Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
768 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C5×Dic10 | C2 | semidirect |
| 3. C2×C42×C52 | C2 | semidirect |
| 4. C2×C5×#685 | C2 | semidirect |
| 5. C5×#4021 | C2 | direct (N × H) |
| 13. C2×C5×Dic10 | C22 | semidirect |
| 14. C42×C52 | C22 | semidirect |
| 15. C5×#685 | C22 | semidirect |
| 17. C2×#4021 | C5 | direct (N × H) |
| 33. C22×Dic10 | C2×C5 | semidirect |
| 37. C2×C42×C5 | D5 | semidirect |
| 38. C2×C42×C5 | C2×C5 | semidirect |
| 39. C2×#685 | C2×C5 | semidirect |
| 40. #4021 | C2×C5 | direct (N × H) |
| 67. C2×Dic10 | C22×C5 | semidirect |
| 70. C42×C5 | C2×D5 | semidirect |
| 71. C42×C5 | C22×C5 | semidirect |
| 72. #685 | C22×C5 | semidirect |
| 74. C2×C52 | #124 | semidirect |
| 111. C2×C42 | C5×D5 | semidirect |
| 112. C52 | C2×#124 | semidirect |
| 145. C42 | C2×C5×D5 | semidirect |
| 150. C2×C5 | #4021 | direct (N × H) |
| 151. C2×C5 | C5×#124 | semidirect |
| 170. C5 | C2×#4021 | direct (N × H) |
| 171. C5 | C2×C5×#124 | semidirect |
| 182. C2 | C5×#4021 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×C5×Dic10 | 2 |
| C2×C42×C52 | 2 |
| C2×C5×#685 | 2 |
| C5×#4021 | 2 |
| C2×C5×#124 | 5 |
| C2×#4021 | 5 |