Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C22×A4 |
| commutator, cosocle, hypocenter | Q8 | C23×C3×C5 |
| Frattini | C2 | C23×C5×A4 |
| Fitting | C2×C5×H(5,𝔽2) | C3 |
| hypercenter | C2×C5×Q8 | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#994 | C2 | direct (N × H) |
| 2. C2×C5×#41⋊C3 | C2 | semidirect |
| 3. C2×C5×H(5,𝔽2) | C3 | semidirect |
| 5. C5×#41⋊C3 | C22 | semidirect |
| 6. C2×C5×SL(2,𝔽3) | C22 | semidirect |
| 7. C2×#994 | C5 | direct (N × H) |
| 9. C5×H(5,𝔽2) | C2×C3 | semidirect |
| 15. C5×SL(2,𝔽3) | C23 | semidirect |
| 16. #994 | C2×C5 | direct (N × H) |
| 17. C2×#41⋊C3 | C2×C5 | semidirect |
| 30. C2×H(5,𝔽2) | C3×C5 | semidirect |
| 34. #41⋊C3 | C22×C5 | semidirect |
| 35. C2×SL(2,𝔽3) | C22×C5 | semidirect |
| 50. H(5,𝔽2) | C2×C3×C5 | semidirect |
| 58. SL(2,𝔽3) | C23×C5 | semidirect |
| 82. C2×C5 | #994 | direct (N × H) |
| 99. C5 | C2×#994 | direct (N × H) |
| 109. C2 | C5×#994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#994 | 2 |
| C2×C5×#41⋊C3 | 2 |
| C2×C5×H(5,𝔽2) | 3 |
| C2×C3×C5×Q8 | 4 |
| C2×#994 | 5 |