Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
896 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C5×Dic10 | C2 | semidirect |
| 3. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 4. C5×#4082 | C2 | direct (N × H) |
| 5. C2×C4×C5×Dic5 | C2 | semidirect |
| 13. C2×C5×Dic10 | C22 | semidirect |
| 14. C5×C22⋊Dic5 | C22 | semidirect |
| 15. C4×C5×Dic5 | C22 | semidirect |
| 17. C2×#4082 | C5 | direct (N × H) |
| 34. C22×Dic10 | C2×C5 | semidirect |
| 38. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 39. #4082 | C2×C5 | direct (N × H) |
| 40. C2×C4×Dic5 | C2×C5 | semidirect |
| 69. C2×Dic10 | C22×C5 | semidirect |
| 72. C22⋊Dic5 | C22×C5 | semidirect |
| 73. C4×Dic5 | C22×C5 | semidirect |
| 76. C2×C52 | #124 | semidirect |
| 115. C52 | C2×#124 | semidirect |
| 157. C2×C5 | #4082 | direct (N × H) |
| 158. C2×C5 | C5×#124 | semidirect |
| 176. C5 | C2×#4082 | direct (N × H) |
| 177. C5 | C2×C5×#124 | semidirect |
| 188. C2 | C5×#4082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C22×C5×Dic10 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C5×#4082 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×#124 | 5 |
| C2×#4082 | 5 |