Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 13. C5×Dic20 | C4 | semidirect |
| 15. #65005 | C5 | direct (N × H) |
| 59. Dic20 | C4×C5 | semidirect |
| 88. C52 | #441 | semidirect |
| 128. C5 | #65005 | direct (N × H) |
| 129. C5 | C5×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C4×C5×Dic10 | 2 |
| C52×#97 | 2 |
| C5×#3949 | 2 |
| C5×#3948 | 2 |
| C5×#441 | 5 |
| #65005 | 5 |