Finite Group Databasebeta

← C3×C5⋊D5×D111 #45686432

Subgroups — C3×C5⋊D5×D111 #45686432

Order 33300.

352 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C32×C37×C5⋊D5C211yesmaximal, characteristic, complemented
2C3×C52×D111C211yesmaximal, characteristic, complemented
3C3×C3⋊(C5⋊D185)C211yesmaximal, characteristic, complemented
4C5⋊D5×D111C311yesmaximal, characteristic, direct product factor
5C3×C5⋊D5×D37—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7C3×D5×D111—56nomaximal
8C3⋊(C5⋊D185)C2×C311yescharacteristic, complemented
9C52×D111C2×C311yescharacteristic, complemented
10C3×C5⋊D185—31no—
11C3×C37×C5⋊D5—21no—
12C3×C37×C5⋊D5D311yescharacteristic, complemented
13C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
14C3×C52×D37—31no—
15C5⋊D5×D37—31noHall
16C3×D555—56no—
17C3×C5×D111D516yescomplemented
18C32×D5×C37—56no—
19C3×C52×C37—21no—
20C3×C52×C37C2×D311yescharacteristic, complemented
21C3×C52×C37C22×C311yescharacteristic, complemented
22D5×D111—56no—
23C3×D5×D37—156no—
24C5⋊D185—31no—
25C37×C5⋊D5C3×D311yescharacteristic, complemented
26C52×D37—31no—
27C32×C5×C37C2×D516yescomplemented
28C2×C3×D111—251noHall
29D555—56no—
30C5×D111C3×D516yescomplemented
31C3×D185—156no—
32C3×D5×C37—56no—
33C3×D5×C37—56no—
34C3×D5×C37—106no—
35C3×C5×D37—36no—
36C52×C37C2×C3×D311yescharacteristic, complemented, Hall
37C3×D3×C5⋊D5—371nomaximal, Hall
38D5×D37—156no—
39C2×C32×C37—251no—
40C3×D111—251no—
41C3×D111C5⋊D511yescharacteristic, direct product factor
42C3×C5×C37—26no—
43C3×C5×C37D3×D516yescomplemented
44C3×C5×C37C2×C3×D516yescomplemented
45C3×C3⋊(C5⋊D5)—371no—
46C3×C52×D3—371no—
47C32×C5⋊D5D3711yescharacteristic, complemented
48C2×D111—251no—
49C2×C3×D37—751no—
50D185—156no—
51C5×D37—36no—
52D5×C37—56no—
53C32×C37C2×C5⋊D511yescharacteristic, complemented, Hall
54C2×C3×C5⋊D5—1111no—
55D3×C5⋊D5—371no—
56C32×C52C2×D3711yescharacteristic, complemented, Hall
57C2×C3×C37—251no—
58C2×C3×C37—251no—
59C2×C3×C37—501no—
60D111—251no—
61D111C3×C5⋊D511yescharacteristic, direct product factor
62C3×D37—31no—
63C3×D37—751no—
64C5×C37C3×D3×D516yescomplemented
65C3×D3×D5—1856no—
66C2×C3×C52—1111no—
67C3⋊(C5⋊D5)—371no—
68C52×D3—371no—
69C3×C5⋊D5—21no—
70C3×C5⋊D5—1111no—
71C3×C5⋊D5C3×D3711yescharacteristic, complemented
72C3×C5⋊D5D11111yescharacteristic, direct product factor
73C2×D37—751noHall
74C3×C37—21no—
75C3×C37D3×C5⋊D511yescharacteristic, complemented
76C3×C37C2×C3×C5⋊D511yescharacteristic, complemented
77C2×C5⋊D5—1111noHall
78C3×D15—1856no—
79C3×C5×D3—376no—
80C32×D5—56no—
81C3×C52—21no—
82C3×C52C2×C3×D3711yescharacteristic, complemented
