Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
750 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | C42⋊C3 |
| commutator, cosocle, hypocenter | #95 | C22×C3×C5 |
| Frattini | C23 | C22×C5×A4 |
| Fitting | C22×C5×#95 | C3 |
| socle | C25×C5 | A4 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C23×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#95⋊C3 | C2 | direct (N × H) |
| 2. C22×C5×#95 | C3 | semidirect |
| 4. C5×#95⋊C3 | C22 | direct (N × H) |
| 5. C22×#95⋊C3 | C5 | direct (N × H) |
| 8. C2×C5×#95 | C2×C3 | semidirect |
| 11. C2×#95⋊C3 | C2×C5 | direct (N × H) |
| 20. C5×#95 | C22×C3 | semidirect |
| 21. C22×#95 | C3×C5 | semidirect |
| 26. #95⋊C3 | C22×C5 | direct (N × H) |
| 44. C2×#95 | C2×C3×C5 | semidirect |
| 78. #95 | C22×C3×C5 | semidirect |
| 93. C22×C5 | #95⋊C3 | direct (N × H) |
| 120. C2×C5 | C2×#95⋊C3 | direct (N × H) |
| 144. C5 | C22×#95⋊C3 | direct (N × H) |
| 154. C22 | C5×#95⋊C3 | direct (N × H) |
| 163. C2 | C2×C5×#95⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#95⋊C3 | 2 |
| C22×C5×#95 | 3 |
| C23×C5×A4 | 4 |
| C22×#95⋊C3 | 5 |