Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 4. C5×#3946 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 16. #65007 | C5 | direct (N × H) |
| 22. C2×C5×Dic5 | C8 | semidirect |
| 38. #3946 | C2×C5 | semidirect |
| 39. C8×Dic5 | C2×C5 | semidirect |
| 94. C2×Dic5 | C5×C8 | semidirect |
| 109. C52 | #431 | semidirect |
| 170. C5 | #65007 | direct (N × H) |
| 171. C5 | C5×#431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Dic5 | 2 |
| C52×C22⋊C8 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#3946 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#431 | 5 |
| #65007 | 5 |