Finite Group Databasebeta

← C2×C3⋊(D31⋊(C52⋊C3)) #42124854

Subgroups — C2×C3⋊(D31⋊(C52⋊C3)) #42124854

Order 27900.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C52⋊(C31⋊C3)C211yesmaximal, characteristic, complemented
2C3⋊(D31⋊(C52⋊C3))C212yesmaximal, direct product factor
3C2×C52×D93C311yesmaximal, characteristic, complemented
4C2×D31⋊(C52⋊C3)—31nomaximal
5C3×C52⋊(C31⋊C3)C2211yescharacteristic, complemented, Hall
6C52×D93C2×C312yescomplemented
7C2×C52⋊(C31⋊C3)—21no—
8C2×C52⋊(C31⋊C3)D311yescharacteristic, complemented
9D31⋊(C52⋊C3)—32no—
10C2×C3×C52×C31C2×C311yescharacteristic, complemented
11C2×C52×D31—31noHall
12C52⋊(C31⋊C3)—21no—
13C52⋊(C31⋊C3)C2×D311yescharacteristic, complemented
14C3×C52×C31C22×C311yescharacteristic, complemented
15C2×C5×D93—32no—
16C2×C52×C31C3×D311yescharacteristic, complemented
17C52×D31—32no—
18C2×C3⋊(D31⋊C3)—251nomaximal, Hall
19C2×C3×C5×C31—32no—
20C5×D93—34no—
21C2×D3×C52⋊C3—311nomaximal, Hall
22C52×C31C2×C3×D311yescharacteristic, complemented, Hall
23C2×C5×D31—92no—
24C2×C3×C31⋊C3—251no—
25C3⋊(D31⋊C3)—252no—
26C3×C5×C31—32no—
27C2×C3×C52⋊C3—311no—
28D3×C52⋊C3—312no—
29C2×D93C52⋊C311yescharacteristic, complemented
30C2×D31⋊C3—751no—
31C2×C5×C31—32no—
32C5×D31—94no—
33C2×C52×D3—311no—
34C22×C52⋊C3—931no—
35C3×C31⋊C3—251noHall
36C3×C52⋊C3—311noHall
37C2×C3×C31C2×C52⋊C311yescharacteristic, complemented
38D93C2×C52⋊C312yescomplemented
39C2×C31⋊C3—251no—
40C2×C31⋊C3—501no—
41D31⋊C3—752no—
42C5×C31—32no—
43C2×C3×C52D31⋊C311yescharacteristic, complemented
44C52×D3—312no—
45C2×C52⋊C3—311no—
46C2×C52⋊C3—621no—
47C2×C52⋊C3—932no—
48C2×D31—31noHall
49C22×C52—931noHall
50C3×C31C22×C52⋊C311yescharacteristic, complemented
51C31⋊C3—251no—
52C31⋊C3—501no—
53C3×C52C2×D31⋊C311yescharacteristic, complemented
54C52⋊C3—311no—
55C52⋊C3—621no—
56C2×C31D3×C52⋊C311yescharacteristic, complemented
57D31—32no—
58C2×C5×D3—932no—
59C2×C52—932no—
60C2×C52C3⋊(D31⋊C3)11yescharacteristic, complemented
61C2×C3×D3—7751noHall
62C31C2×D3×C52⋊C311yescharacteristic, complemented, Sylow
63C2×C3×C5—32no—
64C5×D3—934no—
65C52C2×C3⋊(D31⋊C3)11yescharacteristic, complemented, Sylow
66C22×C5—2792no—
67C2×C32—7751no—
68C3×D3—7752no—
69C3×C5—32no—
70C22×C3—23251no—
71C2×D3—311no—
72C2×C5—32no—
73C2×C5—2794no—
74C32—7751noSylow
75C2×C3—7751no—
76C2×C3—15501no—
77C2×C3—23252no—
78C2×C3D31⋊(C52⋊C3)11yescharacteristic, complemented
79D3—312no—
80C5—32no—
81C22—931noSylow
82C3—7751no—
83C3—15501no—
84C3C2×D31⋊(C52⋊C3)11yescharacteristic, complemented
85C2—932no—
86C2C3⋊(D31⋊(C52⋊C3))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(D31⋊(C52⋊C3))
commutator, cosocle, hypocenterC3×C52×C31C22×C3
FrattiniC1G
Fitting, socleC2×C3×C52×C31C2×C3
LCSG ▷ C3×C52×C31
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C52⋊(C31⋊C3)C2semidirect
2. C3⋊(D31⋊(C52⋊C3))C2direct (N × H)
3. C2×C52×D93C3semidirect
5. C3×C52⋊(C31⋊C3)C22semidirect
6. C52×D93C2×C3semidirect
8. C2×C52⋊(C31⋊C3)D3semidirect
10. C2×C3×C52×C31C2×C3semidirect
13. C52⋊(C31⋊C3)C2×D3semidirect
14. C3×C52×C31C22×C3semidirect
16. C2×C52×C31C3×D3semidirect
22. C52×C31C2×C3×D3semidirect
29. C2×D93C52⋊C3semidirect
37. C2×C3×C31C2×C52⋊C3semidirect
38. D93C2×C52⋊C3semidirect
43. C2×C3×C52D31⋊C3semidirect
50. C3×C31C22×C52⋊C3semidirect
53. C3×C52C2×D31⋊C3semidirect
56. C2×C31D3×C52⋊C3semidirect
60. C2×C52C3⋊(D31⋊C3)semidirect
62. C31C2×D3×C52⋊C3semidirect
65. C52C2×C3⋊(D31⋊C3)semidirect
78. C2×C3D31⋊(C52⋊C3)semidirect
84. C3C2×D31⋊(C52⋊C3)semidirect
86. C2C3⋊(D31⋊(C52⋊C3))direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C52⋊(C31⋊C3)2
C3⋊(D31⋊(C52⋊C3))2
C2×C52×D933
C2×D31⋊(C52⋊C3)3
C2×C3⋊(D31⋊C3)25
C2×D3×C52⋊C331