Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
340 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 114 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×D4×Dic5 | C2 | semidirect |
| 3. C5×#3964 | C2 | semidirect |
| 4. C5×#3949 | C2 | semidirect |
| 5. C5×#3947 | C2 | semidirect |
| 8. C52×D8 | C4 | semidirect |
| 15. #65441 | C5 | direct (N × H) |
| 18. C52×D4 | C2×C4 | semidirect |
| 23. C52×C8 | C2×C4 | semidirect |
| 29. D4×Dic5 | C2×C5 | semidirect |
| 33. #3964 | C2×C5 | semidirect |
| 34. #3949 | C2×C5 | semidirect |
| 35. #3947 | C2×C5 | semidirect |
| 50. C5×D8 | Dic5 | semidirect |
| 51. C5×D8 | C4×C5 | semidirect |
| 74. C5×D4 | C2×Dic5 | semidirect |
| 75. C5×D4 | C2×C4×C5 | semidirect |
| 87. C5×C8 | C2×Dic5 | semidirect |
| 88. C5×C8 | C2×C4×C5 | semidirect |
| 95. C52 | #442 | semidirect |
| 120. D8 | C5×Dic5 | semidirect |
| 137. D4 | C2×C5×Dic5 | semidirect |
| 143. C8 | C2×C5×Dic5 | semidirect |
| 145. C5 | #65441 | direct (N × H) |
| 146. C5 | C5×#442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C5×D4×Dic5 | 2 |
| C5×#3964 | 2 |
| C5×#3949 | 2 |
| C5×#3947 | 2 |
| C5×#442 | 5 |
| #65441 | 5 |