Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
710 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#91184 | C2 | semidirect |
| 3. C2×C5×#859 | C2 | semidirect |
| 4. #11751605 | C2 | direct (N × H) |
| 7. C2×D5×SL(2,𝔽3) | C4 | semidirect |
| 10. #91184 | C22 | semidirect |
| 11. C5×#859 | C22 | semidirect |
| 27. D5×SL(2,𝔽3) | C2×C4 | semidirect |
| 32. C2×#859 | D5 | semidirect |
| 36. C2×Q8×D5 | Dic3 | semidirect |
| 72. #859 | C2×D5 | semidirect |
| 85. Q8×D5 | C2×Dic3 | semidirect |
| 253. C2×C5 | #5420 | semidirect |
| 290. C5 | C2×#5420 | semidirect |
| 307. C2 | #11751605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×SL(2,𝔽3) | 2 |
| C2×#91184 | 2 |
| C2×C5×#859 | 2 |
| #11751605 | 2 |
| C2×#65091 | 3 |
| C2×#6665 | 4 |
| C2×#5420 | 5 |