Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×C52×D4 | C2 | semidirect |
| 2. C5×#1220 | C2 | semidirect |
| 3. C2×C5×Dic15 | C2 | semidirect |
| 4. C4×C5×D15 | C2 | semidirect |
| 5. C5×Dic30 | C2 | semidirect |
| 12. #6819 | C5 | direct (N × H) |
| 14. C52×D4 | D3 | semidirect |
| 23. C3×C5×D4 | D5 | semidirect |
| 24. C3×C5×D4 | C2×C5 | semidirect |
| 25. #1220 | C2×C5 | semidirect |
| 26. C2×Dic15 | C2×C5 | semidirect |
| 27. C4×D15 | C2×C5 | semidirect |
| 28. Dic30 | C2×C5 | semidirect |
| 40. C3×C52 | #41 | semidirect |
| 60. C5×D4 | C5×D3 | semidirect |
| 61. C5×D4 | D15 | semidirect |
| 76. C52 | #237 | semidirect |
| 77. C3×D4 | C5×D5 | semidirect |
| 96. C3×C5 | #711 | semidirect |
| 97. C3×C5 | C5×#41 | semidirect |
| 113. D4 | C5×D15 | semidirect |
| 120. C5 | C5×#237 | semidirect |
| 121. C5 | #6819 | direct (N × H) |
| 127. C3 | C5×#711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C52×D4 | 2 |
| C5×#1220 | 2 |
| C2×C5×Dic15 | 2 |
| C4×C5×D15 | 2 |
| C5×Dic30 | 2 |
| C5×#711 | 3 |
| #6819 | 5 |
| C5×#237 | 5 |