Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
420 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 4. #11925351 | C2 | semidirect |
| 5. Dic3⋊#1044 | C2 | semidirect |
| 6. Dic3⋊#1043 | C2 | semidirect |
| 7. C3×#87832 | C2 | semidirect |
| 16. Dic5×D15 | C4 | semidirect |
| 18. C5×#1200 | C4 | semidirect |
| 27. #87832 | D3 | semidirect |
| 36. C3⋊#1039 | C2×C4 | semidirect |
| 37. C52×Dic3 | C2×C4 | semidirect |
| 38. C3×C5×Dic5 | C2×C4 | semidirect |
| 60. C5×D15 | C4⋊C4 | semidirect |
| 75. #1200 | AGL(1,𝔽5) | semidirect |
| 89. C5×Dic5 | C4×D3 | semidirect |
| 99. C3×C52 | C2×C4⋊C4 | semidirect |
| 115. C3×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 117. C5×Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 148. D15 | C4⋊AGL(1,𝔽5) | semidirect |
| 154. C52 | D3×C4⋊C4 | semidirect |
| 183. Dic5 | D3×AGL(1,𝔽5) | semidirect |
| 192. C3×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 203. Dic3 | D5⋊AGL(1,𝔽5) | semidirect |
| 228. C5 | D3×C4⋊AGL(1,𝔽5) | semidirect |
| 240. C3 | D5⋊(C4⋊AGL(1,𝔽5)) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597183 | 2 |
| C2×#10597182 | 2 |
| #11925416 | 2 |
| #11925351 | 2 |
| Dic3⋊#1044 | 2 |
| Dic3⋊#1043 | 2 |
| C3×#87832 | 2 |
| D5⋊(C4⋊AGL(1,𝔽5)) | 3 |
| D3×C4⋊AGL(1,𝔽5) | 5 |