Finite Group Databasebeta

← Dic3×(C181⋊C3)⋊C5 #45656405

Subgroups — Dic3×(C181⋊C3)⋊C5 #45656405

Order 32580.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C181⋊C3)⋊C5C211yesmaximal, characteristic
2Dic3×C181⋊C5C311yesmaximal, characteristic, complemented
3C4×(C181⋊C3)⋊C5—31nomaximal
4C3×(C181⋊C3)⋊C5C411yescharacteristic, complemented, Hall
5Dic3×C181⋊C3C511yesmaximal, characteristic, complemented, Hall
6C2×(C181⋊C3)⋊C5—21no—
7C2×(C181⋊C3)⋊C5D311yescharacteristic
8C2×C3×C181⋊C5C2×C311yescharacteristic
9C4×C181⋊C5—31noHall
10C2×C3×C181⋊C3C2×C511yescharacteristic
11C3×C181⋊C5C3×C411yescharacteristic, complemented
12(C181⋊C3)⋊C5—21no—
13(C181⋊C3)⋊C5Dic311yescharacteristic, direct product factor
14Dic3×C181C3×C511yescharacteristic, complemented
15C4×C181⋊C3—31no—
16C2×C181⋊C5C3×D311yescharacteristic
17C3×C181⋊C3C4×C511yescharacteristic, complemented, Hall
18C2×C3×C181C2×C3×C511yescharacteristic
19C2×C181⋊C3—21no—
20C2×C181⋊C3C5×D311yescharacteristic
21C181⋊C5C3×Dic311yescharacteristic, complemented, Hall
22C4×C181—31noHall
23C3×C181C3×C4×C511yescharacteristic, complemented
24C181⋊C3—21no—
25C181⋊C3C5×Dic311yescharacteristic, complemented
26C2×C181C3×C5×D311yescharacteristic
27C181C3×C5×Dic311yescharacteristic, complemented, Sylow
28C3×C5×Dic3—1811nomaximal, Hall
29C2×C32×C5—1811no—
30C3×C4×C5—5431no—
31C5×Dic3—1811no—
32C32×C5—1811noHall
33C3×Dic3—1811noHall
34C2×C3×C5—3621no—
35C2×C3×C5—1811no—
36C2×C3×C5—1811no—
37C4×C5—5431noHall
38C2×C32—1811no—
39C3×C5—3621no—
40C3×C5—1811no—
41C3×C5—1811no—
42C3×C4—5431no—
43Dic3(C181⋊C3)⋊C511yescharacteristic, direct product factor
44C2×C5—1811no—
45C32—1811noSylow
46C2×C3—3621no—
47C2×C3—1811no—
48C2×C3C2×(C181⋊C3)⋊C511yescharacteristic
49C5—1811noSylow
50C4—31noSylow
51C3—3621no—
52C3—1811no—
53C3C4×(C181⋊C3)⋊C511yescharacteristic, complemented
54C2D3×(C181⋊C3)⋊C511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×(C181⋊C3)⋊C5
commutator, hypocenterC3×C181C3×C4×C5
Fitting, socle, cosocleC2×C3×C181C2×C3×C5
prime radicalC2×C3×(C181⋊C3)⋊C5C2
LCSG ▷ C3×C181
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic3×C181⋊C5C3semidirect
4. C3×(C181⋊C3)⋊C5C4semidirect
5. Dic3×C181⋊C3C5semidirect
11. C3×C181⋊C5C3×C4semidirect
13. (C181⋊C3)⋊C5Dic3direct (N × H)
14. Dic3×C181C3×C5semidirect
17. C3×C181⋊C3C4×C5semidirect
21. C181⋊C5C3×Dic3semidirect
23. C3×C181C3×C4×C5semidirect
25. C181⋊C3C5×Dic3semidirect
27. C181C3×C5×Dic3semidirect
43. Dic3(C181⋊C3)⋊C5direct (N × H)
53. C3C4×(C181⋊C3)⋊C5semidirect

Maximal subgroups

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

subgroupindex
C2×C3×(C181⋊C3)⋊C52
Dic3×C181⋊C53
C4×(C181⋊C3)⋊C53
Dic3×C181⋊C35
C3×C5×Dic3181