Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1584 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 494 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. C23×C4×C52 | C2 | semidirect |
| 3. C23×C5×Dic5 | C2 | semidirect |
| 4. C2×C5×#685 | C2 | direct (N × H) |
| 8. C23×C5×D5 | C4 | semidirect |
| 11. C22×C4×C52 | C22 | semidirect |
| 13. C22×C5×Dic5 | C22 | semidirect |
| 14. C5×#685 | C22 | direct (N × H) |
| 16. C22×#685 | C5 | direct (N × H) |
| 24. C22×C5×D5 | C2×C4 | semidirect |
| 27. C2×C4×C52 | C23 | semidirect |
| 29. C2×C5×Dic5 | C23 | semidirect |
| 34. C23×C4×C5 | D5 | semidirect |
| 35. C23×C4×C5 | C2×C5 | semidirect |
| 36. C23×Dic5 | C2×C5 | semidirect |
| 38. C2×#685 | C2×C5 | direct (N × H) |
| 39. C22×C52 | C22⋊C4 | semidirect |
| 47. C2×C5×D5 | C22×C4 | semidirect |
| 59. C23×D5 | C4×C5 | semidirect |
| 67. C22×C4×C5 | C2×D5 | semidirect |
| 68. C22×C4×C5 | C22×C5 | semidirect |
| 70. C22×Dic5 | C22×C5 | semidirect |
| 72. #685 | C22×C5 | direct (N × H) |
| 74. C2×C52 | C2×C22⋊C4 | semidirect |
| 99. C22×D5 | C2×C4×C5 | semidirect |
| 107. C2×C4×C5 | C22×D5 | semidirect |
| 108. C2×C4×C5 | C23×C5 | semidirect |
| 110. C2×Dic5 | C23×C5 | semidirect |
| 113. C23×C4 | C5×D5 | semidirect |
| 115. C52 | C22×C22⋊C4 | semidirect |
| 125. C22×C5 | #685 | direct (N × H) |
| 126. C22×C5 | C5×C22⋊C4 | semidirect |
| 138. C2×D5 | C22×C4×C5 | semidirect |
| 152. C22×C4 | C2×C5×D5 | semidirect |
| 159. C2×C5 | C2×#685 | direct (N × H) |
| 160. C2×C5 | C2×C5×C22⋊C4 | semidirect |
| 180. C2×C4 | C22×C5×D5 | semidirect |
| 182. C5 | C22×#685 | direct (N × H) |
| 183. C5 | C22×C5×C22⋊C4 | semidirect |
| 188. C22 | C5×#685 | direct (N × H) |
| 196. C2 | C2×C5×#685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×D5 | 2 |
| C23×C4×C52 | 2 |
| C23×C5×Dic5 | 2 |
| C2×C5×#685 | 2 |
| C22×C5×C22⋊C4 | 5 |
| C22×#685 | 5 |