Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
236 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 44 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. C5×#5386 | C2 | semidirect |
| 3. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 9. #73021 | C5 | direct (N × H) |
| 13. C5×C8×Q8 | D3 | semidirect |
| 24. #5386 | C2×C5 | semidirect |
| 25. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 47. C5×SL(2,𝔽3) | SD16 | semidirect |
| 73. C8×Q8 | C5×D3 | semidirect |
| 94. C5×Q8 | #204 | semidirect |
| 107. C5×C8 | GL(2,𝔽3) | semidirect |
| 132. SL(2,𝔽3) | C5×SD16 | semidirect |
| 177. Q8 | C5×#204 | semidirect |
| 190. C8 | C5×GL(2,𝔽3) | semidirect |
| 195. C5 | #73021 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#5386 | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×#1666 | 3 |
| C2×C5×#204 | 4 |
| #73021 | 5 |