Finite Group Databasebeta

← #45686464

Subgroups — #45686464

Order 33300.

352 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 79 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×C37×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D185)C211yesmaximal, characteristic, complemented
3C52×C3⋊D111C211yesmaximal, characteristic, complemented
4D111⋊(C5⋊D5)—31nomaximal
5C5⋊D5×D111—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7D15⋊D111—56nomaximal
8C3⋊(C5⋊D185)D311yescharacteristic, complemented
9C37×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C52×D111—31no—
11C52×D111—31no—
12C52×D111—61no—
13C3×C5⋊D185—31no—
14C3×C37×C5⋊D5—31no—
15C5⋊D5×D37—91noHall
16C5×C3⋊D111D516yescomplemented
17C3×D555—56no—
18C3×D15×C37—56no—
19C3×C52×C37—21no—
20C3×C52×C37C2×D311yescharacteristic, complemented
21C3×C52×C37C2×D311yescharacteristic, complemented
22D15⋊D37—156no—
23D5×D111—156no—
24C5⋊D185—31no—
25C37×C5⋊D5—31no—
26C52×D37—91no—
27C32×C5×C37C2×D516yescomplemented
28D3×D111—251noHall
29D555—56no—
30D15×C37—56no—
31C5×D111—36no—
32C5×D111—36no—
33C5×D111—66no—
34C3×D185—156no—
35C3×D5×C37—156no—
36C52×C37D3211yescharacteristic, complemented, Hall
37(C3⋊D3)⋊(C5⋊D5)—371nomaximal, Hall
38D5×D37—456no—
39C3⋊D111C5⋊D511yescharacteristic, complemented
40C3×D111—251no—
41C3×D3×C37—251no—
42C3×C5×C37—26no—
43C3×C5×C37D3×D516yescomplemented
44C3×C5×C37D3×D516yescomplemented
45C52×C3⋊D3—371no—
46C3×C3⋊(C5⋊D5)—371no—
47C3×C3⋊(C5⋊D5)D3711yescharacteristic, complemented
48C2×D111—751no—
49D3×D37—751no—
50D185—156no—
51C5×D37—96no—
52D5×C37—156no—
53C32×C37C2×C5⋊D511yescharacteristic, complemented, Hall
54D3×C5⋊D5—1111no—
55D3×C5⋊D5—1111no—
56C32×C52C2×D3711yescharacteristic, complemented, Hall
57C2×C3×C37—751no—
58D111—31no—
59D111—31no—
60D111—61no—
61D111—251no—
62C3×D37—751no—
63D3×C37—251no—
64C5×C37(C3⋊D3)⋊D516yescomplemented
65(C3⋊D3)⋊D5—1856no—
66C3⋊(C5⋊D5)—371no—
67C3⋊(C5⋊D5)D11111yescharacteristic, complemented
68C52×D3—1111no—
69C52×D3—1111no—
70C52×D3—2221no—
71C3×C5⋊D5—31no—
72C3×C5⋊D5—1111no—
73C2×D37—2251noHall
74C3×C37—21no—
75C3×C37D3×C5⋊D511yescharacteristic, complemented
76C3×C37D3×C5⋊D511yescharacteristic, complemented
77C2×C5⋊D5—3331noHall
78C5×C3⋊D3—376no—
79C3×D15—56no—
80C3×D15—1856no—
81C3×C52—21no—
82C3×C52D3×D3711yescharacteristic, complemented
83C3×C52C2×D11111yescharacteristic, complemented
84C2×C37—751no—
85D37—91no—
86D37—751no—
87D3×D5—5556no—
88D3×D5—5556no—
89C2×C52—3331no—
90C5⋊D5—31no—
91C5⋊D5—1111no—
92C32×C5D5×D3716yescomplemented
93C37(C3⋊D3)⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
94D32—9251noHall
95D15—56no—
96D15—1856no—
97C3×D5—156no—
98C3×D5—5556no—
99C5×D3—1116no—
100C5×D3—1116no—
101C5×D3—2226no—
102C52D3×D11111yescharacteristic, complemented, Sylow
103C2×D5—16656no—
104C3⋊D3—371no—
105C3×D3—251no—
106C3×D3—9251no—
107C3×C5—26no—
108C3×C5D5×D11116yescomplemented
109C3×C5D15⋊D3716yescomplemented
110C2×D3—27751no—
111C2×D3—27751no—
112C2×C5—3336no—
113D5—156no—
114D5—5556no—
115C32C5⋊D5×D3711yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—27751no—
118D3—251no—
119D3—1111no—
120D3—1111no—
121D3—9251no—
122D3—2221no—
123C5D15⋊D11116yescomplemented
124C22—83251noSylow
125C3—21no—
126C3C5⋊D5×D11111yescharacteristic, complemented
127C3D111⋊(C5⋊D5)11yescharacteristic, complemented
128C2—751no—
129C2—3331no—
130C2—27751no—
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×C37×C3⋊(C5⋊D5)C2semidirect
2. C3×C3⋊(C5⋊D185)C2semidirect
3. C52×C3⋊D111C2semidirect
6. C32×C52×C37C22semidirect
8. C3⋊(C5⋊D185)D3semidirect
9. C37×C3⋊(C5⋊D5)D3semidirect
16. C5×C3⋊D111D5semidirect
20. C3×C52×C37C2×D3semidirect
21. C3×C52×C37C2×D3semidirect
27. C32×C5×C37C2×D5semidirect
36. C52×C37D32semidirect
39. C3⋊D111C5⋊D5semidirect
43. C3×C5×C37D3×D5semidirect
44. C3×C5×C37D3×D5semidirect
47. C3×C3⋊(C5⋊D5)D37semidirect
53. C32×C37C2×C5⋊D5semidirect
56. C32×C52C2×D37semidirect
64. C5×C37(C3⋊D3)⋊D5semidirect
67. C3⋊(C5⋊D5)D111semidirect
75. C3×C37D3×C5⋊D5semidirect
76. C3×C37D3×C5⋊D5semidirect
82. C3×C52D3×D37semidirect
83. C3×C52C2×D111semidirect
92. C32×C5D5×D37semidirect
93. C37(C3⋊D3)⋊(C5⋊D5)semidirect
102. C52D3×D111semidirect
108. C3×C5D5×D111semidirect
109. C3×C5D15⋊D37semidirect
115. C32C5⋊D5×D37semidirect
123. C5D15⋊D111semidirect
126. C3C5⋊D5×D111semidirect
127. C3D111⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C37×C3⋊(C5⋊D5)2
C3×C3⋊(C5⋊D185)2
C52×C3⋊D1112
D111⋊(C5⋊D5)3
C5⋊D5×D1113
D15⋊D1115
(C3⋊D3)⋊(C5⋊D5)37