Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
520 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 5. #11717036 | C2 | semidirect |
| 6. C4×#6039 | C2 | semidirect |
| 7. #11716988 | C2 | semidirect |
| 26. C2×C4×C52 | Q8 | semidirect |
| 107. C2×C4×C5 | Dic10 | semidirect |
| 108. C2×C4×C5 | Dic10 | semidirect |
| 129. C52 | #533 | semidirect |
| 185. C2×C4 | #6039 | semidirect |
| 189. C5 | #65804 | semidirect |
| 190. C5 | #65851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717246 | 2 |
| C5×#4072 | 2 |
| C2×C4×C5×Dic5 | 2 |
| #11717082 | 2 |
| #11717036 | 2 |
| C4×#6039 | 2 |
| #11716988 | 2 |
| #65851 | 5 |
| #65804 | 5 |