Finite Group DatabasebetaFinite Group DatabasebetaOrder 17170.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C17×C101⋊C5 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D1717 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C17×C101 | C2×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D101⋊C5 | — | 17 | 1 | no | maximal, Hall |
| 5 | C101⋊C5 | D17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D101 | — | 17 | 1 | no | Hall |
| 7 | C5×D17 | — | 101 | 1 | no | maximal, Hall |
| 8 | C101 | C5×D17 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C5×C17 | — | 101 | 1 | no | Hall |
| 10 | D17 | — | 505 | 1 | no | Hall |
| 11 | C17 | D101⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C5 | — | 1717 | 1 | no | Hall |
| 13 | C5 | — | 101 | 1 | no | Sylow |
| 14 | C2 | — | 8585 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C101 | C2×C5 |
| LCS | G ▷ C17×C101 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C101⋊C5 | C2 | semidirect |
| 2. D1717 | C5 | semidirect |
| 3. C17×C101 | C2×C5 | semidirect |
| 5. C101⋊C5 | D17 | semidirect |
| 8. C101 | C5×D17 | semidirect |
| 11. C17 | D101⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C101⋊C5 | 2 |
| D1717 | 5 |
| D101⋊C5 | 17 |
| C5×D17 | 101 |