Finite Group Databasebeta

← C3×D123⋊(C5⋊D5) #49147133

Subgroups — C3×D123⋊(C5⋊D5) #49147133

Order 36900.

352 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 90 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⋊D205C211yesmaximal, characteristic, complemented
2C3×C52×D123C211yesmaximal, characteristic, complemented
3C3×C41×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4D123⋊(C5⋊D5)C311yesmaximal, characteristic, direct product factor
5C3×C5⋊D5×D41—31nomaximal
6C32×C52×C41C2211yescharacteristic, complemented, Hall
7C3×D15⋊D41—56nomaximal
8C41×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D123C2×C311yescharacteristic, complemented
10C3×C5⋊D205—21no—
11C3×C5⋊D205D311yescharacteristic, complemented
12C3×C5⋊D205C2×C311yescharacteristic, complemented
13C3×C41×C5⋊D5—31no—
14C3×C52×D41—31no—
15C5⋊D5×D41—31noHall
16C3×D15×C41—56no—
17C3×C5×D123D516yescomplemented
18C32×D205—56no—
19C3×C52×C41—21no—
20C3×C52×C41C2×D311yescharacteristic, complemented
21C3×C52×C41C22×C311yescharacteristic, complemented
22D15⋊D41—56no—
23C3×D5×D41—156no—
24C5⋊D205C3×D311yescharacteristic, complemented
25C41×C5⋊D5—31no—
26C52×D41—31no—
27C32×C5×C41C2×D516yescomplemented
28C3×D3×D41—251noHall
29D15×C41—56no—
30C5×D123C3×D516yescomplemented
31C3×D205—56no—
32C3×D205—56no—
33C3×D205—106no—
34C3×D5×C41—156no—
35C3×C5×D41—36no—
36C52×C41C2×C3×D311yescharacteristic, complemented, Hall
37C3×D3×C5⋊D5—411nomaximal, Hall
38D5×D41—156no—
39C3×D123C5⋊D511yescharacteristic, complemented
40C3×D3×C41—251no—
41C32×D41—251no—
42C3×C5×C41—26no—
43C3×C5×C41D3×D516yescomplemented
44C3×C5×C41C2×C3×D516yescomplemented
45C2×C3×D41—751no—
46D3×D41—251no—
47C3×C3⋊(C5⋊D5)D4111yescharacteristic, complemented
48C3×C52×D3—411no—
49C32×C5⋊D5—411no—
50D205—56no—
51C5×D41—36no—
52D5×C41—156no—
53C32×C41C2×C5⋊D511yescharacteristic, complemented, Hall
54C2×C3×C5⋊D5—1231no—
55D3×C5⋊D5—411no—
56C2×C3×C41—751no—
57D123C3×C5⋊D511yescharacteristic, complemented
58C3×D41—31no—
59C3×D41—251no—
60C3×D41—251no—
61C3×D41—501no—
62D3×C41—251no—
63C32×C52C2×D4111yescharacteristic, complemented, Hall
64C5×C41C3×D3×D516yescomplemented
65C3×D3×D5—2056no—
66C2×D41—751noHall
67C2×C3×C52—1231no—
68C3⋊(C5⋊D5)C3×D4111yescharacteristic, complemented
69C52×D3—411no—
70C3×C5⋊D5—31no—
71C3×C5⋊D5—411no—
72C3×C5⋊D5—411no—
73C3×C5⋊D5—821no—
74C3×C41—21no—
75C3×C41D3×C5⋊D511yescharacteristic, complemented
76C3×C41C2×C3×C5⋊D511yescharacteristic, complemented
77C2×C5⋊D5—1231noHall
78C3×D15—56no—
79C3×C5×D3—416no—
80C32×D5—2056no—
81C2×C41—751no—
82D41—31no—
83D41—251no—
