Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 92 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. #87804 | C4 | semidirect |
| 10. C5×C4⋊Dic5 | C4 | semidirect |
| 13. C4×C5×Dic5 | C4 | semidirect |
| 55. C4⋊Dic5 | Dic5 | semidirect |
| 58. C4×Dic5 | Dic5 | semidirect |
| 106. C52 | #339 | semidirect |
| 169. C5 | #64743 | semidirect |
| 170. C5 | #64752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87804 | 2 |
| C5×#4072 | 2 |
| C2×C4×C5×Dic5 | 2 |
| #64752 | 5 |
| #64743 | 5 |