Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
520 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 10. #65518 | C5 | direct (N × H) |
| 18. C2×C5×Dic5 | Q8 | semidirect |
| 67. C2×Dic5 | C5×Q8 | semidirect |
| 71. C52 | #395 | semidirect |
| 111. C5 | #65518 | direct (N × H) |
| 112. C5 | C5×#395 | 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×#683 | 2 |
| C5×#3963 | 2 |
| C5×#395 | 5 |
| #65518 | 5 |