Finite Group DatabasebetaFinite Group DatabasebetaOrder 10700.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×D5×C107 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C52×C107 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | C107⋊AGL(1,𝔽5) | — | 5 | 1 | no | maximal |
| 4 | Dic535 | — | 5 | 1 | no | maximal |
| 5 | C2×C5×C107 | — | 5 | 1 | no | — |
| 6 | D5×C107 | D5 | 1 | 1 | yes | characteristic |
| 7 | C5×C107 | — | 4 | 1 | no | — |
| 8 | C5×C107 | Dic5 | 1 | 1 | yes | characteristic, complemented |
| 9 | C5×C107 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 10 | Dic107 | — | 25 | 1 | no | Hall |
| 11 | C2×C107 | — | 5 | 1 | no | — |
| 12 | C107 | #1042 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | #1042 | — | 107 | 1 | no | maximal, Hall |
| 14 | C5×D5 | D107 | 1 | 1 | yes | characteristic |
| 15 | C52 | Dic107 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | AGL(1,𝔽5) | — | 535 | 1 | no | — |
| 17 | Dic5 | — | 535 | 1 | no | — |
| 18 | C2×C5 | — | 5 | 1 | no | — |
| 19 | D5 | D535 | 1 | 1 | yes | characteristic |
| 20 | C5 | — | 4 | 1 | no | — |
| 21 | C5 | Dic535 | 1 | 1 | yes | characteristic, complemented |
| 22 | C5 | C107⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 23 | C4 | — | 2675 | 1 | no | Sylow |
| 24 | C2 | — | 5 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C107 | C4 |
| prime radical, cosocle | C5×D5×C107 | C2 |
| LCS | G ▷ C52×C107 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C52×C107 | C4 | semidirect |
| 8. C5×C107 | Dic5 | semidirect |
| 9. C5×C107 | AGL(1,𝔽5) | semidirect |
| 12. C107 | #1042 | semidirect |
| 15. C52 | Dic107 | semidirect |
| 21. C5 | Dic535 | semidirect |
| 22. C5 | C107⋊AGL(1,𝔽5) | semidirect |