Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
596 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 77 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×#10597183 | C2 | semidirect |
| 3. #11925533 | C2 | semidirect |
| 4. C3×C22⋊#1044 | C2 | semidirect |
| 5. #11925360 | C2 | semidirect |
| 7. C22×C5×D15 | C4 | semidirect |
| 10. C2×D15⋊D5 | C4 | semidirect |
| 13. C2×C3⋊#1043 | C22 | semidirect |
| 14. C2×C3×#1044 | C22 | semidirect |
| 19. C22⋊#1044 | D3 | semidirect |
| 22. C22×C3×C52 | C2×C4 | semidirect |
| 25. C2×C5×D15 | C2×C4 | semidirect |
| 27. C2×C3×C5⋊D5 | C2×C4 | semidirect |
| 46. C2×#1044 | C2×D3 | semidirect |
| 53. C5×D15 | C22⋊C4 | semidirect |
| 56. C22×D15 | AGL(1,𝔽5) | semidirect |
| 69. C22×C52 | C4×D3 | semidirect |
| 71. C2×C5⋊D5 | C4×D3 | semidirect |
| 88. C3×C52 | C2×C22⋊C4 | semidirect |
| 90. C22×C3×C5 | C2×AGL(1,𝔽5) | semidirect |
| 93. C2×D15 | C2×AGL(1,𝔽5) | semidirect |
| 140. D15 | C22⋊AGL(1,𝔽5) | semidirect |
| 147. C52 | D3×C22⋊C4 | semidirect |
| 161. C22×C5 | D3×AGL(1,𝔽5) | semidirect |
| 184. C3×C5 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 188. C22×C3 | D5⋊AGL(1,𝔽5) | semidirect |
| 225. C5 | D3×C22⋊AGL(1,𝔽5) | semidirect |
| 235. C22 | #10597183 | semidirect |
| 238. C3 | D5⋊(C22⋊AGL(1,𝔽5)) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D15⋊D5 | 2 |
| C2×#10597183 | 2 |
| #11925533 | 2 |
| C3×C22⋊#1044 | 2 |
| #11925360 | 2 |
| D5⋊(C22⋊AGL(1,𝔽5)) | 3 |
| D3×C22⋊AGL(1,𝔽5) | 5 |