Finite Group Databasebeta

← C3×D3×C37×C5⋊D5 #45686431

Subgroups — C3×D3×C37×C5⋊D5 #45686431

Order 33300.

352 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 112 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×D3×C37C211yesmaximal, characteristic, complemented
3C3×C37×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4C2×C3×C37×C5⋊D5—31nomaximal
5D3×C37×C5⋊D5C311yesmaximal, characteristic, direct product factor
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7C3×D3×D5×C37—56nomaximal
8C37×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D3×C37C2×C311yescharacteristic, complemented
10C3×C37×C5⋊D5—21no—
11C3×C37×C5⋊D5—31no—
12C3×C37×C5⋊D5D311yescharacteristic, direct product factor
13C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
14C2×C3×C52×C37—31no—
15C2×C37×C5⋊D5—31noHall
16C3×D15×C37—56no—
17C3×C5×D3×C37D516yescomplemented
18C32×D5×C37—56no—
19C3×C52×C37—21no—
20C3×C52×C37C2×D311yescharacteristic, complemented
21C3×C52×C37C22×C311yescharacteristic, complemented
22C2×C3×D5×C37—156no—
23D3×D5×C37—56no—
24C2×C52×C37—31no—
25C37×C5⋊D5—31no—
26C37×C5⋊D5C3×D311yescharacteristic, direct product factor
27C32×C5×C37C2×D516yescomplemented
28C2×C3×D3×C37—251noHall
29C2×C3×C5×C37—36no—
30D15×C37—56no—
31C5×D3×C37C3×D516yescomplemented
32C3×D5×C37—56no—
33C3×D5×C37—56no—
34C3×D5×C37—106no—
35C3×D5×C37—156no—
36C52×C37C2×C3×D311yescharacteristic, complemented, Hall
37C3×D3×C5⋊D5C3711yesmaximal, characteristic, direct product factor, Hall
38C2×D5×C37—156no—
39C2×C32×C37—251no—
40C3×D3×C37—251no—
41C3×D3×C37C5⋊D511yescharacteristic, direct product factor
42C3×C5×C37—26no—
43C3×C5×C37D3×D516yescomplemented
44C3×C5×C37C2×C3×D516yescomplemented
45C3×C3⋊(C5⋊D5)C2×C3711yescharacteristic, complemented
46C3×C52×D3C2×C3711yescharacteristic, complemented
47C32×C5⋊D5C2×C3711yescharacteristic, complemented
48C22×C3×C37—751no—
49C2×D3×C37—251no—
50C2×C5×C37—36no—
51D5×C37—56no—
52D5×C37—156no—
53C32×C37C2×C5⋊D511yescharacteristic, complemented, Hall
54C2×C3×C5⋊D5—31no—
55D3×C5⋊D5C3×C3711yescharacteristic, direct product factor
56C32×C52C22×C3711yescharacteristic, complemented, Hall
57C2×C3×C37—31no—
58C2×C3×C37—251no—
59C2×C3×C37—251no—
60C2×C3×C37—501no—
61C2×C3×C37—751no—
62D3×C37—251no—
63D3×C37C3×C5⋊D511yescharacteristic, direct product factor
64C5×C37C3×D3×D516yescomplemented
65C3×D3×D5—56no—
66C2×C3×C52—31no—
67C3⋊(C5⋊D5)C2×C3×C3711yescharacteristic, complemented
68C52×D3C2×C3×C3711yescharacteristic, complemented
69C3×C5⋊D5—21no—
70C3×C5⋊D5—31no—
71C3×C5⋊D5D3×C3711yescharacteristic, direct product factor
72C3×C5⋊D5C2×C3×C3711yescharacteristic, complemented
73C22×C37—751noHall
74C3×C37—21no—
75C3×C37D3×C5⋊D511yescharacteristic, direct product factor
76C3×C37C2×C3×C5⋊D511yescharacteristic, complemented
77C2×C5⋊D5—31noHall
78C3×D15—56no—
79C3×C5×D3D5×C3716yescomplemented
80C32×D5—56no—
81C3×C52—21no—
82C3×C52C2×D3×C3711yescharacteristic, complemented
83C3×C52C22×C3×C3711yescharacteristic, complemented
84C2×C37—31no—
85C2×C37—251no—
86C2×C37—751no—
87C2×C3×D5—156no—
88D3×D5—56no—
89C2×C52—31no—
90C5⋊D5—31no—
91C5⋊D5C3×D3×C3711yescharacteristic, direct product factor
92C32×C5C2×D5×C3716yescomplemented
93C37C3×D3×C5⋊D511yescharacteristic, direct product factor, Sylow
94C2×C3×D3—251noHall
95C2×C3×C5—36no—
96D15—56no—
97C3×D5—56no—
98C3×D5—56no—
99C3×D5—106no—
100C3×D5—156no—
101C5×D3C3×D5×C3716yescomplemented
102C52C2×C3×D3×C3711yescharacteristic, complemented, Sylow
103C2×D5—156no—
104C2×C32—251no—
105C3×D3—251no—
106C3×D3C37×C5⋊D511yescharacteristic, direct product factor
107C3×C5—26no—
108C3×C5D3×D5×C3716yescomplemented
109C3×C5C2×C3×D5×C3716yescomplemented
110C22×C3—751no—
111C2×D3—251no—
112C2×C5—36no—
113D5—56no—
114D5—156no—
115C32C2×C37×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—251no—
118C2×C3—251no—
119C2×C3—501no—
120C2×C3—751no—
121D3—251no—
122D3C3×C37×C5⋊D511yescharacteristic, direct product factor
123C5C3×D3×D5×C3716yescomplemented
124C22—751noSylow
125C3—21no—
126C3D3×C37×C5⋊D511yescharacteristic, direct product factor
127C3C2×C3×C37×C5⋊D511yescharacteristic, complemented
128C2—31no—
129C2—251no—
130C2—751no—
subgroupG/H
center, hypercenterC3×C37D3×C5⋊D5
commutator, cosocle, hypocenterC3×C52C22×C3×C37
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C3×C52
UCSC1 ◁ C3×C37

