Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1672 conjugacy classes of subgroups; only the 435 normal subgroups are shown.
This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 435 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 |
|---|---|---|
| 3. C2×C52×C4⋊C4 | C2 | semidirect |
| 4. C2×C4⋊#1039 | C2 | semidirect |
| 5. C2×#87806 | C2 | semidirect |
| 6. C4⋊C4×C5⋊D5 | C2 | direct (N × H) |
| 13. C2×C4×C5⋊D5 | C4 | semidirect |
| 16. C52×C4⋊C4 | C22 | semidirect |
| 17. C4⋊#1039 | C22 | semidirect |
| 18. #87806 | C22 | semidirect |
| 26. C2×C4×C52 | C2×C4 | semidirect |
| 30. C2×#1039 | C2×C4 | semidirect |
| 34. C4×C5⋊D5 | C2×C4 | semidirect |
| 37. C2×C5×C4⋊C4 | D5 | semidirect |
| 45. C2×C5⋊D5 | C4⋊C4 | direct (N × H) |
| 50. C4×C52 | C22×C4 | semidirect |
| 52. #1039 | C22×C4 | semidirect |
| 62. C5×C4⋊C4 | C2×D5 | semidirect |
| 66. C2×C52 | C2×C4⋊C4 | semidirect |
| 70. C5⋊D5 | C2×C4⋊C4 | direct (N × H) |
| 77. C2×C4×C5 | C4×D5 | semidirect |
| 91. C2×C4⋊C4 | C5⋊D5 | direct (N × H) |
| 92. C52 | C22×C4⋊C4 | semidirect |
| 102. C4×C5 | C2×C4×D5 | semidirect |
| 116. C4⋊C4 | C2×C5⋊D5 | direct (N × H) |
| 117. C2×C5 | D5×C4⋊C4 | semidirect |
| 134. C2×C4 | C4×C5⋊D5 | semidirect |
| 137. C5 | C2×D5×C4⋊C4 | semidirect |
| 149. C4 | C2×C4×C5⋊D5 | semidirect |
| 151. C2 | C4⋊C4×C5⋊D5 | 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 |
| C2×C52×C4⋊C4 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×#87806 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| C2×D5×C4⋊C4 | 5 |