Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 3. C52×#97 | C2 | semidirect |
| 4. C5×C8×Dic5 | C2 | semidirect |
| 5. C5×#3935 | C2 | semidirect |
| 13. C5×#676 | C4 | semidirect |
| 15. #64996 | C5 | direct (N × H) |
| 23. C52×C8 | C2×C4 | semidirect |
| 24. C5×#168 | C2×C4 | semidirect |
| 31. C5×#97 | D5 | semidirect |
| 32. C5×#97 | C2×C5 | semidirect |
| 34. C8×Dic5 | C2×C5 | semidirect |
| 35. #3935 | C2×C5 | semidirect |
| 42. C5×Dic5 | M16 | semidirect |
| 60. #676 | C4×C5 | semidirect |
| 83. C5×C8 | C4×D5 | semidirect |
| 84. C5×C8 | C2×C4×C5 | semidirect |
| 85. #168 | C2×C4×C5 | semidirect |
| 89. #97 | C5×D5 | semidirect |
| 91. C52 | C4×M16 | semidirect |
| 108. Dic5 | C5×M16 | semidirect |
| 133. C8 | C4×C5×D5 | semidirect |
| 135. C5 | #64996 | direct (N × H) |
| 136. C5 | C4×C5×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#676 | 2 |
| C42×C5×D5 | 2 |
| C52×#97 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#3935 | 2 |
| C4×C5×M16 | 5 |
| #64996 | 5 |