Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1288 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 1288 conjugacy classes of subgroups — too many to draw. Only its 363 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. #11717266 | C2 | direct (N × H) |
| 5. C2×C4⋊#1039 | C2 | semidirect |
| 6. C2×#87806 | C2 | semidirect |
| 9. C2×C52×Q8 | C22 | semidirect |
| 17. C4⋊#1039 | C22 | semidirect |
| 18. #87806 | C22 | semidirect |
| 23. C22×C5⋊D5 | Q8 | semidirect |
| 35. C22×C5×Q8 | D5 | semidirect |
| 48. C2×C5⋊D5 | C2×Q8 | semidirect |
| 55. C2×C5×Q8 | C2×D5 | semidirect |
| 66. C2×C52 | C22⋊Q8 | semidirect |
| 86. C22×Q8 | C5⋊D5 | semidirect |
| 92. C52 | C2×C22⋊Q8 | semidirect |
| 107. C2×Q8 | C2×C5⋊D5 | semidirect |
| 117. C2×C5 | #4092 | semidirect |
| 137. C5 | C2×#4092 | semidirect |
| 151. C2 | #11717266 | 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 |
| #11717266 | 2 |
| C2×#87808 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×#87806 | 2 |
| C2×#4092 | 5 |