Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
|---|---|---|
| 3. C5×#4070 | C2 | semidirect |
| 4. C5×#4024 | C2 | semidirect |
| 8. C2×C5×Dic10 | C22 | semidirect |
| 12. C5×C4⋊Dic5 | C22 | semidirect |
| 13. C5×#683 | C22 | semidirect |
| 15. #65817 | C5 | direct (N × H) |
| 17. C23×C52 | Q8 | semidirect |
| 32. #4070 | C2×C5 | semidirect |
| 33. #4024 | C2×C5 | semidirect |
| 51. C2×Dic10 | C22×C5 | semidirect |
| 61. C4⋊Dic5 | C22×C5 | semidirect |
| 62. #683 | C22×C5 | semidirect |
| 74. C23×C5 | Dic10 | semidirect |
| 75. C23×C5 | C5×Q8 | semidirect |
| 96. C52 | #543 | semidirect |
| 142. C23 | C5×Dic10 | semidirect |
| 151. C5 | #65817 | direct (N × H) |
| 152. C5 | C5×#543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×C22⋊C4 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C5×#4070 | 2 |
| C5×#4024 | 2 |
| C5×#543 | 5 |
| #65817 | 5 |