Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 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. C5×Dic30 | C2 | semidirect |
| 3. C3×C5×Dic10 | C2 | semidirect |
| 4. C5×#1204 | C2 | semidirect |
| 13. D3×Dic10 | C5 | direct (N × H) |
| 18. C5×Dic10 | D3 | direct (N × H) |
| 20. C52×D3 | Q8 | semidirect |
| 22. Dic30 | C2×C5 | semidirect |
| 29. C3×Dic10 | C2×C5 | semidirect |
| 30. #1204 | C2×C5 | semidirect |
| 39. C3×C52 | C2×Q8 | semidirect |
| 66. Dic10 | C5×D3 | direct (N × H) |
| 71. C5×D3 | Dic10 | direct (N × H) |
| 72. C5×D3 | C5×Q8 | semidirect |
| 73. C52 | D3×Q8 | semidirect |
| 94. C3×C5 | C2×Dic10 | semidirect |
| 95. C3×C5 | C2×C5×Q8 | semidirect |
| 113. D3 | C5×Dic10 | direct (N × H) |
| 115. C5 | D3×Dic10 | direct (N × H) |
| 116. C5 | C5×D3×Q8 | semidirect |
| 122. C3 | C2×C5×Dic10 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Dic30 | 2 |
| C4×C52×D3 | 2 |
| C3×C5×Dic10 | 2 |
| C5×#1204 | 2 |
| C5×D3×Dic5 | 2 |
| C2×C5×Dic10 | 3 |
| C5×D3×Q8 | 5 |
| D3×Dic10 | 5 |