Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
398 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 398 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. C52×#123 | C2 | semidirect |
| 3. C5×#4075 | C2 | semidirect |
| 4. C5×#3966 | C2 | semidirect |
| 5. C5×#3938 | C2 | semidirect |
| 7. C22×C4×C52 | C22 | semidirect |
| 15. C52×C22⋊C4 | C22 | semidirect |
| 16. C5×C22⋊Dic5 | C22 | semidirect |
| 20. #65342 | C5 | direct (N × H) |
| 43. C5×#123 | D5 | semidirect |
| 44. C5×#123 | C2×C5 | semidirect |
| 45. #4075 | C2×C5 | semidirect |
| 48. #3966 | C2×C5 | semidirect |
| 49. #3938 | C2×C5 | semidirect |
| 72. C22×C4×C5 | C2×D5 | semidirect |
| 73. C22×C4×C5 | C22×C5 | semidirect |
| 89. C5×C22⋊C4 | C2×D5 | semidirect |
| 90. C5×C22⋊C4 | C22×C5 | semidirect |
| 91. C22⋊Dic5 | C22×C5 | semidirect |
| 145. #123 | C5×D5 | semidirect |
| 148. C52 | #458 | semidirect |
| 189. C22×C4 | C2×C5×D5 | semidirect |
| 195. C22⋊C4 | C2×C5×D5 | semidirect |
| 229. C5 | #65342 | direct (N × H) |
| 230. 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 |
| C52×#123 | 2 |
| C5×#4075 | 2 |
| C5×#3966 | 2 |
| C5×#3938 | 2 |
| C5×#458 | 5 |
| #65342 | 5 |