Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
534 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C23×A4 |
| commutator, cosocle | C2×Q8 | C23×C3×C5 |
| Frattini | C22 | C23×C5×A4 |
| Fitting | C5×#3517 | C3 |
| hypercenter | C5×#125 | A4 |
| hypocenter | Q8 | C3×C5×#41 |
| LCS | G ▷ C2×Q8 ▷ Q8 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#557⋊C3 | C2 | semidirect |
| 2. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 3. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 4. C5×#520⋊C3 | C2 | semidirect |
| 5. C4×C5×#41⋊C3 | C2 | semidirect |
| 6. C5×#3517 | C3 | semidirect |
| 13. #3517⋊C3 | C5 | direct (N × H) |
| 33. #557⋊C3 | C2×C5 | semidirect |
| 34. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 35. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 36. #520⋊C3 | C2×C5 | semidirect |
| 37. C4×#41⋊C3 | C2×C5 | semidirect |
| 72. #3517 | C3×C5 | semidirect |
| 78. C5×SL(2,𝔽3) | #41 | semidirect |
| 220. SL(2,𝔽3) | C5×#41 | semidirect |
| 321. C5 | #3517⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C5×#520⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#3517 | 3 |
| C3×C5×#125 | 4 |
| #3517⋊C3 | 5 |