Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
350 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 350 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×#4082 | C2 | semidirect |
| 3. C5×#4055 | C2 | semidirect |
| 4. C52×#100 | C2 | semidirect |
| 5. C5×#3957 | C2 | semidirect |
| 11. C2×C5×Dic10 | C22 | semidirect |
| 12. C52×M16 | C22 | semidirect |
| 14. C4×C5×Dic5 | C22 | semidirect |
| 18. #65035 | C5 | direct (N × H) |
| 37. #4082 | C2×C5 | semidirect |
| 38. #4055 | C2×C5 | semidirect |
| 41. C5×#100 | D5 | semidirect |
| 42. C5×#100 | C2×C5 | semidirect |
| 43. #3957 | C2×C5 | semidirect |
| 65. C2×Dic10 | C22×C5 | semidirect |
| 69. C5×M16 | C2×D5 | semidirect |
| 70. C5×M16 | C22×C5 | semidirect |
| 74. C4×Dic5 | C22×C5 | semidirect |
| 118. #100 | C5×D5 | semidirect |
| 119. C52 | #455 | semidirect |
| 150. M16 | C2×C5×D5 | semidirect |
| 179. C5 | #65035 | direct (N × H) |
| 180. C5 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4144 | 2 |
| C5×#4082 | 2 |
| C5×#4055 | 2 |
| C52×#100 | 2 |
| C5×#3957 | 2 |
| C5×#455 | 5 |
| #65035 | 5 |