Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 94 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×C52×D8 | C2 | semidirect |
| 2. C5×#4086 | C2 | semidirect |
| 3. C2×C5×#686 | C2 | semidirect |
| 4. C2×C5×D40 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 16. #65440 | C5 | direct (N × H) |
| 26. C52×C8 | D4 | semidirect |
| 27. C5×#168 | D4 | semidirect |
| 31. C2×C5×D8 | D5 | semidirect |
| 32. C2×C5×D8 | C2×C5 | semidirect |
| 34. #4086 | C2×C5 | semidirect |
| 35. C2×#686 | C2×C5 | semidirect |
| 36. C2×D40 | C2×C5 | semidirect |
| 38. C8×Dic5 | C2×C5 | semidirect |
| 46. C5×Dic5 | D8 | semidirect |
| 97. C5×C8 | C22⋊D5 | semidirect |
| 98. C5×C8 | C5×D4 | semidirect |
| 99. #168 | C5×D4 | semidirect |
| 102. C2×D8 | C5×D5 | semidirect |
| 105. C52 | #493 | semidirect |
| 126. Dic5 | C5×D8 | semidirect |
| 157. C8 | C5×C22⋊D5 | semidirect |
| 159. C5 | #65440 | direct (N × H) |
| 160. C5 | C5×#493 | 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×#4086 | 2 |
| C2×C5×#686 | 2 |
| C2×C5×D40 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#493 | 5 |
| #65440 | 5 |