Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
508 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| prime radical | #11717034 | C2 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #542 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717192 | C2 | semidirect |
| 2. C5×#4021 | C2 | semidirect |
| 3. C5×#4015 | C2 | semidirect |
| 5. #11717025 | C2 | semidirect |
| 6. #11717017 | C2 | semidirect |
| 7. #11717011 | C2 | semidirect |
| 8. #11717006 | C2 | semidirect |
| 9. #11716990 | C2 | semidirect |
| 10. #11716976 | C2 | semidirect |
| 11. #11716961 | C2 | semidirect |
| 72. #4021 | D5 | semidirect |
| 76. #4015 | D5 | semidirect |
| 205. C52 | #542 | semidirect |
| 303. C5 | #66016 | semidirect |
| 304. C5 | #66067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717192 | 2 |
| C5×#4021 | 2 |
| C5×#4015 | 2 |
| #11717034 | 2 |
| #11717025 | 2 |
| #11717017 | 2 |
| #11717011 | 2 |
| #11717006 | 2 |
| #11716990 | 2 |
| #11716976 | 2 |
| #11716961 | 2 |
| #66067 | 5 |
| #66016 | 5 |