Finite Group Databasebeta

← D3×C37×C3⋊(C5⋊D5) #45686459

Subgroups — D3×C37×C3⋊(C5⋊D5) #45686459

Order 33300.

352 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52×D3×C37C211yesmaximal, characteristic, complemented
2C3×C37×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C37×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4C2×C37×C3⋊(C5⋊D5)—31nomaximal
5D3×C37×C5⋊D5—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7D3×D15×C37—56nomaximal
8C37×C3⋊(C5⋊D5)—31no—
9C37×C3⋊(C5⋊D5)—31no—
10C37×C3⋊(C5⋊D5)—61no—
11C37×C3⋊(C5⋊D5)D311yescharacteristic, direct product factor
12C52×D3×C37D311yescharacteristic, complemented
13C3×C37×C5⋊D5—31no—
14C2×C3×C52×C37—31no—
15C2×C37×C5⋊D5—91noHall
16C37×C3⋊D15—56no—
17C3×D15×C37—56no—
18C3×C5×D3×C37D516yescomplemented
19C3×C52×C37—21no—
20C3×C52×C37C2×D311yescharacteristic, complemented
21C3×C52×C37C2×D311yescharacteristic, complemented
22C2×D15×C37—156no—
23D3×D5×C37—156no—
24C2×C52×C37—31no—
25C37×C5⋊D5—31no—
26C37×C5⋊D5—91no—
27C32×C5×C37C2×D516yescomplemented
28D32×C37—251noHall
29C2×C3×C5×C37—36no—
30D15×C37—56no—
31D15×C37—156no—
32D15×C37—156no—
33D15×C37—306no—
34C5×D3×C37D1516yescomplemented
35C3×D5×C37—156no—
36C52×C37D3211yescharacteristic, complemented, Hall
37D3×C3⋊(C5⋊D5)C3711yesmaximal, characteristic, direct product factor, Hall
38C2×D5×C37—456no—
39C3⋊D3×C37—251no—
40C3×D3×C37—251no—
41C3×D3×C37C5⋊D511yescharacteristic, complemented
42C3×C5×C37—26no—
43C3×C5×C37D3×D516yescomplemented
44C3×C5×C37C2×D1516yescomplemented
45C3⋊(C3⋊(C5⋊D5))C2×C3711yescharacteristic, complemented
46C3×C3⋊(C5⋊D5)C2×C3711yescharacteristic, complemented
47C3×C52×D3C2×C3711yescharacteristic, complemented
48C2×D3×C37—751no—
49C2×D3×C37—751no—
50C2×C5×C37—36no—
51D5×C37—156no—
52D5×C37—456no—
53C32×C37C2×C5⋊D511yescharacteristic, complemented, Hall
54C2×C3⋊(C5⋊D5)—31no—
55D3×C5⋊D5—31no—
56C32×C52C22×C3711yescharacteristic, complemented, Hall
57C2×C3×C37—31no—
58C2×C3×C37—751no—
59D3×C37—251no—
60D3×C37—751no—
61D3×C37—751no—
62D3×C37—1501no—
63D3×C37C3⋊(C5⋊D5)11yescharacteristic, direct product factor
64C5×C37D3×D1516yescomplemented
65D3×D15—56no—
66C2×C3×C52—31no—
67C3⋊(C5⋊D5)—31no—
68C3⋊(C5⋊D5)—31no—
69C3⋊(C5⋊D5)—61no—
70C3⋊(C5⋊D5)D3×C3711yescharacteristic, direct product factor
71C52×D3D3×C3711yescharacteristic, complemented
72C3×C5⋊D5—31no—
73C22×C37—2251noHall
74C3×C37—21no—
75C3×C37D3×C5⋊D511yescharacteristic, complemented
76C3×C37C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
77C2×C5⋊D5—91noHall
78C3⋊D15—56no—
79C3×D15—56no—
80C3×C5×D3D5×C3716yescomplemented
81C3×C52—21no—
82C3×C52C2×D3×C3711yescharacteristic, complemented
83C3×C52C2×D3×C3711yescharacteristic, complemented
84C2×C37—31no—
85C2×C37—751no—
86C2×C37—2251no—
87C2×D15—156no—
88D3×D5—156no—
89C2×C52—31no—
90C5⋊D5—31no—
91C5⋊D5—91no—
92C32×C5C2×D5×C3716yescomplemented
93C37D3×C3⋊(C5⋊D5)11yescharacteristic, direct product factor, Sylow
94D32—251noHall
95C2×C3×C5—36no—
96D15—56no—
97D15—156no—
98D15—156no—
99D15—306no—
100C3×D5—156no—
101C5×D3D15×C3716yescomplemented
102C52D32×C3711yescharacteristic, complemented, Sylow
103C2×D5—456no—
104C3⋊D3—251no—
105C3×D3—251no—
106C3×D3C37×C5⋊D511yescharacteristic, complemented
107C3×C5—26no—
108C3×C5D3×D5×C3716yescomplemented
109C3×C5C2×D15×C3716yescomplemented
110C2×D3—751no—
111C2×D3—751no—
112C2×C5—36no—
113D5—156no—
114D5—456no—
115C32C2×C37×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—751no—
118D3—251no—
119D3—751no—
120D3—751no—
121D3—1501no—
122D3C37×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
123C5D3×D15×C3716yescomplemented
124C22—2251noSylow
125C3—21no—
126C3D3×C37×C5⋊D511yescharacteristic, complemented
127C3C2×C37×C3⋊(C5⋊D5)11yescharacteristic, complemented
128C2—31no—
129C2—751no—
130C2—2251no—
subgroupG/H
center, hypercenterC37D3×C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC32×C52C22×C37
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C32×C52
UCSC1 ◁ C37

