Finite Group DatabasebetaFinite Group DatabasebetaOrder 38125.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21439346 | C5 | 1 | 4 | yes | maximal, complemented |
| 2 | C52⋊(C61⋊C5) | C5 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×C25×C61 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C52×C61 | C52 | 1 | 1 | yes | characteristic |
| 5 | C5×C61⋊C5 | — | 5 | 1 | no | — |
| 6 | C25×C61 | — | 5 | 1 | no | — |
| 7 | C61⋊C25 | — | 5 | 4 | no | — |
| 8 | #10597832 | — | 61 | 1 | no | maximal, Sylow |
| 9 | C5×C61 | — | 5 | 1 | no | — |
| 10 | C5×C61 | H(3,𝔽5) | 1 | 1 | yes | characteristic |
| 11 | C61⋊C5 | — | 25 | 1 | no | — |
| 12 | 5−1+2 | — | 61 | 4 | no | — |
| 13 | H(3,𝔽5) | — | 61 | 1 | no | — |
| 14 | C5×C25 | C61⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 15 | C61 | #10597832 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C52 | — | 305 | 1 | no | — |
| 17 | C52 | C5×C61⋊C5 | 1 | 1 | yes | characteristic |
| 18 | C25 | — | 5 | 1 | no | — |
| 19 | C25 | — | 305 | 4 | no | — |
| 20 | C5 | — | 5 | 1 | no | — |
| 21 | C5 | — | 1525 | 1 | no | — |
| 22 | C5 | C52⋊(C61⋊C5) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21439346 | C5 | semidirect |
| 3. C5×C25×C61 | C5 | semidirect |
| 14. C5×C25 | C61⋊C5 | semidirect |
| 15. C61 | #10597832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439346 | 5 |
| C52⋊(C61⋊C5) | 5 |
| C5×C25×C61 | 5 |
| #10597832 | 61 |