Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2696 conjugacy classes of subgroups; only the 715 normal subgroups are shown.
This group has 2696 conjugacy classes of subgroups — too many to draw. Only its 715 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. C23×C4×C52 | C2 | semidirect |
| 3. C23×#1039 | C2 | semidirect |
| 4. C2×#87808 | C2 | direct (N × H) |
| 8. C23×C5⋊D5 | C4 | semidirect |
| 11. C22×C4×C52 | C22 | semidirect |
| 13. C22×#1039 | C22 | semidirect |
| 14. #87808 | C22 | direct (N × H) |
| 23. C22×C5⋊D5 | C2×C4 | semidirect |
| 26. C2×C4×C52 | C23 | semidirect |
| 28. C2×#1039 | C23 | semidirect |
| 30. C23×C4×C5 | D5 | semidirect |
| 33. C22×C52 | C22⋊C4 | semidirect |
| 41. C2×C5⋊D5 | C22×C4 | semidirect |
| 50. C22×C4×C5 | C2×D5 | semidirect |
| 55. C2×C52 | C2×C22⋊C4 | semidirect |
| 70. C2×C4×C5 | C22×D5 | semidirect |
| 75. C23×C4 | C5⋊D5 | semidirect |
| 77. C52 | C22×C22⋊C4 | semidirect |
| 78. C22×C5 | #685 | semidirect |
| 97. C22×C4 | C2×C5⋊D5 | semidirect |
| 99. C2×C5 | C2×#685 | semidirect |
| 116. C2×C4 | C22×C5⋊D5 | semidirect |
| 117. C5 | C22×#685 | semidirect |
| 122. C22 | #87808 | direct (N × H) |
| 130. C2 | C2×#87808 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5⋊D5 | 2 |
| C23×C4×C52 | 2 |
| C23×#1039 | 2 |
| C2×#87808 | 2 |
| C22×#685 | 5 |