Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 7. C42×C52 | C4 | semidirect |
| 10. C4×C5×Dic5 | C4 | semidirect |
| 13. C2×C5×#168 | C4 | semidirect |
| 15. #64751 | C5 | direct (N × H) |
| 59. C42×C5 | Dic5 | semidirect |
| 60. C42×C5 | C4×C5 | semidirect |
| 63. C4×Dic5 | C4×C5 | semidirect |
| 66. C2×#168 | C4×C5 | semidirect |
| 103. C52 | H(3,ℤ/4) | semidirect |
| 142. C42 | C5×Dic5 | semidirect |
| 166. C5 | #64751 | direct (N × H) |
| 167. C5 | C5×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#117 | 2 |
| C5×#4072 | 2 |
| C2×C5×#681 | 2 |
| C5×H(3,ℤ/4) | 5 |
| #64751 | 5 |