Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1120 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 259 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. C2×Q8×C5⋊D5 | C2 | semidirect |
| 2. C52×C4⋊Q8 | C2 | semidirect |
| 3. #11717266 | C2 | semidirect |
| 4. #11717216 | C2 | semidirect |
| 6. #11717208 | C2 | semidirect |
| 8. C4×#6045 | C2 | semidirect |
| 36. C4⋊(C5⋊D5) | Q8 | semidirect |
| 40. #6045 | D4 | semidirect |
| 42. C5×C4⋊Q8 | D5 | semidirect |
| 52. C2×C5⋊D5 | C2×Q8 | semidirect |
| 56. C4×C52 | C2×Q8 | semidirect |
| 98. C4⋊Q8 | C5⋊D5 | semidirect |
| 104. C52 | D4×Q8 | semidirect |
| 112. C4×C5 | Q8×D5 | semidirect |
| 151. C5 | #66061 | semidirect |
| 162. C4 | Q8×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C52×C4⋊Q8 | 2 |
| #11717266 | 2 |
| #11717216 | 2 |
| #11717213 | 2 |
| #11717208 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C4×#6045 | 2 |
| #66061 | 5 |