Finite Group DatabasebetaFinite Group DatabasebetaOrder 15600.
105 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | PSL(2,𝔽25) | C2 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 2 | C2×#1043⋊C3 | — | 26 | 1 | no | maximal |
| 3 | C2×(C5⋊D5)⋊C3 | — | 26 | 1 | no | — |
| 4 | #1043⋊C3 | — | 26 | 1 | no | — |
| 5 | #1043⋊C3 | — | 26 | 1 | no | — |
| 6 | C2×S5 | — | 65 | 2 | no | maximal |
| 7 | C2×#1043 | — | 26 | 1 | no | — |
| 8 | C2×C52⋊C3 | — | 26 | 1 | no | — |
| 9 | (C5⋊D5)⋊C3 | — | 26 | 1 | no | — |
| 10 | (C5⋊D5)⋊C3 | — | 26 | 1 | no | — |
| 11 | C2×A5 | — | 65 | 2 | no | — |
| 12 | S5 | — | 65 | 2 | no | — |
| 13 | S5 | — | 65 | 2 | no | — |
| 14 | C2×C5⋊D5 | — | 26 | 1 | no | — |
| 15 | #1043 | — | 26 | 1 | no | — |
| 16 | #1043 | — | 26 | 1 | no | — |
| 17 | C52⋊C3 | — | 26 | 1 | no | Hall |
| 18 | A5 | — | 65 | 2 | no | — |
| 19 | C2×D13 | — | 300 | 1 | no | maximal |
| 20 | C2×C52 | — | 26 | 1 | no | — |
| 21 | C5⋊D5 | — | 26 | 1 | no | — |
| 22 | C5⋊D5 | — | 26 | 1 | no | — |
| 23 | C2×S4 | — | 325 | 2 | no | Hall |
| 24 | C2×D12 | — | 325 | 1 | no | maximal, Hall |
| 25 | C2×AGL(1,𝔽5) | — | 390 | 2 | no | — |
| 26 | C2×C13 | — | 300 | 1 | no | — |
| 27 | D13 | — | 300 | 1 | no | — |
| 28 | D13 | — | 300 | 1 | no | — |
| 29 | C52 | — | 26 | 1 | no | Sylow |
| 30 | C22×D3 | — | 325 | 2 | no | — |
| 31 | C2×A4 | — | 325 | 2 | no | — |
| 32 | S4 | — | 325 | 2 | no | — |
| 33 | S4 | — | 325 | 2 | no | — |
| 34 | C2×C3×C4 | — | 325 | 1 | no | — |
| 35 | D12 | — | 325 | 1 | no | — |
| 36 | D12 | — | 325 | 2 | no | — |
| 37 | D12 | — | 325 | 1 | no | — |
| 38 | C2×D5 | — | 390 | 2 | no | — |
| 39 | AGL(1,𝔽5) | — | 390 | 2 | no | — |
| 40 | AGL(1,𝔽5) | — | 390 | 2 | no | — |
| 41 | C2×D4 | — | 975 | 1 | no | Sylow |
| 42 | C13 | — | 300 | 1 | no | Sylow |
| 43 | C22×C3 | — | 325 | 1 | no | — |
| 44 | C2×D3 | — | 325 | 2 | no | — |
| 45 | C2×D3 | — | 325 | 2 | no | — |
| 46 | C2×D3 | — | 650 | 2 | no | — |
| 47 | C2×D3 | — | 650 | 2 | no | — |
| 48 | A4 | — | 325 | 2 | no | — |
| 49 | C3×C4 | — | 325 | 1 | no | — |
| 50 | C3×C4 | — | 325 | 1 | no | — |
| 51 | C2×C5 | — | 78 | 2 | no | — |
| 52 | D5 | — | 390 | 2 | no | — |
| 53 | D5 | — | 390 | 2 | no | — |
| 54 | C23 | — | 325 | 2 | no | — |
| 55 | D4 | — | 975 | 1 | no | — |
| 56 | D4 | — | 975 | 2 | no | — |
| 57 | D4 | — | 975 | 1 | no | — |
| 58 | C2×C4 | — | 325 | 1 | no | — |
| 59 | C2×C3 | — | 325 | 1 | no | — |
| 60 | C2×C3 | — | 325 | 1 | no | — |
| 61 | C2×C3 | — | 325 | 1 | no | — |
| 62 | D3 | — | 650 | 2 | no | — |
| 63 | D3 | — | 650 | 2 | no | — |
| 64 | C5 | — | 78 | 2 | no | — |
| 65 | C22 | — | 325 | 2 | no | — |
| 66 | C22 | — | 325 | 1 | no | — |
| 67 | C22 | — | 975 | 2 | no | — |
| 68 | C4 | — | 325 | 1 | no | — |
| 69 | C4 | — | 325 | 1 | no | — |
| 70 | C3 | — | 325 | 1 | no | Sylow |
| 71 | C2 | — | 325 | 1 | no | — |
| 72 | C2 | — | 325 | 1 | no | — |
| 73 | C2 | PSL(2,𝔽25) | 1 | 1 | yes | maximal normal, characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | PSL(2,𝔽25) |
| commutator, hypocenter | PSL(2,𝔽25) | C2 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽25) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. PSL(2,𝔽25) | C2 | direct (N × H) |
| 73. C2 | PSL(2,𝔽25) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| PSL(2,𝔽25) | 2 |
| C2×#1043⋊C3 | 26 |
| C2×S5 | 65 |
| C2×D13 | 300 |
| C2×D12 | 325 |