Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
| 5. C5×#3940 | C2 | semidirect |
| 6. C5×#3939 | C2 | semidirect |
| 7. C5×C4⋊#168 | C2 | semidirect |
| 20. #65355 | C5 | direct (N × H) |
| 34. C5×#125 | D5 | semidirect |
| 35. C5×#125 | C2×C5 | semidirect |
| 45. #3940 | C2×C5 | semidirect |
| 46. #3939 | C2×C5 | semidirect |
| 47. C4⋊#168 | C2×C5 | semidirect |
| 120. #125 | C5×D5 | semidirect |
| 127. C52 | #478 | semidirect |
| 192. C5 | #65355 | direct (N × H) |
| 193. C5 | C5×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| C4×C5×D20 | 2 |
| C5×#3941 | 2 |
| C5×#3940 | 2 |
| C5×#3939 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#478 | 5 |
| #65355 | 5 |