Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
263 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 116 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. C5×#4004 | C2 | semidirect |
| 4. C4×C5×#170 | C2 | semidirect |
| 13. #65754 | C5 | direct (N × H) |
| 20. C2×C5×Dic5 | C8 | semidirect |
| 29. #4004 | C2×C5 | semidirect |
| 30. C4×#170 | C2×C5 | semidirect |
| 85. C2×Dic5 | C5×C8 | semidirect |
| 96. C52 | #431 | semidirect |
| 155. C5 | C5×#431 | semidirect |
| 156. C5 | #65754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Dic5 | 2 |
| C5×C22⋊#170 | 2 |
| C5×#4004 | 2 |
| C4×C5×#170 | 2 |
| #65754 | 5 |
| C5×#431 | 5 |