Complements

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

NH ≅ G/Ntype
1. C32×C37×C5⋊D5C2semidirect
2. C3×C52×D3×C37C2semidirect
3. C3×C37×C3⋊(C5⋊D5)C2semidirect
5. D3×C37×C5⋊D5C3direct (N × H)
6. C32×C52×C37C22semidirect
8. C37×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D3×C37C2×C3semidirect
12. C3×C37×C5⋊D5D3direct (N × H)
13. C3×C37×C5⋊D5C2×C3semidirect
17. C3×C5×D3×C37D5semidirect
20. C3×C52×C37C2×D3semidirect
21. C3×C52×C37C22×C3semidirect
26. C37×C5⋊D5C3×D3direct (N × H)
27. C32×C5×C37C2×D5semidirect
31. C5×D3×C37C3×D5semidirect
36. C52×C37C2×C3×D3semidirect
37. C3×D3×C5⋊D5C37direct (N × H)
41. C3×D3×C37C5⋊D5direct (N × H)
43. C3×C5×C37D3×D5semidirect
44. C3×C5×C37C2×C3×D5semidirect
45. C3×C3⋊(C5⋊D5)C2×C37semidirect
46. C3×C52×D3C2×C37semidirect
47. C32×C5⋊D5C2×C37semidirect
53. C32×C37C2×C5⋊D5semidirect
55. D3×C5⋊D5C3×C37direct (N × H)
56. C32×C52C22×C37semidirect
63. D3×C37C3×C5⋊D5direct (N × H)
64. C5×C37C3×D3×D5semidirect
67. C3⋊(C5⋊D5)C2×C3×C37semidirect
68. C52×D3C2×C3×C37semidirect
71. C3×C5⋊D5D3×C37direct (N × H)
72. C3×C5⋊D5C2×C3×C37semidirect
75. C3×C37D3×C5⋊D5direct (N × H)
76. C3×C37C2×C3×C5⋊D5semidirect
79. C3×C5×D3D5×C37semidirect
82. C3×C52C2×D3×C37semidirect
83. C3×C52C22×C3×C37semidirect
91. C5⋊D5C3×D3×C37direct (N × H)
92. C32×C5C2×D5×C37semidirect
93. C37C3×D3×C5⋊D5direct (N × H)
101. C5×D3C3×D5×C37semidirect
102. C52C2×C3×D3×C37semidirect
106. C3×D3C37×C5⋊D5direct (N × H)
108. C3×C5D3×D5×C37semidirect
109. C3×C5C2×C3×D5×C37semidirect
115. C32C2×C37×C5⋊D5semidirect
122. D3C3×C37×C5⋊D5direct (N × H)
123. C5C3×D3×D5×C37semidirect
126. C3D3×C37×C5⋊D5direct (N × H)
127. C3C2×C3×C37×C5⋊D5semidirect

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×D3×C372
C3×C37×C3⋊(C5⋊D5)2
C2×C3×C37×C5⋊D53
D3×C37×C5⋊D53
C3×D3×D5×C375
C3×D3×C5⋊D537