Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4094 | C2 | semidirect |
| 3. C5×#3969 | C2 | semidirect |
| 4. C5×#3951 | C2 | semidirect |
| 5. C5×#3947 | C2 | semidirect |
| 7. C52×Q16 | C4 | semidirect |
| 8. C52×SD16 | C4 | semidirect |
| 9. C52×D8 | C4 | semidirect |
| 17. #65486 | C5 | direct (N × H) |
| 32. #4094 | C2×C5 | semidirect |
| 36. #3969 | C2×C5 | semidirect |
| 37. #3951 | C2×C5 | semidirect |
| 38. #3947 | C2×C5 | semidirect |
| 49. C5×Q16 | Dic5 | semidirect |
| 50. C5×Q16 | C4×C5 | semidirect |
| 52. C5×SD16 | Dic5 | semidirect |
| 53. C5×SD16 | C4×C5 | semidirect |
| 55. C5×D8 | Dic5 | semidirect |
| 56. C5×D8 | C4×C5 | semidirect |
| 106. C52 | #444 | semidirect |
| 125. Q16 | C5×Dic5 | semidirect |
| 126. SD16 | C5×Dic5 | semidirect |
| 127. D8 | C5×Dic5 | semidirect |
| 154. C5 | #65486 | direct (N × H) |
| 155. C5 | C5×#444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| C5×#4094 | 2 |
| C5×#3969 | 2 |
| C5×#3951 | 2 |
| C5×#3947 | 2 |
| C5×#444 | 5 |
| #65486 | 5 |