Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 118 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. C5×D4×Dic5 | C2 | semidirect |
| 3. C5×#3964 | C2 | semidirect |
| 4. C5×#3950 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 8. C52×D8 | C4 | semidirect |
| 15. D8×Dic5 | C5 | direct (N × H) |
| 18. C52×D4 | C2×C4 | semidirect |
| 24. C52×C8 | C2×C4 | semidirect |
| 30. D4×Dic5 | C2×C5 | semidirect |
| 34. #3964 | C2×C5 | semidirect |
| 35. #3950 | C2×C5 | semidirect |
| 36. C8×Dic5 | C2×C5 | semidirect |
| 45. C5×Dic5 | D8 | direct (N × H) |
| 52. C5×D8 | Dic5 | direct (N × H) |
| 53. C5×D8 | C4×C5 | semidirect |
| 77. C5×D4 | C2×Dic5 | semidirect |
| 78. C5×D4 | C2×C4×C5 | semidirect |
| 92. C5×C8 | C2×Dic5 | semidirect |
| 93. C5×C8 | C2×C4×C5 | semidirect |
| 100. C52 | C4×D8 | semidirect |
| 124. Dic5 | C5×D8 | direct (N × H) |
| 127. D8 | C5×Dic5 | direct (N × H) |
| 147. D4 | C2×C5×Dic5 | semidirect |
| 154. C8 | C2×C5×Dic5 | semidirect |
| 156. C5 | D8×Dic5 | direct (N × H) |
| 157. C5 | C4×C5×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C5×D4×Dic5 | 2 |
| C5×#3964 | 2 |
| C5×#3950 | 2 |
| C5×C8×Dic5 | 2 |
| C4×C5×D8 | 5 |
| D8×Dic5 | 5 |