Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 100 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×#3998 | C2 | semidirect |
| 3. C5×#3990 | C2 | semidirect |
| 4. C5×D5⋊C16 | C2 | semidirect |
| 12. C5×#674 | C22 | semidirect |
| 13. D5⋊M32 | C5 | direct (N × H) |
| 28. #3998 | C2×C5 | semidirect |
| 29. #3990 | C2×C5 | semidirect |
| 30. D5⋊C16 | C2×C5 | semidirect |
| 57. #674 | C22×C5 | semidirect |
| 63. C5×D5 | M32 | semidirect |
| 93. C52 | C2×M32 | semidirect |
| 130. D5 | C5×M32 | semidirect |
| 143. C5 | C2×C5×M32 | semidirect |
| 144. C5 | D5⋊M32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×D5 | 2 |
| C5×#3998 | 2 |
| C5×#3990 | 2 |
| C5×D5⋊C16 | 2 |
| D5⋊M32 | 5 |
| C2×C5×M32 | 5 |