Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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×C4⋊Q8 | C2 | semidirect |
| 3. C5×#3941 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 14. #65377 | C5 | direct (N × H) |
| 26. C5×C4⋊Q8 | D5 | semidirect |
| 27. C5×C4⋊Q8 | C2×C5 | semidirect |
| 32. #3941 | C2×C5 | semidirect |
| 33. C4×#168 | C2×C5 | semidirect |
| 92. C4⋊Q8 | C5×D5 | semidirect |
| 96. C52 | #486 | semidirect |
| 148. C5 | #65377 | direct (N × H) |
| 149. C5 | C5×#486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C5×#4020 | 2 |
| C5×#3941 | 2 |
| C4×C5×#168 | 2 |
| C5×#486 | 5 |
| #65377 | 5 |