Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 11. C4×C5×Dic5 | C4 | semidirect |
| 13. #64940 | C5 | direct (N × H) |
| 62. C4×Dic5 | C4×C5 | semidirect |
| 108. C52 | #383 | semidirect |
| 172. C5 | #64940 | direct (N × H) |
| 173. C5 | C5×#383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Dic5 | 2 |
| C52×#95 | 2 |
| C5×#3963 | 2 |
| C5×#383 | 5 |
| #64940 | 5 |