Finite Group Databasebeta

← C3×D93⋊(C5⋊D5) #42124918

Subgroups — C3×D93⋊(C5⋊D5) #42124918

Order 27900.

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⋊D155C211yesmaximal, characteristic, complemented
2C3×C52×D93C211yesmaximal, characteristic, complemented
3C3×C31×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4D93⋊(C5⋊D5)C311yesmaximal, characteristic, direct product factor
5C3×C5⋊D5×D31—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C3×D15⋊D31—56nomaximal
8C31×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D93C2×C311yescharacteristic, complemented
10C3×C5⋊D155—21no—
11C3×C5⋊D155D311yescharacteristic, complemented
12C3×C5⋊D155C2×C311yescharacteristic, complemented
13C3×C31×C5⋊D5—31no—
14C3×C52×D31—31no—
15C5⋊D5×D31—31noHall
16C3×D15×C31—56no—
17C3×C5×D93D516yescomplemented
18C32×D155—56no—
19C3×C52×C31—21no—
20C3×C52×C31C2×D311yescharacteristic, complemented
21C3×C52×C31C22×C311yescharacteristic, complemented
22D15⋊D31—56no—
23C3×D5×D31—156no—
24C5⋊D155C3×D311yescharacteristic, complemented
25C31×C5⋊D5—31no—
26C52×D31—31no—
27C32×C5×C31C2×D516yescomplemented
28C3×D3×D31—251noHall
29D15×C31—56no—
30C5×D93C3×D516yescomplemented
31C3×D155—56no—
32C3×D155—56no—
33C3×D155—106no—
34C3×D5×C31—156no—
35C3×C5×D31—36no—
36C3×D3×C5⋊D5—311nomaximal, Hall
37C52×C31C2×C3×D311yescharacteristic, complemented, Hall
38D5×D31—156no—
39C3×D93C5⋊D511yescharacteristic, complemented
40C3×D3×C31—251no—
41C32×D31—251no—
42C3×C5×C31—26no—
43C3×C5×C31D3×D516yescomplemented
44C3×C5×C31C2×C3×D516yescomplemented
45C3×C3⋊(C5⋊D5)D3111yescharacteristic, complemented
46C3×C52×D3—311no—
47C32×C5⋊D5—311no—
48C2×C3×D31—751no—
49D3×D31—251no—
50D155—56no—
51C5×D31—36no—
52D5×C31—156no—
53C2×C3×C5⋊D5—931no—
54D3×C5⋊D5—311no—
55C32×C31C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—751no—
58D93C3×C5⋊D511yescharacteristic, complemented
59C3×D31—31no—
60C3×D31—251no—
61C3×D31—251no—
62C3×D31—501no—
63D3×C31—251no—
64C3×D3×D5—1556no—
65C5×C31C3×D3×D516yescomplemented
66C2×C3×C52—931no—
67C3⋊(C5⋊D5)C3×D3111yescharacteristic, complemented
68C52×D3—311no—
69C3×C5⋊D5—31no—
70C3×C5⋊D5—311no—
71C3×C5⋊D5—311no—
72C3×C5⋊D5—621no—
73C2×D31—751noHall
74C2×C5⋊D5—931noHall
75C3×C31—21no—
76C3×C31D3×C5⋊D511yescharacteristic, complemented
77C3×C31C2×C3×C5⋊D511yescharacteristic, complemented
78C3×D15—56no—
79C3×C5×D3—316no—
80C32×D5—1556no—
81C3×C52—21no—
82C3×C52D3×D3111yescharacteristic, complemented
83C3×C52C2×C3×D3111yescharacteristic, complemented
84C2×C31—751no—
85D31—31no—
86D31—251no—
87C2×C3×D5—4656no—
88D3×D5—1556no—
89C2×C52—931no—
90C5⋊D5—31no—
91C5⋊D5—311no—
92C32×C5D5×D3116yescomplemented
93C2×C3×D3—7751noHall
94C31C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
95C2×C3×C5—936no—
96D15—56no—
97C3×D5—156no—
98C3×D5—3106no—
99C3×D5—1556no—
100C3×D5—1556no—
101C5×D3—316no—
102C52C3×D3×D3111yescharacteristic, complemented, Sylow
103C2×D5—4656no—
104C2×C32—7751no—
105C3×D3—251no—
106C3×D3—311no—
107C3×C5—26no—
108C3×C5C3×D5×D3116yescomplemented
109C3×C5D15⋊D3116yescomplemented
110C22×C3—23251no—
111C2×D3—7751no—
112C2×C5—936no—
113D5—156no—
114D5—1556no—
115C32C5⋊D5×D3111yescharacteristic, complemented, Sylow
116C2×C3—7751no—
117C2×C3—7751no—
118C2×C3—15501no—
119C2×C3—751no—
120C2×C3—931no—
121D3—251no—
122D3—311no—
123C5C3×D15⋊D3116yescomplemented
124C22—23251noSylow
125C3—21no—
126C3C3×C5⋊D5×D3111yescharacteristic, complemented
127C3D93⋊(C5⋊D5)11yescharacteristic, direct product factor
128C2—7751no—
129C2—751no—
130C2—931no—
subgroupG/H
center, hypercenterC3D93⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C31C22×C3
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C3×C52×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊D155C2semidirect
2. C3×C52×D93C2semidirect
3. C3×C31×C3⋊(C5⋊D5)C2semidirect
4. D93⋊(C5⋊D5)C3direct (N × H)
6. C32×C52×C31C22semidirect
8. C31×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D93C2×C3semidirect
11. C3×C5⋊D155D3semidirect
12. C3×C5⋊D155C2×C3semidirect
17. C3×C5×D93D5semidirect
20. C3×C52×C31C2×D3semidirect
21. C3×C52×C31C22×C3semidirect
24. C5⋊D155C3×D3semidirect
27. C32×C5×C31C2×D5semidirect
30. C5×D93C3×D5semidirect
37. C52×C31C2×C3×D3semidirect
39. C3×D93C5⋊D5semidirect
43. C3×C5×C31D3×D5semidirect
44. C3×C5×C31C2×C3×D5semidirect
45. C3×C3⋊(C5⋊D5)D31semidirect
55. C32×C31C2×C5⋊D5semidirect
56. C32×C52C2×D31semidirect
58. D93C3×C5⋊D5semidirect
65. C5×C31C3×D3×D5semidirect
67. C3⋊(C5⋊D5)C3×D31semidirect
76. C3×C31D3×C5⋊D5semidirect
77. C3×C31C2×C3×C5⋊D5semidirect
82. C3×C52D3×D31semidirect
83. C3×C52C2×C3×D31semidirect
92. C32×C5D5×D31semidirect
94. C31C3×D3×C5⋊D5semidirect
102. C52C3×D3×D31semidirect
108. C3×C5C3×D5×D31semidirect
109. C3×C5D15⋊D31semidirect
115. C32C5⋊D5×D31semidirect
123. C5C3×D15⋊D31semidirect
126. C3C3×C5⋊D5×D31semidirect
127. C3D93⋊(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⋊D1552
C3×C52×D932
C3×C31×C3⋊(C5⋊D5)2
D93⋊(C5⋊D5)3
C3×C5⋊D5×D313
C3×D15⋊D315
C3×D3×C5⋊D531