Complements

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

NH ≅ G/Ntype
1. C3×C52×D3×C37C2semidirect
2. C3×C37×C3⋊(C5⋊D5)C2semidirect
3. C37×C3⋊(C3⋊(C5⋊D5))C2semidirect
6. C32×C52×C37C22semidirect
11. C37×C3⋊(C5⋊D5)D3direct (N × H)
12. C52×D3×C37D3semidirect
18. C3×C5×D3×C37D5semidirect
20. C3×C52×C37C2×D3semidirect
21. C3×C52×C37C2×D3semidirect
27. C32×C5×C37C2×D5semidirect
34. C5×D3×C37D15semidirect
36. C52×C37D32semidirect
37. D3×C3⋊(C5⋊D5)C37direct (N × H)
41. C3×D3×C37C5⋊D5semidirect
43. C3×C5×C37D3×D5semidirect
44. C3×C5×C37C2×D15semidirect
45. C3⋊(C3⋊(C5⋊D5))C2×C37semidirect
46. C3×C3⋊(C5⋊D5)C2×C37semidirect
47. C3×C52×D3C2×C37semidirect
53. C32×C37C2×C5⋊D5semidirect
56. C32×C52C22×C37semidirect
63. D3×C37C3⋊(C5⋊D5)direct (N × H)
64. C5×C37D3×D15semidirect
70. C3⋊(C5⋊D5)D3×C37direct (N × H)
71. C52×D3D3×C37semidirect
75. C3×C37D3×C5⋊D5semidirect
76. C3×C37C2×C3⋊(C5⋊D5)semidirect
80. C3×C5×D3D5×C37semidirect
82. C3×C52C2×D3×C37semidirect
83. C3×C52C2×D3×C37semidirect
92. C32×C5C2×D5×C37semidirect
93. C37D3×C3⋊(C5⋊D5)direct (N × H)
101. C5×D3D15×C37semidirect
102. C52D32×C37semidirect
106. C3×D3C37×C5⋊D5semidirect
108. C3×C5D3×D5×C37semidirect
109. C3×C5C2×D15×C37semidirect
115. C32C2×C37×C5⋊D5semidirect
122. D3C37×C3⋊(C5⋊D5)direct (N × H)
123. C5D3×D15×C37semidirect
126. C3D3×C37×C5⋊D5semidirect
127. C3C2×C37×C3⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D3×C372
C3×C37×C3⋊(C5⋊D5)2
C37×C3⋊(C3⋊(C5⋊D5))2
C2×C37×C3⋊(C5⋊D5)3
D3×C37×C5⋊D53
D3×D15×C375
D3×C3⋊(C5⋊D5)37