Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 78 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. C52×C22⋊C8 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 6. C5×#3950 | C2 | semidirect |
| 7. C5×#3949 | C2 | semidirect |
| 20. #65026 | C5 | direct (N × H) |
| 38. #4072 | C2×C5 | semidirect |
| 44. C5×C22⋊C8 | D5 | semidirect |
| 45. C5×C22⋊C8 | C2×C5 | semidirect |
| 46. #3953 | C2×C5 | semidirect |
| 47. #3953 | C2×C5 | semidirect |
| 48. #3950 | C2×C5 | semidirect |
| 49. #3949 | C2×C5 | semidirect |
| 135. C22⋊C8 | C5×D5 | semidirect |
| 136. C52 | #482 | semidirect |
| 210. C5 | #65026 | direct (N × H) |
| 211. C5 | C5×#482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4076 | 2 |
| C5×#4072 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#3950 | 2 |
| C5×#3949 | 2 |
| C5×#482 | 5 |
| #65026 | 5 |