Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
351 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. C4×#6032 | C2 | semidirect |
| 4. C4×C5×#170 | C2 | semidirect |
| 5. Dic5×#170 | C2 | semidirect |
| 11. #87827 | C4 | direct (N × H) |
| 21. C4×C5⋊D5 | C8 | semidirect |
| 26. #6036 | C8 | semidirect |
| 28. #6032 | C2×C4 | semidirect |
| 29. C5×#170 | C2×C4 | semidirect |
| 36. C4×#170 | D5 | semidirect |
| 44. C4×C52 | C2×C8 | semidirect |
| 45. #1039 | C2×C8 | semidirect |
| 47. C5×Dic5 | C2×C8 | semidirect |
| 48. C5×Dic5 | C2×C8 | semidirect |
| 75. C5⋊D5 | C4×C8 | semidirect |
| 101. #170 | C4×D5 | semidirect |
| 109. C52 | C2×C4×C8 | semidirect |
| 127. C4×C5 | C8×D5 | semidirect |
| 128. C4×C5 | D5⋊C8 | semidirect |
| 132. Dic5 | C8×D5 | semidirect |
| 133. Dic5 | D5⋊C8 | semidirect |
| 171. C5 | C4×C8×D5 | semidirect |
| 172. C5 | C4×D5⋊C8 | semidirect |
| 182. C4 | #87827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87827 | 2 |
| C4×#6036 | 2 |
| C4×#6032 | 2 |
| C4×C5×#170 | 2 |
| Dic5×#170 | 2 |
| C4×D5⋊C8 | 5 |
| C4×C8×D5 | 5 |