Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
832 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 232 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. C22×C5×#168 | C2 | semidirect |
| 3. C2×#87769 | C2 | direct (N × H) |
| 9. C2×C5×#168 | C22 | semidirect |
| 10. #87769 | C22 | direct (N × H) |
| 20. C5×#168 | C23 | semidirect |
| 24. C22×#168 | D5 | semidirect |
| 26. C22×C52 | M16 | semidirect |
| 44. C2×#168 | C2×D5 | semidirect |
| 47. C2×C52 | C2×M16 | semidirect |
| 67. #168 | C22×D5 | semidirect |
| 71. C52 | C22×M16 | semidirect |
| 74. C22×C5 | #676 | semidirect |
| 95. C2×C5 | C2×#676 | semidirect |
| 109. C5 | C22×#676 | semidirect |
| 112. C22 | #87769 | direct (N × H) |
| 118. C2 | C2×#87769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C22×C5×#168 | 2 |
| C2×#87769 | 2 |
| C22×#676 | 5 |