Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
528 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 182 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. C2×C52×Q8 | C4 | semidirect |
| 15. #65519 | C5 | direct (N × H) |
| 28. C2×C5×Dic5 | Q8 | semidirect |
| 54. C2×C5×Q8 | Dic5 | semidirect |
| 55. C2×C5×Q8 | C4×C5 | semidirect |
| 109. C2×Dic5 | C5×Q8 | semidirect |
| 114. C52 | #391 | semidirect |
| 142. C2×Q8 | C5×Dic5 | semidirect |
| 178. C5 | #65519 | direct (N × H) |
| 179. C5 | C5×#391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C5×#3963 | 2 |
| C5×#391 | 5 |
| #65519 | 5 |