Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
290 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. C52×C4⋊C8 | C2 | semidirect |
| 4. C5×#3946 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 17. #65126 | C5 | direct (N × H) |
| 38. C5×C4⋊C8 | D5 | semidirect |
| 39. C5×C4⋊C8 | C2×C5 | semidirect |
| 40. #3946 | C2×C5 | semidirect |
| 41. C4⋊#168 | C2×C5 | semidirect |
| 47. C4×C52 | M16 | semidirect |
| 52. C5×Dic5 | M16 | semidirect |
| 114. C4⋊C8 | C5×D5 | semidirect |
| 115. C52 | #423 | semidirect |
| 134. C4×C5 | #676 | semidirect |
| 135. C4×C5 | C5×M16 | semidirect |
| 142. Dic5 | C5×M16 | semidirect |
| 178. C5 | #65126 | direct (N × H) |
| 179. C5 | C5×#423 | semidirect |
| 188. C4 | C5×#676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#676 | 2 |
| C42×C5×D5 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3946 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#423 | 5 |
| #65126 | 5 |