Finite Group DatabasebetaFinite Group DatabasebetaOrder 19375.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #16838874 | C5 | 1 | 3 | yes | maximal, complemented |
| 2 | C52⋊ΓL(1,𝔽32) | C5 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×C31⋊C25 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C31×5−1+2 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C52×C31 | C52 | 1 | 1 | yes | characteristic |
| 6 | C5×ΓL(1,𝔽32) | — | 5 | 1 | no | — |
| 7 | C25×C31 | — | 5 | 1 | no | — |
| 8 | C31⋊C25 | — | 5 | 1 | no | — |
| 9 | C31⋊C25 | — | 5 | 3 | no | — |
| 10 | #10597832 | — | 31 | 1 | no | maximal, Sylow |
| 11 | C5×C31 | — | 5 | 1 | no | — |
| 12 | C5×C31 | H(3,𝔽5) | 1 | 1 | yes | characteristic |
| 13 | ΓL(1,𝔽32) | — | 25 | 1 | no | — |
| 14 | 5−1+2 | — | 31 | 3 | no | — |
| 15 | 5−1+2 | ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented |
| 16 | H(3,𝔽5) | — | 31 | 1 | no | — |
| 17 | C5×C25 | — | 31 | 1 | no | — |
| 18 | C31 | #10597832 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | C52 | — | 155 | 1 | no | — |
| 20 | C52 | C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic |
| 21 | C25 | — | 5 | 1 | no | — |
| 22 | C25 | — | 155 | 1 | no | — |
| 23 | C25 | — | 155 | 3 | no | — |
| 24 | C5 | — | 5 | 1 | no | — |
| 25 | C5 | — | 775 | 1 | no | — |
| 26 | C5 | C52⋊ΓL(1,𝔽32) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838874 | C5 | semidirect |
| 3. C5×C31⋊C25 | C5 | semidirect |
| 4. C31×5−1+2 | C5 | semidirect |
| 15. 5−1+2 | ΓL(1,𝔽32) | semidirect |
| 18. C31 | #10597832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #16838874 | 5 |
| C52⋊ΓL(1,𝔽32) | 5 |
| C5×C31⋊C25 | 5 |
| C31×5−1+2 | 5 |
| #10597832 | 31 |