Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
912 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 382 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. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 3. C5×D4×Dic5 | C2 | semidirect |
| 4. C5×#4072 | C2 | semidirect |
| 6. C2×C52×D4 | C4 | semidirect |
| 9. C22×C5×Dic5 | C22 | semidirect |
| 11. C5×C22⋊Dic5 | C22 | semidirect |
| 12. C5×C4⋊Dic5 | C22 | semidirect |
| 13. C4×C5×Dic5 | C22 | semidirect |
| 15. #66132 | C5 | direct (N × H) |
| 17. C23×C52 | C2×C4 | semidirect |
| 20. C52×D4 | C2×C4 | semidirect |
| 21. C2×C4×C52 | C2×C4 | semidirect |
| 31. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 32. D4×Dic5 | C2×C5 | semidirect |
| 33. #4072 | C2×C5 | semidirect |
| 47. C2×C5×D4 | Dic5 | semidirect |
| 48. C2×C5×D4 | C4×C5 | semidirect |
| 55. C22×Dic5 | C22×C5 | semidirect |
| 61. C22⋊Dic5 | C22×C5 | semidirect |
| 62. C4⋊Dic5 | C22×C5 | semidirect |
| 63. C4×Dic5 | C22×C5 | semidirect |
| 75. C23×C5 | C2×Dic5 | semidirect |
| 76. C23×C5 | C2×C4×C5 | semidirect |
| 82. C5×D4 | C2×Dic5 | semidirect |
| 83. C5×D4 | C2×C4×C5 | semidirect |
| 88. C2×C4×C5 | C2×Dic5 | semidirect |
| 89. C2×C4×C5 | C2×C4×C5 | semidirect |
| 98. C52 | #518 | semidirect |
| 123. C2×D4 | C5×Dic5 | semidirect |
| 144. C23 | C2×C5×Dic5 | semidirect |
| 147. D4 | C2×C5×Dic5 | semidirect |
| 150. C2×C4 | C2×C5×Dic5 | semidirect |
| 153. C5 | #66132 | direct (N × H) |
| 154. C5 | C5×#518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C5×D4×Dic5 | 2 |
| C5×#4072 | 2 |
| C5×#518 | 5 |
| #66132 | 5 |