Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 206 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 |
|---|---|---|
| 1. C2×C5×#711 | C2 | semidirect |
| 2. C2×C52×D8 | C2 | semidirect |
| 3. C2×C5×#687 | C2 | semidirect |
| 4. C5×#4058 | C2 | direct (N × H) |
| 5. C2×C5×Dic20 | C2 | semidirect |
| 6. C2×C5×C8×D5 | C2 | semidirect |
| 11. C5×#711 | C22 | semidirect |
| 14. C52×D8 | C22 | semidirect |
| 16. C5×#687 | C22 | semidirect |
| 18. C5×Dic20 | C22 | semidirect |
| 19. C5×C8×D5 | C22 | semidirect |
| 21. C2×#4058 | C5 | direct (N × H) |
| 38. C2×#711 | C2×C5 | semidirect |
| 43. C2×C5×D8 | D5 | semidirect |
| 44. C2×C5×D8 | C2×C5 | semidirect |
| 46. C2×#687 | C2×C5 | semidirect |
| 47. #4058 | C2×C5 | direct (N × H) |
| 48. C2×Dic20 | C2×C5 | semidirect |
| 49. C2×C8×D5 | C2×C5 | semidirect |
| 71. #711 | C22×C5 | semidirect |
| 77. C5×D8 | C2×D5 | semidirect |
| 78. C5×D8 | C22×C5 | semidirect |
| 84. #687 | C22×C5 | semidirect |
| 86. Dic20 | C22×C5 | semidirect |
| 87. C8×D5 | C22×C5 | semidirect |
| 90. C2×C52 | #135 | semidirect |
| 132. C2×D8 | C5×D5 | semidirect |
| 134. C52 | C2×#135 | semidirect |
| 167. D8 | C2×C5×D5 | semidirect |
| 177. C2×C5 | #4058 | direct (N × H) |
| 178. C2×C5 | C5×#135 | semidirect |
| 198. C5 | C2×#4058 | direct (N × H) |
| 199. C5 | C2×C5×#135 | semidirect |
| 211. C2 | C5×#4058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C2×C52×D8 | 2 |
| C2×C5×#687 | 2 |
| C5×#4058 | 2 |
| C2×C5×Dic20 | 2 |
| C2×C5×C8×D5 | 2 |
| C2×C5×#135 | 5 |
| C2×#4058 | 5 |