83C3×C52C2×D11111yescharacteristic, complemented
84C2×C37—251no—
85D37—31no—
86D37—751no—
87C2×C3×D5—5556no—
88D3×D5—1856no—
89C2×C52—1111no—
90C5⋊D5—1111no—
91C5⋊D5C3×D11111yescharacteristic, direct product factor
92C32×C5D5×D3716yescomplemented
93C37C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
94C2×C3×D3—9251noHall
95C2×C3×C5—1116no—
96D15—1856no—
97C3×D5—56no—
98C3×D5—56no—
99C3×D5—106no—
100C3×D5—5556no—
101C5×D3—376no—
102C52C2×C3×D11111yescharacteristic, complemented, Sylow
103C2×D5—5556no—
104C2×C32—251no—
105C3×D3—371no—
106C3×D3—9251no—
107C3×C5—26no—
108C3×C5C3×D5×D3716yescomplemented
109C3×C5D5×D11116yescomplemented
110C22×C3—27751no—
111C2×D3—9251no—
112C2×C5—1116no—
113D5—56no—
114D5—5556no—
115C32C5⋊D5×D3711yescharacteristic, complemented, Sylow
116C2×C3—251no—
117C2×C3—251no—
118C2×C3—501no—
119C2×C3—1111no—
120C2×C3—27751no—
121D3—371no—
122D3—9251no—
123C5C3×D5×D11116yescomplemented
124C22—27751noSylow
125C3—21no—
126C3C3×C5⋊D5×D3711yescharacteristic, complemented
127C3C5⋊D5×D11111yescharacteristic, direct product factor
128C2—251no—
129C2—1111no—
130C2—27751no—
subgroupG/H
center, hypercenterC3C5⋊D5×D111
commutator, cosocle, hypocenterC3×C52×C37C22×C3
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C3×C52×C37
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C37×C5⋊D5C2semidirect
2. C3×C52×D111C2semidirect
3. C3×C3⋊(C5⋊D185)C2semidirect
4. C5⋊D5×D111C3direct (N × H)
6. C32×C52×C37C22semidirect
8. C3⋊(C5⋊D185)C2×C3semidirect
9. C52×D111C2×C3semidirect
12. C3×C37×C5⋊D5D3semidirect
13. C3×C37×C5⋊D5C2×C3semidirect
17. C3×C5×D111D5semidirect
20. C3×C52×C37C2×D3semidirect
21. C3×C52×C37C22×C3semidirect
25. C37×C5⋊D5C3×D3semidirect
27. C32×C5×C37C2×D5semidirect
30. C5×D111C3×D5semidirect
36. C52×C37C2×C3×D3semidirect
41. C3×D111C5⋊D5direct (N × H)
43. C3×C5×C37D3×D5semidirect
44. C3×C5×C37C2×C3×D5semidirect
47. C32×C5⋊D5D37semidirect
53. C32×C37C2×C5⋊D5semidirect
56. C32×C52C2×D37semidirect
61. D111C3×C5⋊D5direct (N × H)
64. C5×C37C3×D3×D5semidirect
71. C3×C5⋊D5C3×D37semidirect
72. C3×C5⋊D5D111direct (N × H)
75. C3×C37D3×C5⋊D5semidirect
76. C3×C37C2×C3×C5⋊D5semidirect
82. C3×C52C2×C3×D37semidirect
83. C3×C52C2×D111semidirect
91. C5⋊D5C3×D111direct (N × H)
92. C32×C5D5×D37semidirect
93. C37C3×D3×C5⋊D5semidirect
102. C52C2×C3×D111semidirect
108. C3×C5C3×D5×D37semidirect
109. C3×C5D5×D111semidirect
115. C32C5⋊D5×D37semidirect
123. C5C3×D5×D111semidirect
126. C3C3×C5⋊D5×D37semidirect
127. C3C5⋊D5×D111direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C37×C5⋊D52
C3×C52×D1112
C3×C3⋊(C5⋊D185)2
C5⋊D5×D1113
C3×C5⋊D5×D373
C3×D5×D1115
C3×D3×C5⋊D537