Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 102 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. C4×C5×D20 | C2 | semidirect |
| 3. C52×#97 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3949 | C2 | semidirect |
| 13. C5×D40 | C4 | semidirect |
| 15. #65000 | C5 | direct (N × H) |
| 21. C5×D20 | C2×C4 | semidirect |
| 24. C52×C8 | C2×C4 | semidirect |
| 28. C4×D20 | C2×C5 | semidirect |
| 32. C5×#97 | D5 | semidirect |
| 33. C5×#97 | C2×C5 | semidirect |
| 34. #3953 | C2×C5 | semidirect |
| 35. #3949 | C2×C5 | semidirect |
| 62. D40 | C4×C5 | semidirect |
| 81. D20 | C2×C4×C5 | semidirect |
| 87. C5×C8 | C4×D5 | semidirect |
| 88. C5×C8 | C2×C4×C5 | semidirect |
| 93. #97 | C5×D5 | semidirect |
| 94. C52 | #442 | semidirect |
| 139. C8 | C4×C5×D5 | semidirect |
| 141. C5 | #65000 | direct (N × H) |
| 142. C5 | C5×#442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D40 | 2 |
| C4×C5×D20 | 2 |
| C52×#97 | 2 |
| C5×#3953 | 2 |
| C5×#3949 | 2 |
| C5×#442 | 5 |
| #65000 | 5 |