Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
| 3. C2×C5×#688 | C2 | direct (N × H) |
| 4. C22×C5×#168 | C2 | semidirect |
| 7. C2×C52×Q8 | C22 | semidirect |
| 12. C5×#688 | C22 | direct (N × H) |
| 13. C2×C5×#168 | C22 | semidirect |
| 15. C22×#688 | C5 | direct (N × H) |
| 20. C52×Q8 | C23 | semidirect |
| 26. C5×#168 | C23 | semidirect |
| 28. C22×C5×Q8 | D5 | semidirect |
| 29. C22×C5×Q8 | C2×C5 | semidirect |
| 34. C2×#688 | C2×C5 | direct (N × H) |
| 35. C22×#168 | C2×C5 | semidirect |
| 36. C22×C52 | SD16 | semidirect |
| 49. C2×C5×Q8 | C2×D5 | semidirect |
| 50. C2×C5×Q8 | C22×C5 | semidirect |
| 63. #688 | C22×C5 | direct (N × H) |
| 64. C2×#168 | C22×C5 | semidirect |
| 66. C2×C52 | C2×SD16 | semidirect |
| 80. C5×Q8 | C22×D5 | semidirect |
| 81. C5×Q8 | C23×C5 | semidirect |
| 96. #168 | C23×C5 | semidirect |
| 97. C22×Q8 | C5×D5 | semidirect |
| 101. C52 | C22×SD16 | semidirect |
| 106. C22×C5 | #688 | direct (N × H) |
| 107. C22×C5 | C5×SD16 | semidirect |
| 123. C2×Q8 | C2×C5×D5 | semidirect |
| 133. C2×C5 | C2×#688 | direct (N × H) |
| 134. C2×C5 | C2×C5×SD16 | semidirect |
| 142. Q8 | C22×C5×D5 | semidirect |
| 150. C5 | C22×#688 | direct (N × H) |
| 151. C5 | C22×C5×SD16 | semidirect |
| 154. C22 | C5×#688 | direct (N × H) |
| 160. C2 | C2×C5×#688 | 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 |
| C22×C5×D20 | 2 |
| C2×C5×#688 | 2 |
| C22×C5×#168 | 2 |
| C22×C5×SD16 | 5 |
| C22×#688 | 5 |