Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
276 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C52×#125 | C2 | semidirect |
| 3. C5×#3941 | C2 | semidirect |
| 4. C5×#3935 | C2 | semidirect |
| 12. #65356 | C5 | direct (N × H) |
| 22. C5×#125 | D5 | semidirect |
| 23. C5×#125 | C2×C5 | semidirect |
| 27. #3941 | C2×C5 | semidirect |
| 28. #3935 | C2×C5 | semidirect |
| 72. #125 | C5×D5 | semidirect |
| 75. C52 | #490 | semidirect |
| 114. C5 | #65356 | direct (N × H) |
| 115. C5 | C5×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| C5×#4020 | 2 |
| C5×#3941 | 2 |
| C5×#3935 | 2 |
| C5×#490 | 5 |
| #65356 | 5 |