Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
372 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4081 | C2 | semidirect |
| 3. C5×#4032 | C2 | semidirect |
| 4. C52×#99 | C2 | semidirect |
| 5. C5×#3938 | C2 | semidirect |
| 9. C22×C5×Dic5 | C22 | semidirect |
| 13. C52×C22⋊C4 | C22 | semidirect |
| 15. C5×C22⋊Dic5 | C22 | semidirect |
| 20. #65031 | C5 | direct (N × H) |
| 43. #4081 | C2×C5 | semidirect |
| 44. #4032 | C2×C5 | semidirect |
| 47. C5×#99 | D5 | semidirect |
| 48. C5×#99 | C2×C5 | semidirect |
| 49. #3938 | C2×C5 | semidirect |
| 74. C22×Dic5 | C22×C5 | semidirect |
| 84. C5×C22⋊C4 | C2×D5 | semidirect |
| 85. C5×C22⋊C4 | C22×C5 | semidirect |
| 87. C22⋊Dic5 | C22×C5 | semidirect |
| 142. #99 | C5×D5 | semidirect |
| 143. C52 | #458 | semidirect |
| 189. C22⋊C4 | C2×C5×D5 | semidirect |
| 223. C5 | #65031 | direct (N × H) |
| 224. C5 | C5×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4144 | 2 |
| C5×#4081 | 2 |
| C5×#4032 | 2 |
| C52×#99 | 2 |
| C5×#3938 | 2 |
| C5×#458 | 5 |
| #65031 | 5 |