Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1072 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 494 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 |
|---|---|---|
| 4. C2×C5×#683 | C2 | direct (N × H) |
| 9. C22×C5×Dic5 | C4 | semidirect |
| 12. C5×#683 | C22 | direct (N × H) |
| 14. C22×#683 | C5 | direct (N × H) |
| 22. C2×C5×Dic5 | C2×C4 | semidirect |
| 33. C2×#683 | C2×C5 | direct (N × H) |
| 34. C22×C52 | C4⋊C4 | semidirect |
| 41. C5×Dic5 | C22×C4 | semidirect |
| 56. C22×Dic5 | C4×C5 | semidirect |
| 60. #683 | C22×C5 | direct (N × H) |
| 62. C2×C52 | C2×C4⋊C4 | semidirect |
| 89. C2×Dic5 | C2×C4×C5 | semidirect |
| 96. C52 | C22×C4⋊C4 | semidirect |
| 102. C22×C5 | #683 | direct (N × H) |
| 103. C22×C5 | C5×C4⋊C4 | semidirect |
| 118. Dic5 | C22×C4×C5 | semidirect |
| 131. C2×C5 | C2×#683 | direct (N × H) |
| 132. C2×C5 | C2×C5×C4⋊C4 | semidirect |
| 150. C5 | C22×#683 | direct (N × H) |
| 151. C5 | C22×C5×C4⋊C4 | semidirect |
| 152. C22 | C5×#683 | direct (N × H) |
| 160. C2 | C2×C5×#683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C23×C5×Dic5 | 2 |
| C2×C5×#683 | 2 |
| C22×C5×C4⋊C4 | 5 |
| C22×#683 | 5 |