Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
224 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C52×Q16 | C2 | semidirect |
| 3. C5×#3961 | C2 | semidirect |
| 4. C5×#3960 | C2 | semidirect |
| 5. C5×#3944 | C2 | semidirect |
| 16. #65468 | C5 | direct (N × H) |
| 29. C2×C5×Q16 | D5 | semidirect |
| 30. C2×C5×Q16 | C2×C5 | semidirect |
| 35. #3961 | C2×C5 | semidirect |
| 36. #3960 | C2×C5 | semidirect |
| 37. #3944 | C2×C5 | semidirect |
| 97. C2×Q16 | C5×D5 | semidirect |
| 101. C52 | #510 | semidirect |
| 146. C5 | #65468 | direct (N × H) |
| 147. C5 | C5×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C5×#4050 | 2 |
| C5×#3961 | 2 |
| C5×#3960 | 2 |
| C5×#3944 | 2 |
| C5×#510 | 5 |
| #65468 | 5 |