Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
551 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 280 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. C5×#4133 | C2 | direct (N × H) |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. C2×C5×D5⋊C8 | C2 | semidirect |
| 12. C5×#700 | C22 | semidirect |
| 13. C5×D5⋊C8 | C22 | semidirect |
| 14. C2×#4133 | C5 | direct (N × H) |
| 27. #4133 | C2×C5 | direct (N × H) |
| 28. C2×#700 | C2×C5 | semidirect |
| 29. C2×D5⋊C8 | C2×C5 | semidirect |
| 52. #700 | C22×C5 | semidirect |
| 53. D5⋊C8 | C22×C5 | semidirect |
| 59. C2×C52 | #131 | semidirect |
| 86. C52 | C2×#131 | semidirect |
| 113. C2×C5 | C5×#131 | semidirect |
| 114. C2×C5 | #4133 | direct (N × H) |
| 128. C5 | C2×C5×#131 | semidirect |
| 129. C5 | C2×#4133 | direct (N × H) |
| 137. C2 | C5×#4133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C5×#4133 | 2 |
| C2×C5×#700 | 2 |
| C2×C5×D5⋊C8 | 2 |
| C2×#4133 | 5 |
| C2×C5×#131 | 5 |