Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 496 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 | C2×C3×C5 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C3×C5 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C5 ◁ C2×C3×C5×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×H(3,𝔽4) | C2 | semidirect |
| 2. C3×C5×#454 | C2 | semidirect |
| 3. C3×C5×#355 | C2 | semidirect |
| 4. C5×#2202 | C3 | direct (N × H) |
| 5. C3×C5×2−1+4 | C22 | semidirect |
| 11. C3×C5×#101 | C22 | semidirect |
| 12. C3×#2202 | C5 | direct (N × H) |
| 13. C5×H(3,𝔽4) | C2×C3 | semidirect |
| 14. C5×#454 | C2×C3 | semidirect |
| 15. C5×#355 | C2×C3 | semidirect |
| 30. C3×H(3,𝔽4) | C2×C5 | semidirect |
| 31. C3×#454 | C2×C5 | semidirect |
| 32. C3×#355 | C2×C5 | semidirect |
| 33. C5×2−1+4 | C22×C3 | semidirect |
| 39. C5×#101 | C22×C3 | semidirect |
| 40. #2202 | C3×C5 | direct (N × H) |
| 55. C3×2−1+4 | C22×C5 | semidirect |
| 61. C3×#101 | C22×C5 | semidirect |
| 76. H(3,𝔽4) | C2×C3×C5 | semidirect |
| 77. #454 | C2×C3×C5 | semidirect |
| 78. #355 | C2×C3×C5 | semidirect |
| 115. 2−1+4 | C22×C3×C5 | semidirect |
| 121. #101 | C22×C3×C5 | semidirect |
| 162. C3×C5 | #2202 | direct (N × H) |
| 193. C5 | C3×#2202 | direct (N × H) |
| 202. C3 | C5×#2202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×H(3,𝔽4) | 2 |
| C3×C5×#454 | 2 |
| C3×C5×#355 | 2 |
| C5×#2202 | 3 |
| C3×#2202 | 5 |