Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
494 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 174 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, prime radical, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | Q82 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C52×Q8 | Q8 | semidirect |
| 23. #6039 | Q8 | direct (N × H) |
| 58. C5×Q8 | Dic10 | semidirect |
| 76. C52 | Q82 | semidirect |
| 106. Q8 | #6039 | direct (N × H) |
| 113. C5 | Q8×Dic10 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1039 | 2 |
| C5×Q8×Dic5 | 2 |
| #11717037 | 2 |
| #11717036 | 2 |
| C4×#6039 | 2 |
| Q8×Dic10 | 5 |