Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C2×C5×Dic20 | C2 | semidirect |
| 3. C5×#3959 | C2 | direct (N × H) |
| 4. C2×C5×#672 | C2 | semidirect |
| 11. C5×Dic20 | C22 | semidirect |
| 12. C5×#672 | C22 | semidirect |
| 14. C2×#3959 | C5 | direct (N × H) |
| 28. C2×Dic20 | C2×C5 | semidirect |
| 31. #3959 | C2×C5 | direct (N × H) |
| 32. C2×#672 | C2×C5 | semidirect |
| 56. Dic20 | C22×C5 | semidirect |
| 58. #672 | C22×C5 | semidirect |
| 61. C2×C52 | SD32 | semidirect |
| 91. C52 | C2×SD32 | semidirect |
| 122. C2×C5 | #3959 | direct (N × H) |
| 123. C2×C5 | C5×SD32 | semidirect |
| 136. C5 | C2×#3959 | direct (N × H) |
| 137. C5 | C2×C5×SD32 | semidirect |
| 145. C2 | C5×#3959 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#3959 | 2 |
| C2×C5×#672 | 2 |
| C2×C5×SD32 | 5 |
| C2×#3959 | 5 |