Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
407 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 116 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×#700 | C2 | semidirect |
| 3. C5×C22⋊#170 | C2 | semidirect |
| 4. C5×#4003 | C2 | semidirect |
| 13. C2×C5×#170 | C22 | semidirect |
| 15. #65756 | C5 | direct (N × H) |
| 36. C2×#700 | C2×C5 | semidirect |
| 38. C22⋊#170 | C2×C5 | semidirect |
| 39. #4003 | C2×C5 | semidirect |
| 44. C22×C52 | M16 | semidirect |
| 52. C2×C5×D5 | M16 | semidirect |
| 74. C2×#170 | C22×C5 | semidirect |
| 127. C52 | #407 | semidirect |
| 143. C22×C5 | C5×M16 | semidirect |
| 144. C22×C5 | #700 | semidirect |
| 153. C2×D5 | C5×M16 | semidirect |
| 208. C5 | C5×#407 | semidirect |
| 209. C5 | #65756 | direct (N × H) |
| 219. C22 | C5×#700 | 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×C5×#700 | 2 |
| C5×C22⋊#170 | 2 |
| C5×#4003 | 2 |
| #65756 | 5 |
| C5×#407 | 5 |