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. C22×#6045 | C2 | semidirect |
| 3. C52×C22⋊Q8 | C2 | semidirect |
| 4. #11717264 | C2 | semidirect |
| 6. #11717217 | C2 | semidirect |
| 7. #11717216 | C2 | semidirect |
| 8. #11717208 | C2 | semidirect |
| 9. #11717207 | C2 | semidirect |
| 11. #11717198 | C2 | semidirect |
| 46. C22⋊(C5⋊D5) | Q8 | semidirect |
| 58. #6045 | D4 | semidirect |
| 61. C5×C22⋊Q8 | D5 | semidirect |
| 72. C22×C52 | C2×Q8 | semidirect |
| 76. C2×C5⋊D5 | C2×Q8 | semidirect |
| 85. #1039 | C2×Q8 | semidirect |
| 145. C22⋊Q8 | C5⋊D5 | semidirect |
| 149. C52 | D4×Q8 | semidirect |
| 152. C22×C5 | Q8×D5 | semidirect |
| 217. C5 | #65966 | semidirect |
| 223. C22 | 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 |
| C22×#6045 | 2 |
| C52×C22⋊Q8 | 2 |
| #11717264 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717217 | 2 |
| #11717216 | 2 |
| #11717208 | 2 |
| #11717207 | 2 |
| #11717201 | 2 |
| #11717198 | 2 |
| #65966 | 5 |