Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
116 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C5 | #120⋊C3 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C2×C3×C5 |
| Frattini | C23 | C2×C5×A4 |
| Fitting | C5×B(4,𝔽2) | C3 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#997 | C2 | semidirect |
| 2. C5×B(4,𝔽2) | C3 | semidirect |
| 4. B(4,𝔽2)⋊C3 | C5 | direct (N × H) |
| 5. C5×H(5,𝔽2) | C2×C3 | semidirect |
| 12. #997 | C2×C5 | semidirect |
| 13. C24×C5 | A4 | semidirect |
| 20. B(4,𝔽2) | C3×C5 | semidirect |
| 37. H(5,𝔽2) | C2×C3×C5 | semidirect |
| 56. C24 | C5×A4 | semidirect |
| 85. C5 | B(4,𝔽2)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#997 | 2 |
| C5×B(4,𝔽2) | 3 |
| C22×C5×A4 | 4 |
| B(4,𝔽2)⋊C3 | 5 |