Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1192 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 355 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×#87811 | C2 | direct (N × H) |
| 4. C22×#6029 | C2 | semidirect |
| 7. C2×C52×Q8 | C22 | semidirect |
| 12. #87811 | C22 | direct (N × H) |
| 13. C2×#6029 | C22 | semidirect |
| 19. C52×Q8 | C23 | semidirect |
| 25. #6029 | C23 | semidirect |
| 26. C22×C5×Q8 | D5 | semidirect |
| 30. C22×C52 | SD16 | semidirect |
| 39. C2×C5×Q8 | C2×D5 | semidirect |
| 47. C2×C52 | C2×SD16 | semidirect |
| 54. C5×Q8 | C22×D5 | semidirect |
| 61. C22×Q8 | C5⋊D5 | semidirect |
| 65. C52 | C22×SD16 | semidirect |
| 66. C22×C5 | #688 | semidirect |
| 75. C2×Q8 | C2×C5⋊D5 | semidirect |
| 82. C2×C5 | C2×#688 | semidirect |
| 89. Q8 | C22×C5⋊D5 | semidirect |
| 96. C5 | C22×#688 | semidirect |
| 99. C22 | #87811 | direct (N × H) |
| 105. C2 | C2×#87811 | 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×C4⋊(C5⋊D5) | 2 |
| C2×#87811 | 2 |
| C22×#6029 | 2 |
| C22×#688 | 5 |