Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
251 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 112 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×#4004 | C2 | semidirect |
| 4. C4×C5×#170 | C2 | semidirect |
| 13. #65678 | C5 | direct (N × H) |
| 24. C4×C5×D5 | C8 | semidirect |
| 28. #4004 | C2×C5 | semidirect |
| 30. C4×#170 | C2×C5 | semidirect |
| 88. C4×D5 | C5×C8 | semidirect |
| 95. C52 | #431 | semidirect |
| 151. C5 | C5×#431 | semidirect |
| 152. C5 | #65678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×D5 | 2 |
| C5×#4004 | 2 |
| C5×#4003 | 2 |
| C4×C5×#170 | 2 |
| #65678 | 5 |
| C5×#431 | 5 |