Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 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×#3942 | C2 | semidirect |
| 5. C4×C5×#168 | C2 | semidirect |
| 14. #65357 | C5 | direct (N × H) |
| 24. C5×#125 | D5 | semidirect |
| 25. C5×#125 | C2×C5 | semidirect |
| 31. #3942 | C2×C5 | semidirect |
| 33. C4×#168 | C2×C5 | semidirect |
| 81. #125 | C5×D5 | semidirect |
| 86. C52 | #488 | semidirect |
| 129. C5 | #65357 | direct (N × H) |
| 130. C5 | C5×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| C5×#4021 | 2 |
| C5×#3942 | 2 |
| C5×#3941 | 2 |
| C4×C5×#168 | 2 |
| C5×#488 | 5 |
| #65357 | 5 |