Finite Group Databasebeta

← C3×D3×C5⋊D145 #39908151

Subgroups — C3×D3×C5⋊D145 #39908151

Order 26100.

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
1C32×C5⋊D145C211yesmaximal, characteristic, complemented
2C3×C52×D3×C29C211yesmaximal, characteristic, complemented
3C3×C3⋊(C5⋊D145)C211yesmaximal, characteristic, complemented
4C2×C3×C5⋊D145—31nomaximal
5D3×C5⋊D145C311yesmaximal, characteristic, direct product factor
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7C3×D3×D145—56nomaximal
8C3⋊(C5⋊D145)C2×C311yescharacteristic, complemented
9C52×D3×C29C2×C311yescharacteristic, complemented
10C3×C5⋊D145—21no—
11C3×C5⋊D145—31no—
12C3×C5⋊D145D311yescharacteristic, direct product factor
13C3×C5⋊D145C2×C311yescharacteristic, complemented
14C2×C3×C52×C29—31no—
15C2×C5⋊D145—31noHall
16C3×D435—56no—
17C3×C5×D3×C29D516yescomplemented
18C32×D145—56no—
19C3×C52×C29—21no—
20C3×C52×C29C2×D311yescharacteristic, complemented
21C3×C52×C29C22×C311yescharacteristic, complemented
22C2×C3×D145—156no—
23D3×D145—56no—
24C2×C52×C29—31no—
25C5⋊D145—31no—
26C5⋊D145C3×D311yescharacteristic, direct product factor
27C32×C5×C29C2×D516yescomplemented
28C3×D3×D29—251noHall
29C3×D3×C5⋊D5—291nomaximal, Hall
30C2×C3×C5×C29—36no—
31D435—56no—
32C5×D3×C29C3×D516yescomplemented
33C3×D145—56no—
34C3×D145—56no—
35C3×D145—106no—
36C3×D145—156no—
37C52×C29C2×C3×D311yescharacteristic, complemented, Hall
38C2×D145—156no—
39C3×D87—251no—
40C3×D3×C29C5⋊D511yescharacteristic, complemented
41C32×D29—251no—
42C3×C3⋊(C5⋊D5)—291no—
43C3×C52×D3D2911yescharacteristic, complemented
44C32×C5⋊D5—291no—
45C3×C5×C29—26no—
46C3×C5×C29D3×D516yescomplemented
47C3×C5×C29C2×C3×D516yescomplemented
48C2×C3×D29—751no—
49D3×D29—251no—
50C2×C3×C5⋊D5—871no—
51D3×C5⋊D5—291no—
52C2×C5×C29—36no—
53D145—56no—
54D145—156no—
55C32×C29C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D2911yescharacteristic, complemented, Hall
57C3×D3×D5—1456no—
58C2×C3×C29—31no—
59D87—251no—
60C3×D29—251no—
61C3×D29—251no—
62C3×D29—501no—
63C3×D29—751no—
64D3×C29C3×C5⋊D511yescharacteristic, complemented
65C2×C3×C52—31no—
66C3⋊(C5⋊D5)—291no—
67C52×D3C3×D2911yescharacteristic, complemented
68C3×C5⋊D5—291no—
69C3×C5⋊D5—291no—
70C3×C5⋊D5—581no—
71C3×C5⋊D5—871no—
72C5×C29C3×D3×D516yescomplemented
73C2×D29—751noHall
74C2×C5⋊D5—871noHall
75C3×D15—1456no—
76C3×C5×D3D14516yescomplemented
77C32×D5—1456no—
78C3×C29—21no—
79C3×C29D3×C5⋊D511yescharacteristic, complemented
80C3×C29C2×C3×C5⋊D511yescharacteristic, complemented
81C3×C52—21no—
82C3×C52D3×D2911yescharacteristic, complemented
83C3×C52C2×C3×D2911yescharacteristic, complemented
84C2×C3×D5—4356no—
85D3×D5—1456no—
86C2×C29—31no—
87D29—251no—
88D29—751no—
