Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
854 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. C22×D5×SL(2,𝔽3) | C2 | semidirect |
| 2. C22×C5×GL(2,𝔽3) | C2 | semidirect |
| 3. C2×#91184 | C2 | semidirect |
| 4. #11751613 | C2 | direct (N × H) |
| 9. C2×D5×SL(2,𝔽3) | C22 | semidirect |
| 11. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 12. #91184 | C22 | semidirect |
| 14. C22×Q8×D5 | D3 | semidirect |
| 26. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 33. C22×GL(2,𝔽3) | D5 | semidirect |
| 42. C2×Q8×D5 | C2×D3 | semidirect |
| 73. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 80. C2×GL(2,𝔽3) | C2×D5 | semidirect |
| 86. C2×C5×Q8 | #67 | semidirect |
| 148. C2×SL(2,𝔽3) | C22⋊D5 | semidirect |
| 158. C22×D5 | GL(2,𝔽3) | semidirect |
| 163. C5×Q8 | C2×#67 | semidirect |
| 227. SL(2,𝔽3) | C2×C22⋊D5 | semidirect |
| 239. C2×D5 | C2×GL(2,𝔽3) | semidirect |
| 257. C2×Q8 | #1201 | semidirect |
| 298. C2×C5 | #5421 | semidirect |
| 318. Q8 | C2×#1201 | semidirect |
| 342. C5 | C2×#5421 | semidirect |
| 363. C2 | #11751613 | 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 |
| C22×C5×GL(2,𝔽3) | 2 |
| C2×#91184 | 2 |
| #11751613 | 2 |
| C2×#65459 | 3 |
| C22×#1201 | 4 |
| C2×#5421 | 5 |