Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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×#87811 | C2 | semidirect |
| 2. C5×Q8×Dic5 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716605 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 26. C52×Q8 | D4 | semidirect |
| 42. Q8×Dic5 | D5 | semidirect |
| 46. C2×#688 | D5 | semidirect |
| 67. C5×Dic5 | SD16 | semidirect |
| 113. C5×Q8 | D20 | semidirect |
| 114. C5×Q8 | C22⋊D5 | semidirect |
| 153. C52 | #460 | semidirect |
| 186. Dic5 | #688 | semidirect |
| 217. Q8 | #6038 | semidirect |
| 232. C5 | #65316 | semidirect |
| 233. C5 | #65452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87811 | 2 |
| C5×Q8×Dic5 | 2 |
| C2×C5×#688 | 2 |
| #11717029 | 2 |
| #11716612 | 2 |
| #11716605 | 2 |
| #11716603 | 2 |
| #65452 | 5 |
| #65316 | 5 |