Finite Group Databasebeta

← AGL(1,𝔽5)×C97⋊C9 #31775482

Subgroups — AGL(1,𝔽5)×C97⋊C9 #31775482

Order 17460.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C97⋊C9C211yesmaximal, characteristic
2C3×AGL(1,𝔽5)×C97C311yesmaximal, characteristic
3C5×C97⋊C9C411yescharacteristic, complemented, Hall
4C4×C97⋊C9—51nomaximal, Hall
5C3×D5×C97C2×C311yescharacteristic
6AGL(1,𝔽5)×C97C911yescharacteristic, complemented, Hall
7C2×C97⋊C9—51no—
8C3×C5×C97C3×C411yescharacteristic
9C3×C4×C97—51no—
10D5×C97C2×C911yescharacteristic
11C97⋊C9AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
12C2×C3×C97—51no—
13C5×C97C4×C911yescharacteristic, complemented, Hall
14C4×C97—51noHall
15C3×C97C3×AGL(1,𝔽5)11yescharacteristic
16C2×C97—51no—
17C9×AGL(1,𝔽5)—971nomaximal, Hall
18C97C9×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
19C9×D5—971no—
20C3×AGL(1,𝔽5)C97⋊C311yescharacteristic
21C5×C9—971noHall
22C4×C9—4851noHall
23C3×D5C2×C97⋊C311yescharacteristic
24AGL(1,𝔽5)C97⋊C911yescharacteristic, direct product factor, Hall
25C2×C9—4851no—
26C3×C5C4×C97⋊C311yescharacteristic
27C3×C4—51no—
28D5C2×C97⋊C911yescharacteristic
29C9—971noSylow
30C2×C3—51no—
31C5C4×C97⋊C911yescharacteristic, complemented, Sylow
32C4—51noSylow
33C3AGL(1,𝔽5)×C97⋊C311yescharacteristic
34C2—51no—
subgroupG/H
center, Frattini, hypercenterC3AGL(1,𝔽5)×C97⋊C3
commutator, hypocenterC5×C97C4×C9
Fitting, socleC3×C5×C97C3×C4
prime radical, cosocleC3×D5×C97C2×C3
LCSG ▷ C5×C97
UCSC1 ◁ C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C5×C97⋊C9C4semidirect
6. AGL(1,𝔽5)×C97C9semidirect
11. C97⋊C9AGL(1,𝔽5)direct (N × H)
13. C5×C97C4×C9semidirect
18. C97C9×AGL(1,𝔽5)semidirect
24. AGL(1,𝔽5)C97⋊C9direct (N × H)
31. C5C4×C97⋊C9semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D5×C97⋊C92
C3×AGL(1,𝔽5)×C973
C4×C97⋊C95
C9×AGL(1,𝔽5)97