Finite Group Databasebeta

← C3⋊(C5⋊D5)×D111 #45686462

Subgroups — C3⋊(C5⋊D5)×D111 #45686462

Order 33300.

352 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 86 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×D111C211yesmaximal, characteristic, complemented
2C3×C37×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D185))C211yesmaximal, characteristic, complemented
4C5⋊D5×D111—31nomaximal
5D37×C3⋊(C5⋊D5)—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7D15×D111—56nomaximal
8C3⋊(C5⋊D185)—31no—
9C3⋊(C5⋊D185)—31no—
10C3⋊(C5⋊D185)—61no—
11C37×C3⋊(C5⋊D5)D311yescharacteristic, complemented
12C52×D111D311yescharacteristic, complemented
13C3×C37×C5⋊D5—31no—
14C3×C52×D37—31no—
15C5⋊D5×D37—91noHall
16C3⋊D555—56no—
17C3×D15×C37—56no—
18C3×C5×D111D516yescomplemented
19C3×C52×C37—21no—
20C3×C52×C37C2×D311yescharacteristic, complemented
21C3×C52×C37C2×D311yescharacteristic, complemented
22D5×D111—156no—
23D15×D37—156no—
24C5⋊D185—91no—
25C37×C5⋊D5—31no—
26C52×D37—31no—
27C32×C5×C37C2×D516yescomplemented
28D3×D111—251noHall
29D555—156no—
30D555—156no—
31D555—306no—
32D15×C37—56no—
33C5×D111D1516yescomplemented
34C3×D5×C37—156no—
35C3×C5×D37—36no—
36C52×C37D3211yescharacteristic, complemented, Hall
37D3×C3⋊(C5⋊D5)—371nomaximal, Hall
38D5×D37—456no—
39C3⋊D111—251no—
40C3×D111C5⋊D511yescharacteristic, complemented
41C3×D3×C37—251no—
42C3×C5×C37—26no—
43C3×C5×C37D3×D516yescomplemented
44C3×C5×C37C2×D1516yescomplemented
45C3⋊(C3⋊(C5⋊D5))—371no—
46C3×C3⋊(C5⋊D5)D3711yescharacteristic, complemented
47C3×C52×D3—371no—
48C2×D111—751no—
49D3×D37—751no—
50D185—456no—
51C5×D37—36no—
52D5×C37—156no—
53C32×C37C2×C5⋊D511yescharacteristic, complemented, Hall
54C2×C3⋊(C5⋊D5)—1111no—
55D3×C5⋊D5—1111no—
56C32×C52C2×D3711yescharacteristic, complemented, Hall
57C2×C3×C37—751no—
58D111—751no—
59D111—751no—
60D111—1501no—
61D111C3⋊(C5⋊D5)11yescharacteristic, direct product factor
62C3×D37—31no—
63D3×C37—251no—
64C5×C37D3×D1516yescomplemented
65D3×D15—1856no—
66C2×C3×C52—1111no—
67C3⋊(C5⋊D5)—1111no—
68C3⋊(C5⋊D5)—1111no—
69C3⋊(C5⋊D5)—2221no—
70C3⋊(C5⋊D5)D11111yescharacteristic, direct product factor
71C52×D3—371no—
72C3×C5⋊D5—31no—
73C2×D37—2251noHall
74C3×C37—21no—
75C3×C37D3×C5⋊D511yescharacteristic, complemented
76C3×C37C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
77C2×C5⋊D5—3331noHall
78C3⋊D15—1856no—
79C3×D15—56no—
80C3×C5×D3—376no—
81C3×C52—21no—
82C3×C52D3×D3711yescharacteristic, complemented
83C3×C52C2×D11111yescharacteristic, complemented
84C2×C37—751no—
85D37—31no—
86D37—2251no—
87C2×D15—5556no—
88D3×D5—5556no—
89C2×C52—1111no—
90C5⋊D5—31no—
91C5⋊D5—3331no—
92C32×C5D5×D3716yescomplemented
93C37D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
94D32—9251noHall
95C2×C3×C5—1116no—
96D15—56no—
97D15—5556no—
98D15—5556no—
99D15—11106no—
100C3×D5—156no—
101C5×D3—376no—
102C52D3×D11111yescharacteristic, complemented, Sylow
103C2×D5—16656no—
104C3⋊D3—9251no—
105C3×D3—251no—
106C3×D3—371no—
107C3×C5—26no—
108C3×C5D15×D3716yescomplemented
109C3×C5D5×D11116yescomplemented
110C2×D3—27751no—
111C2×D3—27751no—
112C2×C5—1116no—
113D5—156no—
114D5—16656no—
115C32C5⋊D5×D3711yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—1111no—
118D3—251no—
119D3—371no—
120D3—55501no—
121D3—27751no—
122D3—27751no—
123C5D15×D11116yescomplemented
124C22—83251noSylow
125C3—21no—
126C3D37×C3⋊(C5⋊D5)11yescharacteristic, complemented
127C3C5⋊D5×D11111yescharacteristic, complemented
128C2—751no—
129C2—1111no—
130C2—83251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C37C22
LCSG ▷ C32×C52×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×D111C2semidirect
2. C3×C37×C3⋊(C5⋊D5)C2semidirect
3. C3⋊(C3⋊(C5⋊D185))C2semidirect
6. C32×C52×C37C22semidirect
11. C37×C3⋊(C5⋊D5)D3semidirect
12. C52×D111D3semidirect
18. C3×C5×D111D5semidirect
20. C3×C52×C37C2×D3semidirect
21. C3×C52×C37C2×D3semidirect
27. C32×C5×C37C2×D5semidirect
33. C5×D111D15semidirect
36. C52×C37D32semidirect
40. C3×D111C5⋊D5semidirect
43. C3×C5×C37D3×D5semidirect
44. C3×C5×C37C2×D15semidirect
46. C3×C3⋊(C5⋊D5)D37semidirect
53. C32×C37C2×C5⋊D5semidirect
56. C32×C52C2×D37semidirect
61. D111C3⋊(C5⋊D5)direct (N × H)
64. C5×C37D3×D15semidirect
70. C3⋊(C5⋊D5)D111direct (N × H)
75. C3×C37D3×C5⋊D5semidirect
76. C3×C37C2×C3⋊(C5⋊D5)semidirect
82. C3×C52D3×D37semidirect
83. C3×C52C2×D111semidirect
92. C32×C5D5×D37semidirect
93. C37D3×C3⋊(C5⋊D5)semidirect
102. C52D3×D111semidirect
108. C3×C5D15×D37semidirect
109. C3×C5D5×D111semidirect
115. C32C5⋊D5×D37semidirect
123. C5D15×D111semidirect
126. C3D37×C3⋊(C5⋊D5)semidirect
127. C3C5⋊D5×D111semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D1112
C3×C37×C3⋊(C5⋊D5)2
C3⋊(C3⋊(C5⋊D185))2
C5⋊D5×D1113
D37×C3⋊(C5⋊D5)3
D15×D1115
D3×C3⋊(C5⋊D5)37