Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
207 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 83 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×#1042 |
| commutator, socle, prime radical | C22×C52 | C22×C4 |
| Fitting | C2×C52×Q8 | C4 |
| cosocle | C2×C5×Dic5 | C23 |
| hypercenter | C2×Q8 | #1042 |
| hypocenter | C52 | #446 |
| 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 |
|---|---|---|
| 24. #6032 | Q8 | semidirect |
| 89. C52 | #446 | semidirect |
| 134. C5 | #65313 | semidirect |
| 135. C5 | #65788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| #11716847 | 2 |
| #11716845 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #65788 | 5 |
| #65313 | 5 |