Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
302 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 2. C2×C5×#689 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3942 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 22. #65340 | C5 | direct (N × H) |
| 44. C2×#689 | C2×C5 | semidirect |
| 50. #3967 | C2×C5 | semidirect |
| 51. #3942 | C2×C5 | semidirect |
| 52. #3939 | C2×C5 | semidirect |
| 55. C22×C52 | Q16 | semidirect |
| 146. C52 | #467 | semidirect |
| 155. C22×C5 | #689 | semidirect |
| 156. C22×C5 | C5×Q16 | semidirect |
| 219. C5 | #65340 | direct (N × H) |
| 220. C5 | C5×#467 | semidirect |
| 223. C22 | C5×#689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| C2×C5×#689 | 2 |
| C5×#4070 | 2 |
| C22×C5×#168 | 2 |
| C5×#3967 | 2 |
| C5×#3942 | 2 |
| C5×#3939 | 2 |
| C5×#467 | 5 |
| #65340 | 5 |