Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
368 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 102 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×#4023 | C2 | semidirect |
| 3. C52×#99 | C2 | semidirect |
| 4. C5×#3966 | C2 | semidirect |
| 5. C5×#3938 | C2 | semidirect |
| 7. C2×C5×C22⋊D5 | C4 | semidirect |
| 9. C22×C5×Dic5 | C4 | semidirect |
| 13. C2×C4×C5×D5 | C4 | semidirect |
| 14. C2×C5×Dic10 | C4 | semidirect |
| 20. #65029 | C5 | direct (N × H) |
| 43. #4023 | C2×C5 | semidirect |
| 47. C5×#99 | D5 | semidirect |
| 48. C5×#99 | C2×C5 | semidirect |
| 49. #3966 | C2×C5 | semidirect |
| 50. #3938 | C2×C5 | semidirect |
| 76. C2×C22⋊D5 | C4×C5 | semidirect |
| 78. C22×Dic5 | C4×C5 | semidirect |
| 82. C2×C4×D5 | C4×C5 | semidirect |
| 83. C2×Dic10 | C4×C5 | semidirect |
| 146. #99 | C5×D5 | semidirect |
| 147. C52 | #410 | semidirect |
| 230. C5 | #65029 | direct (N × H) |
| 231. C5 | C5×#410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C5×#4023 | 2 |
| C52×#99 | 2 |
| C5×#3966 | 2 |
| C5×#3938 | 2 |
| C5×#410 | 5 |
| #65029 | 5 |