Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
430 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 122 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×#676 | C2 | semidirect |
| 3. C52×C22⋊C8 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 5. C5×#3952 | C2 | semidirect |
| 14. C2×C52×C8 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 18. #65015 | C5 | direct (N × H) |
| 40. C2×#676 | C2×C5 | semidirect |
| 44. C5×C22⋊C8 | D5 | semidirect |
| 45. C5×C22⋊C8 | C2×C5 | semidirect |
| 46. C22⋊#168 | C2×C5 | semidirect |
| 47. #3952 | C2×C5 | semidirect |
| 50. C22×C52 | M16 | semidirect |
| 58. C2×C5×D5 | M16 | semidirect |
| 83. C2×C5×C8 | C2×D5 | semidirect |
| 84. C2×C5×C8 | C22×C5 | semidirect |
| 85. C2×#168 | C22×C5 | semidirect |
| 139. C22⋊C8 | C5×D5 | semidirect |
| 140. C52 | #407 | semidirect |
| 156. C22×C5 | #676 | semidirect |
| 157. C22×C5 | C5×M16 | semidirect |
| 166. C2×D5 | C5×M16 | semidirect |
| 187. C2×C8 | C2×C5×D5 | semidirect |
| 223. C5 | #65015 | direct (N × H) |
| 224. C5 | C5×#407 | semidirect |
| 234. C22 | C5×#676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×C5×#676 | 2 |
| C52×C22⋊C8 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#3952 | 2 |
| C5×#407 | 5 |
| #65015 | 5 |