84C3×C52—21no—
85C3×C52D3×D4111yescharacteristic, complemented
86C3×C52C2×C3×D4111yescharacteristic, complemented
87C2×C3×D5—6156no—
88D3×D5—2056no—
89C2×C52—1231no—
90C5⋊D5—31no—
91C5⋊D5—411no—
92C32×C5D5×D4116yescomplemented
93C41C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
94C2×C3×D3—10251noHall
95C2×C3×C5—1236no—
96D15—56no—
97C3×D5—156no—
98C3×D5—4106no—
99C3×D5—2056no—
100C3×D5—2056no—
101C5×D3—416no—
102C52C3×D3×D4111yescharacteristic, complemented, Sylow
103C2×D5—6156no—
104C2×C32—10251no—
105C3×D3—251no—
106C3×D3—411no—
107C3×C5—26no—
108C3×C5C3×D5×D4116yescomplemented
109C3×C5D15⋊D4116yescomplemented
110C22×C3—30751no—
111C2×D3—10251no—
112C2×C5—1236no—
113D5—156no—
114D5—2056no—
115C32C5⋊D5×D4111yescharacteristic, complemented, Sylow
116C2×C3—10251no—
117C2×C3—10251no—
118C2×C3—20501no—
119C2×C3—751no—
120C2×C3—1231no—
121D3—251no—
122D3—411no—
123C5C3×D15⋊D4116yescomplemented
124C22—30751noSylow
125C3—21no—
126C3C3×C5⋊D5×D4111yescharacteristic, complemented
127C3D123⋊(C5⋊D5)11yescharacteristic, direct product factor
128C2—10251no—
129C2—751no—
130C2—1231no—
subgroupG/H
center, hypercenterC3D123⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C41C22×C3
FrattiniC1G
Fitting, socleC32×C52×C41C22
LCSG ▷ C3×C52×C41
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊D205C2semidirect
2. C3×C52×D123C2semidirect
3. C3×C41×C3⋊(C5⋊D5)C2semidirect
4. D123⋊(C5⋊D5)C3direct (N × H)
6. C32×C52×C41C22semidirect
8. C41×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D123C2×C3semidirect
11. C3×C5⋊D205D3semidirect
12. C3×C5⋊D205C2×C3semidirect
17. C3×C5×D123D5semidirect
20. C3×C52×C41C2×D3semidirect
21. C3×C52×C41C22×C3semidirect
24. C5⋊D205C3×D3semidirect
27. C32×C5×C41C2×D5semidirect
30. C5×D123C3×D5semidirect
36. C52×C41C2×C3×D3semidirect
39. C3×D123C5⋊D5semidirect
43. C3×C5×C41D3×D5semidirect
44. C3×C5×C41C2×C3×D5semidirect
47. C3×C3⋊(C5⋊D5)D41semidirect
53. C32×C41C2×C5⋊D5semidirect
57. D123C3×C5⋊D5semidirect
63. C32×C52C2×D41semidirect
64. C5×C41C3×D3×D5semidirect
68. C3⋊(C5⋊D5)C3×D41semidirect
75. C3×C41D3×C5⋊D5semidirect
76. C3×C41C2×C3×C5⋊D5semidirect
85. C3×C52D3×D41semidirect
86. C3×C52C2×C3×D41semidirect
92. C32×C5D5×D41semidirect
93. C41C3×D3×C5⋊D5semidirect
102. C52C3×D3×D41semidirect
108. C3×C5C3×D5×D41semidirect
109. C3×C5D15⋊D41semidirect
115. C32C5⋊D5×D41semidirect
123. C5C3×D15⋊D41semidirect
126. C3C3×C5⋊D5×D41semidirect
127. C3D123⋊(C5⋊D5)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5⋊D2052
C3×C52×D1232
C3×C41×C3⋊(C5⋊D5)2
D123⋊(C5⋊D5)3
C3×C5⋊D5×D413
C3×D15⋊D415
C3×D3×C5⋊D541