Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1120 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 315 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 |
| 2. C2×Q8×C5⋊D5 | C2 | semidirect |
| 3. #11717266 | C2 | semidirect |
| 4. Q8×#1039 | C2 | semidirect |
| 5. #11717264 | C2 | semidirect |
| 7. #11717244 | C2 | semidirect |
| 26. C52×Q8 | D4 | semidirect |
| 30. C22⋊(C5⋊D5) | Q8 | direct (N × H) |
| 36. C22×C5×Q8 | D5 | semidirect |
| 45. C22×C52 | C2×Q8 | semidirect |
| 49. C2×C5⋊D5 | C2×Q8 | semidirect |
| 54. #1039 | C2×Q8 | semidirect |
| 78. C5×Q8 | C22⋊D5 | semidirect |
| 89. C22×Q8 | C5⋊D5 | semidirect |
| 95. C52 | D4×Q8 | semidirect |
| 98. C22×C5 | Q8×D5 | semidirect |
| 131. Q8 | C22⋊(C5⋊D5) | direct (N × H) |
| 140. C5 | Q8×C22⋊D5 | semidirect |
| 146. C22 | Q8×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×Q8×C5⋊D5 | 2 |
| #11717266 | 2 |
| Q8×#1039 | 2 |
| #11717264 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717244 | 2 |
| Q8×C22⋊D5 | 5 |