89C2×C52—31no—
90C5⋊D5—291no—
91C5⋊D5—871no—
92C32×C5C2×D14516yescomplemented
93C2×C3×D3—7251noHall
94C2×C3×C5—36no—
95D15—1456no—
96C3×D5—2906no—
97C3×D5—1456no—
98C3×D5—1456no—
99C3×D5—4356no—
100C5×D3C3×D14516yescomplemented
101C29C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
102C52C3×D3×D2911yescharacteristic, complemented, Sylow
103C2×D5—4356no—
104C2×C32—7251no—
105C3×D3—7251no—
106C3×D3C5⋊D14511yescharacteristic, direct product factor
107C3×C5—26no—
108C3×C5D3×D14516yescomplemented
109C3×C5C2×C3×D14516yescomplemented
110C22×C3—21751no—
111C2×D3—7251no—
112C2×C5—36no—
113D5—1456no—
114D5—4356no—
115C32C2×C5⋊D14511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—21751no—
118C2×C3—14501no—
119C2×C3—7251no—
120C2×C3—7251no—
121D3—7251no—
122D3C3×C5⋊D14511yescharacteristic, direct product factor
123C5C3×D3×D14516yescomplemented
124C22—21751noSylow
125C3—21no—
126C3D3×C5⋊D14511yescharacteristic, direct product factor
127C3C2×C3×C5⋊D14511yescharacteristic, complemented
128C2—31no—
129C2—21751no—
130C2—7251no—
subgroupG/H
center, hypercenterC3D3×C5⋊D145
commutator, cosocle, hypocenterC3×C52×C29C22×C3
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C3×C52×C29
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊D145C2semidirect
2. C3×C52×D3×C29C2semidirect
3. C3×C3⋊(C5⋊D145)C2semidirect
5. D3×C5⋊D145C3direct (N × H)
6. C32×C52×C29C22semidirect
8. C3⋊(C5⋊D145)C2×C3semidirect
9. C52×D3×C29C2×C3semidirect
12. C3×C5⋊D145D3direct (N × H)
13. C3×C5⋊D145C2×C3semidirect
17. C3×C5×D3×C29D5semidirect
20. C3×C52×C29C2×D3semidirect
21. C3×C52×C29C22×C3semidirect
26. C5⋊D145C3×D3direct (N × H)
27. C32×C5×C29C2×D5semidirect
32. C5×D3×C29C3×D5semidirect
37. C52×C29C2×C3×D3semidirect
40. C3×D3×C29C5⋊D5semidirect
43. C3×C52×D3D29semidirect
46. C3×C5×C29D3×D5semidirect
47. C3×C5×C29C2×C3×D5semidirect
55. C32×C29C2×C5⋊D5semidirect
56. C32×C52C2×D29semidirect
64. D3×C29C3×C5⋊D5semidirect
67. C52×D3C3×D29semidirect
72. C5×C29C3×D3×D5semidirect
76. C3×C5×D3D145semidirect
79. C3×C29D3×C5⋊D5semidirect
80. C3×C29C2×C3×C5⋊D5semidirect
82. C3×C52D3×D29semidirect
83. C3×C52C2×C3×D29semidirect
92. C32×C5C2×D145semidirect
100. C5×D3C3×D145semidirect
101. C29C3×D3×C5⋊D5semidirect
102. C52C3×D3×D29semidirect
106. C3×D3C5⋊D145direct (N × H)
108. C3×C5D3×D145semidirect
109. C3×C5C2×C3×D145semidirect
115. C32C2×C5⋊D145semidirect
122. D3C3×C5⋊D145direct (N × H)
123. C5C3×D3×D145semidirect
126. C3D3×C5⋊D145direct (N × H)
127. C3C2×C3×C5⋊D145semidirect

Maximal subgroups

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

subgroupindex
C32×C5⋊D1452
C3×C52×D3×C292
C3×C3⋊(C5⋊D145)2
C2×C3×C5⋊D1453
D3×C5⋊D1453
C3×D3×D1455
C3×D3×C5⋊D529