Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
1056 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 182 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×#10597113 | C2 | semidirect |
| 3. C52×#217 | C2 | semidirect |
| 4. C3×C22⋊#1039 | C2 | semidirect |
| 5. #11925120 | C2 | semidirect |
| 9. C22×C3⋊(C5⋊D5) | C4 | semidirect |
| 12. C2×C52×Dic3 | C22 | semidirect |
| 13. C2×C3×#1039 | C22 | semidirect |
| 19. C22⋊#1039 | D3 | semidirect |
| 22. C22×C3×C52 | C2×C4 | semidirect |
| 27. C2×C3⋊(C5⋊D5) | C2×C4 | semidirect |
| 33. C5×#217 | D5 | semidirect |
| 42. C2×#1039 | C2×D3 | semidirect |
| 49. C3⋊(C5⋊D5) | C22⋊C4 | semidirect |
| 55. C2×C5×Dic3 | C2×D5 | semidirect |
| 59. C22×C52 | C4×D3 | semidirect |
| 74. C3×C52 | C2×C22⋊C4 | semidirect |
| 76. C22×C3×C5 | C4×D5 | semidirect |
| 93. #217 | C5⋊D5 | semidirect |
| 109. C52 | D3×C22⋊C4 | semidirect |
| 116. C2×Dic3 | C2×C5⋊D5 | semidirect |
| 119. C22×C5 | #1200 | semidirect |
| 133. C3×C5 | D5×C22⋊C4 | semidirect |
| 135. C22×C3 | C4×C5⋊D5 | semidirect |
| 162. C5 | #91561 | semidirect |
| 169. C22 | #10597113 | semidirect |
| 173. C3 | C22⋊C4×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C5⋊D5) | 2 |
| C2×#10597113 | 2 |
| C52×#217 | 2 |
| C3×C22⋊#1039 | 2 |
| #11925120 | 2 |
| C22⋊C4×C5⋊D5 | 3 |
| #91561 | 5 |