Finite Group DatabasebetaFinite Group DatabasebetaOrder 27300.
192 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×#10587723 |
| commutator, cosocle, hypocenter | C5×C7×C13 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C13 | C22×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×#63271 | 2 |
| C5×C5⋊#10587723 | 2 |
| C52×#10587723 | 2 |
| C5×D5×D91 | 3 |
| C2×C5×#10587723 | 5 |
| D5×#10587723 | 5 |
| C5×D5×D13⋊C3 | 7 |
| C5×D5×AGL(1,𝔽7) | 13 |