Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
920 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 1. C23×C4×C52 | C2 | semidirect |
| 3. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 4. C5×#4075 | C2 | direct (N × H) |
| 5. C2×C5×#685 | C2 | semidirect |
| 6. C2×C5×#683 | C2 | semidirect |
| 11. C22×C4×C52 | C22 | semidirect |
| 16. C5×C22⋊Dic5 | C22 | semidirect |
| 17. C5×#685 | C22 | semidirect |
| 18. C5×#683 | C22 | semidirect |
| 20. C2×#4075 | C5 | direct (N × H) |
| 38. C23×C4×C5 | D5 | semidirect |
| 39. C23×C4×C5 | C2×C5 | semidirect |
| 45. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 46. #4075 | C2×C5 | direct (N × H) |
| 47. C2×#685 | C2×C5 | semidirect |
| 48. C2×#683 | C2×C5 | semidirect |
| 76. C22×C4×C5 | C2×D5 | semidirect |
| 78. C22×C4×C5 | C22×C5 | semidirect |
| 86. C22⋊Dic5 | C22×C5 | semidirect |
| 87. #685 | C22×C5 | semidirect |
| 88. #683 | C22×C5 | semidirect |
| 91. C2×C52 | #123 | semidirect |
| 133. C23×C4 | C5×D5 | semidirect |
| 138. C52 | C2×#123 | semidirect |
| 178. C22×C4 | C2×C5×D5 | semidirect |
| 189. C2×C5 | #4075 | direct (N × H) |
| 190. C2×C5 | C5×#123 | semidirect |
| 212. C5 | C2×#4075 | direct (N × H) |
| 213. C5 | C2×C5×#123 | semidirect |
| 228. C2 | C5×#4075 | 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 |
| C22×C5×C22⋊D5 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C5×#4075 | 2 |
| C2×C5×#685 | 2 |
| C2×C5×#683 | 2 |
| C2×C5×#123 | 5 |
| C2×#4075 | 5 |