Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
298 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×C5×#681 | C2 | semidirect |
| 3. C2×C5×C8×D5 | C2 | semidirect |
| 4. C52×C22⋊C8 | C2 | semidirect |
| 5. C5×#3952 | C2 | semidirect |
| 6. C5×#3947 | C2 | semidirect |
| 7. C5×#3946 | C2 | semidirect |
| 22. #65017 | C5 | direct (N × H) |
| 38. C5×#168 | D4 | semidirect |
| 43. C2×#681 | C2×C5 | semidirect |
| 44. C2×C8×D5 | C2×C5 | semidirect |
| 48. C5×C22⋊C8 | D5 | semidirect |
| 49. C5×C22⋊C8 | C2×C5 | semidirect |
| 51. #3952 | C2×C5 | semidirect |
| 52. #3947 | C2×C5 | semidirect |
| 53. #3946 | C2×C5 | semidirect |
| 60. C2×C5×D5 | M16 | semidirect |
| 140. #168 | C5×D4 | semidirect |
| 146. C22⋊C8 | C5×D5 | semidirect |
| 148. C52 | #435 | semidirect |
| 166. C2×D5 | C5×M16 | semidirect |
| 226. C5 | #65017 | direct (N × H) |
| 227. C5 | C5×#435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C22⋊D5 | 2 |
| C2×C5×#681 | 2 |
| C2×C5×C8×D5 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3952 | 2 |
| C5×#3947 | 2 |
| C5×#3946 | 2 |
| C5×#435 | 5 |
| #65017 | 5 |