Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1744 conjugacy classes of subgroups; only the 894 normal subgroups are shown.
This group has 1744 conjugacy classes of subgroups — too many to draw. Only its 894 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 |
|---|---|---|
| 1. C22×C52×Q8 | C2 | semidirect |
| 2. C5×#4147 | C2 | direct (N × H) |
| 3. C2×C5×#713 | C2 | semidirect |
| 4. C2×C5×Q8×D5 | C2 | semidirect |
| 5. C2×C5×#709 | C2 | semidirect |
| 7. C2×C52×Q8 | C22 | semidirect |
| 10. C5×#713 | C22 | semidirect |
| 11. C5×Q8×D5 | C22 | semidirect |
| 12. C5×#709 | C22 | semidirect |
| 17. C2×#4147 | C5 | direct (N × H) |
| 33. C22×C5×Q8 | D5 | semidirect |
| 34. C22×C5×Q8 | C2×C5 | semidirect |
| 35. #4147 | C2×C5 | direct (N × H) |
| 36. C2×#713 | C2×C5 | semidirect |
| 37. C2×Q8×D5 | C2×C5 | semidirect |
| 38. C2×#709 | C2×C5 | semidirect |
| 53. C2×C5×Q8 | C2×D5 | semidirect |
| 55. C2×C5×Q8 | C22×C5 | semidirect |
| 63. #713 | C22×C5 | semidirect |
| 64. Q8×D5 | C22×C5 | semidirect |
| 65. #709 | C22×C5 | semidirect |
| 71. C2×C52 | 2−1+4 | semidirect |
| 102. C22×Q8 | C5×D5 | semidirect |
| 103. C52 | C2×2−1+4 | semidirect |
| 127. C2×Q8 | C2×C5×D5 | semidirect |
| 138. C2×C5 | #4147 | direct (N × H) |
| 139. C2×C5 | C5×2−1+4 | semidirect |
| 154. C5 | C2×#4147 | direct (N × H) |
| 155. C5 | C2×C5×2−1+4 | semidirect |
| 165. C2 | C5×#4147 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C5×#4147 | 2 |
| C2×C5×#713 | 2 |
| C2×C5×Q8×D5 | 2 |
| C2×C5×#709 | 2 |
| C2×C5×2−1+4 | 5 |
| C2×#4147 | 5 |