Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
120 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11758789 |
| commutator, Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×C5×C5⋊D5 | C4 |
| cosocle | C5×#1039 | C22 |
| hypocenter | C53 | M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11758741 | C2 | semidirect |
| 3. C5×#6034 | C2 | semidirect |
| 15. #6034 | D5 | semidirect |
| 22. C53 | M16 | semidirect |
| 63. C52 | #676 | semidirect |
| 64. C52 | #700 | semidirect |
| 65. C52 | #704 | semidirect |
| 97. C5 | #87828 | semidirect |
| 98. C5 | #87829 | semidirect |
| 99. C5 | #87834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758756 | 2 |
| #11758741 | 2 |
| C5×#6034 | 2 |
| #87834 | 5 |
| #87829 | 5 |
| #87828 | 5 |