Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
896 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 152 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 | C24×C52 | C22 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #525 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#1039 | C2 | semidirect |
| 2. C2×#87880 | C2 | semidirect |
| 3. C5×#4099 | C2 | semidirect |
| 4. #11717100 | C2 | semidirect |
| 5. #11717098 | C2 | semidirect |
| 6. #11717091 | C2 | semidirect |
| 7. #11717080 | C2 | semidirect |
| 8. #11717075 | C2 | semidirect |
| 17. C2×#6039 | C22 | semidirect |
| 18. C2×#6037 | C22 | semidirect |
| 20. C2×D5×Dic5 | C22 | semidirect |
| 23. #87781 | C22 | semidirect |
| 24. #87780 | C22 | semidirect |
| 25. #87778 | C22 | semidirect |
| 26. Dic52 | C22 | semidirect |
| 36. C2×#1039 | D4 | semidirect |
| 51. #4099 | D5 | semidirect |
| 64. C22×C52 | #41 | semidirect |
| 154. C52 | #525 | semidirect |
| 169. C22×C5 | #711 | semidirect |
| 231. C5 | #65920 | semidirect |
| 238. C22 | #87880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C2×#87880 | 2 |
| C5×#4099 | 2 |
| #11717100 | 2 |
| #11717098 | 2 |
| #11717091 | 2 |
| #11717080 | 2 |
| #11717075 | 2 |
| #65920 | 5 |