Finite Group Databasebeta

← D93⋊(C3⋊(C5⋊D5)) #42124942

Subgroups — D93⋊(C3⋊(C5⋊D5)) #42124942

Order 27900.

352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 85 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×C52×D93C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D155)C211yesmaximal, characteristic, complemented
3C31×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4D93⋊(C5⋊D5)—31nomaximal
5D31×C3⋊(C5⋊D5)—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7D93⋊D15—56nomaximal
8C3⋊(C5⋊D155)D311yescharacteristic, complemented
9C31×C3⋊(C5⋊D5)—31no—
10C31×C3⋊(C5⋊D5)—31no—
11C31×C3⋊(C5⋊D5)—61no—
12C52×D93D311yescharacteristic, complemented
13C3×C5⋊D155—31no—
14C3×C52×D31—31no—
15C5⋊D5×D31—91noHall
16C31×C3⋊D15—56no—
17C3×D465—56no—
18C3×C5×D93D516yescomplemented
19C3×C52×C31—21no—
20C3×C52×C31C2×D311yescharacteristic, complemented
21C3×C52×C31C2×D311yescharacteristic, complemented
22D15⋊D31—156no—
23D15×D31—156no—
24C5⋊D155—31no—
25C31×C5⋊D5—91no—
26C52×D31—31no—
27C32×C5×C31C2×D516yescomplemented
28(C3⋊D3)⋊D31—251noHall
29D465—56no—
30D15×C31—156no—
31D15×C31—156no—
32D15×C31—306no—
33C5×D93D1516yescomplemented
34C3×D155—156no—
35C3×C5×D31—36no—
36D3×C3⋊(C5⋊D5)—311nomaximal, Hall
37C52×C31D3211yescharacteristic, complemented, Hall
38D5×D31—456no—
39C3⋊D3×C31—251no—
40C3×D93—251no—
41C3×D93C5⋊D511yescharacteristic, complemented
42C3×C5×C31—26no—
43C3×C5×C31D3×D516yescomplemented
44C3×C5×C31C2×D1516yescomplemented
45C3⋊(C3⋊(C5⋊D5))D3111yescharacteristic, complemented
46C3×C3⋊(C5⋊D5)—311no—
47C3×C52×D3—311no—
48D3×D31—751no—
49D3×D31—751no—
50D155—156no—
51C5×D31—36no—
52D5×C31—456no—
53C2×C3⋊(C5⋊D5)—931no—
54D3×C5⋊D5—931no—
55C32×C31C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D3111yescharacteristic, complemented, Hall
57D93—251no—
58D93C3⋊(C5⋊D5)11yescharacteristic, complemented
59C3×D31—31no—
60C3×D31—751no—
61D3×C31—751no—
62D3×C31—751no—
63D3×C31—1501no—
64D3×D15—1556no—
65C5×C31D3×D1516yescomplemented
66C2×C3×C52—931no—
67C3⋊(C5⋊D5)—31no—
68C3⋊(C5⋊D5)—31no—
69C3⋊(C5⋊D5)—61no—
70C3⋊(C5⋊D5)—311no—
71C52×D3—311no—
72C3×C5⋊D5—931no—
73C2×D31—2251noHall
74C2×C5⋊D5—2791noHall
75C3×C31—21no—
76C3×C31D3×C5⋊D511yescharacteristic, complemented
77C3×C31C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
78C3⋊D15—56no—
79C3×D15—1556no—
80C3×C5×D3—316no—
81C3×C52—21no—
82C3×C52D3×D3111yescharacteristic, complemented
83C3×C52D3×D3111yescharacteristic, complemented
84C2×C31—2251no—
85D31—31no—
86D31—751no—
87C2×D15—4656no—
88D3×D5—4656no—
89C2×C52—931no—
90C5⋊D5—91no—
91C5⋊D5—931no—
92C32×C5D5×D3116yescomplemented
93D32—7751noHall
94C31D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
95C2×C3×C5—936no—
96D15—156no—
97D15—156no—
98D15—306no—
99D15—1556no—
100C3×D5—4656no—
101C5×D3—316no—
102C52(C3⋊D3)⋊D3111yescharacteristic, complemented, Sylow
103C2×D5—13956no—
104C3⋊D3—251no—
105C3×D3—7751no—
106C3×D3—311no—
107C3×C5—26no—
108C3×C5D15×D3116yescomplemented
109C3×C5D15⋊D3116yescomplemented
110C2×D3—23251no—
111C2×D3—23251no—
112C2×C5—936no—
113D5—456no—
114D5—4656no—
115C32C5⋊D5×D3111yescharacteristic, complemented, Sylow
116C2×C3—23251no—
117C2×C3—931no—
118D3—7751no—
119D3—311no—
120D3—751no—
121D3—751no—
122D3—1501no—
123C5D93⋊D1516yescomplemented
124C22—69751noSylow
125C3—21no—
126C3D31×C3⋊(C5⋊D5)11yescharacteristic, complemented
127C3D93⋊(C5⋊D5)11yescharacteristic, complemented
128C2—23251no—
129C2—931no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C31C22
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×D93C2semidirect
2. C3×C3⋊(C5⋊D155)C2semidirect
3. C31×C3⋊(C3⋊(C5⋊D5))C2semidirect
6. C32×C52×C31C22semidirect
8. C3⋊(C5⋊D155)D3semidirect
12. C52×D93D3semidirect
18. C3×C5×D93D5semidirect
20. C3×C52×C31C2×D3semidirect
21. C3×C52×C31C2×D3semidirect
27. C32×C5×C31C2×D5semidirect
33. C5×D93D15semidirect
37. C52×C31D32semidirect
41. C3×D93C5⋊D5semidirect
43. C3×C5×C31D3×D5semidirect
44. C3×C5×C31C2×D15semidirect
45. C3⋊(C3⋊(C5⋊D5))D31semidirect
55. C32×C31C2×C5⋊D5semidirect
56. C32×C52C2×D31semidirect
58. D93C3⋊(C5⋊D5)semidirect
65. C5×C31D3×D15semidirect
76. C3×C31D3×C5⋊D5semidirect
77. C3×C31C2×C3⋊(C5⋊D5)semidirect
82. C3×C52D3×D31semidirect
83. C3×C52D3×D31semidirect
92. C32×C5D5×D31semidirect
94. C31D3×C3⋊(C5⋊D5)semidirect
102. C52(C3⋊D3)⋊D31semidirect
108. C3×C5D15×D31semidirect
109. C3×C5D15⋊D31semidirect
115. C32C5⋊D5×D31semidirect
123. C5D93⋊D15semidirect
126. C3D31×C3⋊(C5⋊D5)semidirect
127. C3D93⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D932
C3×C3⋊(C5⋊D155)2
C31×C3⋊(C3⋊(C5⋊D5))2
D93⋊(C5⋊D5)3
D31×C3⋊(C5⋊D5)3
D93⋊D155
D3×C3⋊(C5⋊D5)31