Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
576 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #5464 |
| commutator, cosocle, hypocenter | H(3,𝔽4) | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C2×C5×H(3,𝔽4) | C3 |
| socle | C23×C5 | C22⋊A4 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#5464 | C2 | direct (N × H) |
| 2. C2×C5×H(3,𝔽4) | C3 | semidirect |
| 5. C2×#5464 | C5 | direct (N × H) |
| 8. C5×H(3,𝔽4) | C2×C3 | semidirect |
| 13. #5464 | C2×C5 | direct (N × H) |
| 14. C25×C5 | A4 | semidirect |
| 27. C2×C42×C5 | A4 | semidirect |
| 28. C2×H(3,𝔽4) | C3×C5 | semidirect |
| 37. C24×C5 | C2×A4 | semidirect |
| 52. C42×C5 | C2×A4 | semidirect |
| 55. H(3,𝔽4) | C2×C3×C5 | semidirect |
| 80. C25 | C5×A4 | semidirect |
| 93. C2×C42 | C5×A4 | semidirect |
| 112. C24 | C2×C5×A4 | semidirect |
| 127. C42 | C2×C5×A4 | semidirect |
| 135. C2×C5 | #5464 | direct (N × H) |
| 155. C5 | C2×#5464 | direct (N × H) |
| 172. C2 | C5×#5464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5464 | 2 |
| C2×C5×H(3,𝔽4) | 3 |
| C2×C5×C22⋊A4 | 4 |
| C2×C5×C42⋊C3 | 4 |
| C2×#5464 | 5 |