Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1012 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 149 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×#6763 | C2 | semidirect |
| 4. C24×C3×C5 | C4 | semidirect |
| 6. C23×C3×D5 | C4 | semidirect |
| 8. C22×ΓL(1,𝔽16) | C22 | semidirect |
| 25. C24×C5 | Dic3 | semidirect |
| 27. C23×D5 | Dic3 | semidirect |
| 34. C22×C3×C5 | C22⋊C4 | semidirect |
| 39. C2×C3×D5 | C22⋊C4 | semidirect |
| 45. C24×C3 | AGL(1,𝔽5) | semidirect |
| 76. C22×C5 | #217 | semidirect |
| 81. C2×D5 | #217 | semidirect |
| 87. C24 | ΓL(1,𝔽16) | semidirect |
| 90. C3×C5 | #379 | semidirect |
| 98. C22×C3 | C22⋊AGL(1,𝔽5) | semidirect |
| 119. C5 | #5247 | semidirect |
| 127. C22 | #6763 | semidirect |
| 130. C3 | #65800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×D5 | 2 |
| C2×#6763 | 2 |
| #65800 | 3 |
| #5247 | 5 |