Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
912 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 3. #11717092 | C2 | semidirect |
| 4. #11717075 | C2 | semidirect |
| 5. #11717070 | C2 | semidirect |
| 8. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 11. C22×C5×Dic5 | C22 | semidirect |
| 12. C2×#6036 | C22 | semidirect |
| 14. C5×C22⋊Dic5 | C22 | semidirect |
| 15. #87781 | C22 | semidirect |
| 16. #87779 | C22 | semidirect |
| 17. Dic52 | C22 | semidirect |
| 20. C23×C52 | C2×C4 | semidirect |
| 24. C22×C5⋊D5 | C2×C4 | semidirect |
| 26. C22⋊(C5⋊D5) | C2×C4 | semidirect |
| 27. C2×#1039 | C2×C4 | semidirect |
| 35. C2×C22⋊Dic5 | D5 | semidirect |
| 63. C22×Dic5 | C2×D5 | semidirect |
| 68. C22⋊Dic5 | C2×D5 | semidirect |
| 83. C23×C5 | C4×D5 | semidirect |
| 110. C52 | #518 | semidirect |
| 162. C23 | #6036 | semidirect |
| 172. C5 | #65820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| #11717092 | 2 |
| #11717075 | 2 |
| #11717070 | 2 |
| #65820 | 5 |