Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 1. C2×C5×Dic20 | C2 | semidirect |
| 3. C2×#87756 | C2 | semidirect |
| 4. #11716588 | C2 | direct (N × H) |
| 9. C5×Dic20 | C22 | semidirect |
| 12. #87756 | C22 | semidirect |
| 26. C2×Dic20 | D5 | semidirect |
| 51. Dic20 | C2×D5 | semidirect |
| 58. C2×C52 | SD32 | semidirect |
| 86. C52 | C2×SD32 | semidirect |
| 113. C2×C5 | #3959 | semidirect |
| 114. C2×C5 | #3960 | semidirect |
| 128. C5 | C2×#3959 | semidirect |
| 129. C5 | C2×#3960 | semidirect |
| 137. C2 | #11716588 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C2×C5×D40 | 2 |
| C2×#87756 | 2 |
| #11716588 | 2 |
| C2×#3960 | 5 |
| C2×#3959 | 5 |