect |
| 17. #65410 | C5 | direct (N × H) |
| 27. C52×C8 | C2×C4 | semidirect |
| 37. #3950 | C2×C5 | semidirect |
| 38. #3949 | C2×C5 | semidirect |
| 55. C5×M16 | Dic5 | semidirect |
| 56. C5×M16 | C4×C5 | semidirect |
| 101. C5×C8 | C2×Dic5 | semidirect |
| 102. C5×C8 | C2×C4×C5 | semidirect |
| 108. C52 | #428 | semidirect |
| 138. M16 | C5×Dic5 | semidirect |
| 167. C8 | C2×C5×Dic5 | semidirect |
| 169. C5 | #65410 | direct (N × H) |
| 170. C5 | C5×#428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| C5×#4072 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×#3950 | 2 |
| C5×#3949 | 2 |
| C5×#428 | 5 |
| #65410 | 5 |