Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
176 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11758757 |
| commutator, Fitting, cosocle | C4×C53 | C22 |
| Frattini, hypercenter | C4 | #92566 |
| socle | C2×C53 | D4 |
| prime radical | C5×C4⋊(C5⋊D5) | C2 |
| hypocenter | C53 | SD16 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#6045 | C2 | semidirect |
| 3. C5×#6029 | C2 | semidirect |
| 13. #6045 | D5 | semidirect |
| 20. #6029 | D5 | semidirect |
| 24. C53 | SD16 | semidirect |
| 70. C52 | #677 | semidirect |
| 71. C52 | #687 | semidirect |
| 72. C52 | #688 | semidirect |
| 107. C5 | #87772 | semidirect |
| 108. C5 | #87773 | semidirect |
| 109. C5 | #87774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C4⋊(C5⋊D5) | 2 |
| C5×#6045 | 2 |
| C5×#6029 | 2 |
| #87774 | 5 |
| #87773 | 5 |
| #87772 | 5 |