Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 10. #64896 | C5 | direct (N × H) |
| 71. C52 | #341 | semidirect |
| 116. C5 | C5×#341 | semidirect |
| 117. C5 | #64896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#700 | 2 |
| C2×C5×C8×D5 | 2 |
| #64896 | 5 |
| C5×#341 | 5 |