Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
784 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 208 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×#4072 | C2 | semidirect |
| 3. C2×C4×C5×Dic5 | C2 | semidirect |
| 4. #11717070 | C2 | semidirect |
| 5. #11717013 | C2 | semidirect |
| 6. C4×#6036 | C2 | semidirect |
| 7. #11716992 | C2 | semidirect |
| 8. #11716962 | C2 | semidirect |
| 11. #87900 | C4 | semidirect |
| 30. C2×C4×C52 | C2×C4 | semidirect |
| 33. C22⋊(C5⋊D5) | C2×C4 | semidirect |
| 35. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 36. C4×C5⋊D5 | C2×C4 | semidirect |
| 37. #6045 | C2×C4 | semidirect |
| 49. #4072 | D5 | semidirect |
| 50. C2×C4×Dic5 | D5 | semidirect |
| 70. C5×Dic5 | #41 | semidirect |
| 129. C2×C4×C5 | C4×D5 | semidirect |
| 130. C2×C4×C5 | C4×D5 | semidirect |
| 164. C52 | C4×#41 | semidirect |
| 194. Dic5 | #709 | semidirect |
| 236. C2×C4 | #6036 | semidirect |
| 240. C5 | C4×#709 | semidirect |
| 241. C5 | #65856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C5×#4072 | 2 |
| C2×C4×C5×Dic5 | 2 |
| #11717070 | 2 |
| #11717013 | 2 |
| C4×#6036 | 2 |
| #11716992 | 2 |
| #11716962 | 2 |
| #65856 | 5 |
| C4×#709 | 5 |