Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
592 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 144 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×C5×#713 | C2 | semidirect |
| 2. C2×#87870 | C2 | semidirect |
| 3. C2×#87812 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. #11717065 | C2 | direct (N × H) |
| 6. C2×#87773 | C2 | semidirect |
| 7. C2×#87770 | C2 | semidirect |
| 8. C2×D5×#168 | C2 | semidirect |
| 12. C5×#713 | C22 | semidirect |
| 21. #87870 | C22 | semidirect |
| 22. #87812 | C22 | semidirect |
| 24. C5×#688 | C22 | semidirect |
| 26. #87773 | C22 | semidirect |
| 27. #87770 | C22 | semidirect |
| 28. D5×#168 | C22 | semidirect |
| 55. C2×#713 | D5 | semidirect |
| 63. C2×#688 | D5 | semidirect |
| 97. #713 | C2×D5 | semidirect |
| 116. #688 | C2×D5 | semidirect |
| 128. C2×C52 | #135 | semidirect |
| 195. C52 | C2×#135 | semidirect |
| 250. C2×C5 | #4062 | semidirect |
| 251. C2×C5 | #4096 | semidirect |
| 281. C5 | C2×#4062 | semidirect |
| 282. C5 | C2×#4096 | semidirect |
| 298. C2 | #11717065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×#87870 | 2 |
| C2×#87812 | 2 |
| C2×C5×#688 | 2 |
| #11717065 | 2 |
| C2×#87773 | 2 |
| C2×#87770 | 2 |
| C2×D5×#168 | 2 |
| C2×#4096 | 5 |
| C2×#4062 | 5 |