Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
1548 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1548 conjugacy classes of subgroups — too many to draw. Only its 274 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×C4⋊(C3⋊ΓL(1,𝔽16)) | C2 | semidirect |
| 3. C2×C32×C4×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×(C2×AGL(1,𝔽5))⋊(C3⋊D3) | C2 | semidirect |
| 9. C2×C4⋊(C3⋊D15) | C4 | semidirect |
| 10. C2×C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 12. C2×#67140 | C4 | semidirect |
| 21. C2×C3×C4×AGL(1,𝔽5) | D3 | semidirect |
| 34. C2×C32×AGL(1,𝔽5) | D4 | semidirect |
| 74. C32×C4×C5 | C22⋊C4 | semidirect |
| 75. C32×Dic5 | C22⋊C4 | semidirect |
| 79. C2×C4×AGL(1,𝔽5) | C3⋊D3 | semidirect |
| 88. C2×C4⋊(C3⋊D3) | AGL(1,𝔽5) | semidirect |
| 103. C2×C3×AGL(1,𝔽5) | D12 | semidirect |
| 168. C3×C4×C5 | (C2×D3)⋊C4 | semidirect |
| 169. C3×Dic5 | (C2×D3)⋊C4 | semidirect |
| 182. C32×C5 | #390 | semidirect |
| 194. C2×AGL(1,𝔽5) | C4⋊(C3⋊D3) | semidirect |
| 216. C32×C4 | C22⋊AGL(1,𝔽5) | semidirect |
| 262. C4×C5 | #3752 | semidirect |
| 263. Dic5 | #3752 | semidirect |
| 283. C3×C5 | #4939 | semidirect |
| 298. C3×C4 | (C2×D3)⋊AGL(1,𝔽5) | semidirect |
| 307. C32 | #65780 | semidirect |
| 334. C5 | #10592638 | semidirect |
| 350. C4 | (C2×AGL(1,𝔽5))⋊(C3⋊D3) | semidirect |
| 351. C3 | #11751850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C4⋊(C3⋊D3) | 2 |
| C2×C4⋊(C3⋊ΓL(1,𝔽16)) | 2 |
| C2×C32×C4×AGL(1,𝔽5) | 2 |
| C2×(C2×AGL(1,𝔽5))⋊(C3⋊D3) | 2 |
| #11751850 | 3 |
| #10592638 | 5 |