Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
448 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 134 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×C52×M16 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. C5×#3952 | C2 | semidirect |
| 13. C2×C52×C8 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 17. #65415 | C5 | direct (N × H) |
| 37. C2×C5×M16 | D5 | semidirect |
| 38. C2×C5×M16 | C2×C5 | semidirect |
| 39. C2×#681 | C2×C5 | semidirect |
| 41. #3952 | C2×C5 | semidirect |
| 48. C2×C5×D5 | M16 | semidirect |
| 74. C2×C5×C8 | C2×D5 | semidirect |
| 75. C2×C5×C8 | C22×C5 | semidirect |
| 77. C2×#168 | C22×C5 | semidirect |
| 121. C2×M16 | C5×D5 | semidirect |
| 123. C52 | #407 | semidirect |
| 140. C2×D5 | C5×M16 | semidirect |
| 162. C2×C8 | C2×C5×D5 | semidirect |
| 190. C5 | #65415 | direct (N × H) |
| 191. C5 | C5×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×C52×M16 | 2 |
| C2×C5×#681 | 2 |
| C5×#3952 | 2 |
| C5×#407 | 5 |
| #65415 | 5 |