Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
431 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 140 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×D5⋊C8 | C2 | semidirect |
| 3. C5×C22⋊#170 | C2 | semidirect |
| 4. C5×#4003 | C2 | semidirect |
| 13. C2×C5×#170 | C22 | semidirect |
| 15. D5⋊(C22⋊C8) | C5 | direct (N × H) |
| 20. C22×C5×D5 | C8 | semidirect |
| 36. C2×D5⋊C8 | C2×C5 | semidirect |
| 38. C22⋊#170 | C2×C5 | semidirect |
| 39. #4003 | C2×C5 | semidirect |
| 44. C22×C52 | C2×C8 | semidirect |
| 51. C2×C5×D5 | C2×C8 | semidirect |
| 74. C2×#170 | C22×C5 | semidirect |
| 84. C5×D5 | C22⋊C8 | semidirect |
| 95. C22×D5 | C5×C8 | semidirect |
| 127. C52 | C2×C22⋊C8 | semidirect |
| 143. C22×C5 | C2×C5×C8 | semidirect |
| 144. C22×C5 | D5⋊C8 | semidirect |
| 152. C2×D5 | C2×C5×C8 | semidirect |
| 189. D5 | C5×C22⋊C8 | semidirect |
| 208. C5 | C2×C5×C22⋊C8 | semidirect |
| 209. C5 | D5⋊(C22⋊C8) | direct (N × H) |
| 219. C22 | C5×D5⋊C8 | 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×D5⋊C8 | 2 |
| C5×C22⋊#170 | 2 |
| C5×#4003 | 2 |
| D5⋊(C22⋊C8) | 5 |
| C2×C5×C22⋊C8 | 5 |