Finite Group Databasebeta

← #39908182

Subgroups — #39908182

Order 26100.

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×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D145)C211yesmaximal, characteristic, complemented
3C52×C3⋊D87C211yesmaximal, characteristic, complemented
4D87⋊(C5⋊D5)—31nomaximal
5C5⋊D5×D87—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7D15⋊D87—56nomaximal
8C3⋊(C5⋊D145)D311yescharacteristic, complemented
9C29×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C52×D87—31no—
11C52×D87—31no—
12C52×D87—61no—
13C3×C5⋊D145—31no—
14C3×C29×C5⋊D5—31no—
15C5⋊D5×D29—91noHall
16C5×C3⋊D87D516yescomplemented
17C3×D435—56no—
18C3×C29×D15—56no—
19C3×C52×C29—21no—
20C3×C52×C29C2×D311yescharacteristic, complemented
21C3×C52×C29C2×D311yescharacteristic, complemented
22D15⋊D29—156no—
23D5×D87—156no—
24C5⋊D145—31no—
25C29×C5⋊D5—31no—
26C52×D29—91no—
27C32×C5×C29C2×D516yescomplemented
28D3×D87—251noHall
29(C3⋊D3)⋊(C5⋊D5)—291nomaximal, Hall
30D435—56no—
31C29×D15—56no—
32C5×D87—36no—
33C5×D87—36no—
34C5×D87—66no—
35C3×D145—156no—
36C3×D5×C29—156no—
37C52×C29D3211yescharacteristic, complemented, Hall
38D5×D29—456no—
39C3⋊D87C5⋊D511yescharacteristic, complemented
40C3×D87—251no—
41C3×D3×C29—251no—
42C52×C3⋊D3—291no—
43C3×C3⋊(C5⋊D5)—291no—
44C3×C3⋊(C5⋊D5)D2911yescharacteristic, complemented
45C3×C5×C29—26no—
46C3×C5×C29D3×D516yescomplemented
47C3×C5×C29D3×D516yescomplemented
48C2×D87—751no—
49D3×D29—751no—
50D3×C5⋊D5—871no—
51D3×C5⋊D5—871no—
52D145—156no—
53C5×D29—96no—
54D5×C29—156no—
55C32×C29C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D2911yescharacteristic, complemented, Hall
57(C3⋊D3)⋊D5—1456no—
58C2×C3×C29—751no—
59D87—31no—
60D87—31no—
61D87—61no—
62D87—251no—
63C3×D29—751no—
64D3×C29—251no—
65C3⋊(C5⋊D5)—291no—
66C3⋊(C5⋊D5)D8711yescharacteristic, complemented
67C52×D3—871no—
68C52×D3—871no—
69C52×D3—1741no—
70C3×C5⋊D5—31no—
71C3×C5⋊D5—871no—
72C5×C29(C3⋊D3)⋊D516yescomplemented
73C2×D29—2251noHall
74C2×C5⋊D5—2611noHall
75C5×C3⋊D3—296no—
76C3×D15—56no—
77C3×D15—1456no—
78C3×C29—21no—
79C3×C29D3×C5⋊D511yescharacteristic, complemented
80C3×C29D3×C5⋊D511yescharacteristic, complemented
81C3×C52—21no—
82C3×C52D3×D2911yescharacteristic, complemented
83C3×C52C2×D8711yescharacteristic, complemented
84D3×D5—4356no—
85D3×D5—4356no—
86C2×C29—751no—
87D29—91no—
88D29—751no—
89C2×C52—2611no—
90C5⋊D5—31no—
91C5⋊D5—871no—
92C32×C5D5×D2916yescomplemented
93D32—7251noHall
94D15—56no—
95D15—1456no—
96C3×D5—156no—
97C3×D5—4356no—
98C5×D3—876no—
99C5×D3—876no—
100C5×D3—1746no—
101C29(C3⋊D3)⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
102C52D3×D8711yescharacteristic, complemented, Sylow
103C2×D5—13056no—
104C3⋊D3—291no—
105C3×D3—251no—
106C3×D3—7251no—
107C3×C5—26no—
108C3×C5D5×D8716yescomplemented
109C3×C5D15⋊D2916yescomplemented
110C2×D3—21751no—
111C2×D3—21751no—
112C2×C5—2616no—
113D5—156no—
114D5—4356no—
115C32C5⋊D5×D2911yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—21751no—
118D3—251no—
119D3—871no—
120D3—871no—
121D3—1741no—
122D3—7251no—
123C5D15⋊D8716yescomplemented
124C22—65251noSylow
125C3—21no—
126C3C5⋊D5×D8711yescharacteristic, complemented
127C3D87⋊(C5⋊D5)11yescharacteristic, complemented
128C2—2611no—
129C2—751no—
130C2—21751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C29C22
LCSG ▷ C32×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C29×C3⋊(C5⋊D5)C2semidirect
2. C3×C3⋊(C5⋊D145)C2semidirect
3. C52×C3⋊D87C2semidirect
6. C32×C52×C29C22semidirect
8. C3⋊(C5⋊D145)D3semidirect
9. C29×C3⋊(C5⋊D5)D3semidirect
16. C5×C3⋊D87D5semidirect
20. C3×C52×C29C2×D3semidirect
21. C3×C52×C29C2×D3semidirect
27. C32×C5×C29C2×D5semidirect
37. C52×C29D32semidirect
39. C3⋊D87C5⋊D5semidirect
44. C3×C3⋊(C5⋊D5)D29semidirect
46. C3×C5×C29D3×D5semidirect
47. C3×C5×C29D3×D5semidirect
55. C32×C29C2×C5⋊D5semidirect
56. C32×C52C2×D29semidirect
66. C3⋊(C5⋊D5)D87semidirect
72. C5×C29(C3⋊D3)⋊D5semidirect
79. C3×C29D3×C5⋊D5semidirect
80. C3×C29D3×C5⋊D5semidirect
82. C3×C52D3×D29semidirect
83. C3×C52C2×D87semidirect
92. C32×C5D5×D29semidirect
101. C29(C3⋊D3)⋊(C5⋊D5)semidirect
102. C52D3×D87semidirect
108. C3×C5D5×D87semidirect
109. C3×C5D15⋊D29semidirect
115. C32C5⋊D5×D29semidirect
123. C5D15⋊D87semidirect
126. C3C5⋊D5×D87semidirect
127. C3D87⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C29×C3⋊(C5⋊D5)2
C3×C3⋊(C5⋊D145)2
C52×C3⋊D872
D87⋊(C5⋊D5)3
C5⋊D5×D873
D15⋊D875
(C3⋊D3)⋊(C5⋊D5)29