Finite Group Databasebeta

← C2×C3⋊#19149853 #45686352

Subgroups — C2×C3⋊#19149853 #45686352

Order 33300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C37×C52⋊C3C211yesmaximal, characteristic, complemented
2C3⋊#19149853C212yesmaximal, direct product factor
3C2×C3⋊(C5⋊D185)C311yesmaximal, characteristic, complemented
4C2×#19149853—31nomaximal
5C3×C37×C52⋊C3C2211yescharacteristic, complemented, Hall
6C3⋊(C5⋊D185)C2×C312yescomplemented
7C2×C37×C52⋊C3—21no—
8C2×C37×C52⋊C3D311yescharacteristic, complemented
9#19149853—32no—
10C2×C3×C52×C37C2×C311yescharacteristic, complemented
11C2×C5⋊D185—31noHall
12C37×C52⋊C3—21no—
13C37×C52⋊C3C2×D311yescharacteristic, complemented
14C3×C52×C37C22×C311yescharacteristic, complemented
15C2×D555—152no—
16C2×C52×C37C3×D311yescharacteristic, complemented
17C5⋊D185—32no—
18C2×C3×D111—251nomaximal, Hall
19C2×C3×C5×C37—32no—
20D555—154no—
21C52×C37C2×C3×D311yescharacteristic, complemented, Hall
22C2×C3⋊((C5⋊D5)⋊C3)—371nomaximal, Hall
23C2×D185—452no—
24C2×C32×C37—251no—
25C3×D111—252no—
26C3×C5×C37—32no—
27C2×C3×C52⋊C3D3711yescharacteristic, complemented
28C3⋊((C5⋊D5)⋊C3)—372no—
29C2×D111—251no—
30C2×C3×D37—751no—
31C2×C5×C37—32no—
32D185—454no—
33C32×C37—251noHall
34C2×C3⋊(C5⋊D5)—371no—
35C2×(C5⋊D5)⋊C3—1111no—
36C3×C52⋊C3C2×D3711yescharacteristic, complemented, Hall
37C2×C3×C37—251no—
38C2×C3×C37—501no—
39C2×C3×C37(C5⋊D5)⋊C311yescharacteristic, complemented
40D111—252no—
41C3×D37—752no—
42C5×C37—32no—
43C2×C3×C52C3×D3711yescharacteristic, complemented
44C3⋊(C5⋊D5)—372no—
45C2×C52⋊C3—21no—
46C2×C52⋊C3D11111yescharacteristic, complemented
47(C5⋊D5)⋊C3—1112no—
48C2×D37—751noHall
49C3×C37—251no—
50C3×C37—501no—
51C3×C37C2×(C5⋊D5)⋊C311yescharacteristic, complemented
52C2×C5⋊D5—1111noHall
53C3×C52C2×C3×D3711yescharacteristic, complemented
54C52⋊C3—21no—
55C52⋊C3C2×D11111yescharacteristic, complemented
56C2×C37C3⋊((C5⋊D5)⋊C3)11yescharacteristic, complemented
57D37—752no—
58C2×D15—5552no—
59C2×C52C3×D11111yescharacteristic, complemented
60C5⋊D5—1112no—
61C37C2×C3⋊((C5⋊D5)⋊C3)11yescharacteristic, complemented, Sylow
62C2×C3×D3—9251noHall
63C2×C3×C5—32no—
64D15—5554no—
65C52C2×C3×D11111yescharacteristic, complemented, Sylow
66C2×D5—16652no—
67C2×C32—251no—
68C3×D3—9252no—
69C3×C5—32no—
70C22×C3—27751no—
71C2×D3—9251no—
72C2×C5—32no—
73D5—16654no—
74C32—251noSylow
75C2×C3—251no—
76C2×C3—501no—
77C2×C3—27752no—
78C2×C3#1914985311yescharacteristic, complemented
79D3—9252no—
80C5—32no—
81C22—27751noSylow
82C3—251no—
83C3—501no—
84C3C2×#1914985311yescharacteristic, complemented
85C2—27752no—
86C2C3⋊#1914985311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#19149853
commutator, cosocle, hypocenterC3×C52×C37C22×C3
FrattiniC1G
Fitting, socleC2×C3×C52×C37C2×C3
LCSG ▷ C3×C52×C37
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C37×C52⋊C3C2semidirect
2. C3⋊#19149853C2direct (N × H)
3. C2×C3⋊(C5⋊D185)C3semidirect
5. C3×C37×C52⋊C3C22semidirect
6. C3⋊(C5⋊D185)C2×C3semidirect
8. C2×C37×C52⋊C3D3semidirect
10. C2×C3×C52×C37C2×C3semidirect
13. C37×C52⋊C3C2×D3semidirect
14. C3×C52×C37C22×C3semidirect
16. C2×C52×C37C3×D3semidirect
21. C52×C37C2×C3×D3semidirect
27. C2×C3×C52⋊C3D37semidirect
36. C3×C52⋊C3C2×D37semidirect
39. C2×C3×C37(C5⋊D5)⋊C3semidirect
43. C2×C3×C52C3×D37semidirect
46. C2×C52⋊C3D111semidirect
51. C3×C37C2×(C5⋊D5)⋊C3semidirect
53. C3×C52C2×C3×D37semidirect
55. C52⋊C3C2×D111semidirect
56. C2×C37C3⋊((C5⋊D5)⋊C3)semidirect
59. C2×C52C3×D111semidirect
61. C37C2×C3⋊((C5⋊D5)⋊C3)semidirect
65. C52C2×C3×D111semidirect
78. C2×C3#19149853semidirect
84. C3C2×#19149853semidirect
86. C2C3⋊#19149853direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C37×C52⋊C32
C3⋊#191498532
C2×C3⋊(C5⋊D185)3
C2×#191498533
C2×C3×D11125
C2×C3⋊((C5⋊D5)⋊C3)37