Finite Group Databasebeta

← C3⋊(C5⋊D5)×D93 #42124943

Subgroups — C3⋊(C5⋊D5)×D93 #42124943

Order 27900.

352 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 86 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×C31×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D155))C211yesmaximal, characteristic, complemented
4C5⋊D5×D93—31nomaximal
5D31×C3⋊(C5⋊D5)—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7D15×D93—56nomaximal
8C3⋊(C5⋊D155)—31no—
9C3⋊(C5⋊D155)—31no—
10C3⋊(C5⋊D155)—61no—
11C31×C3⋊(C5⋊D5)D311yescharacteristic, complemented
12C52×D93D311yescharacteristic, complemented
13C3×C31×C5⋊D5—31no—
14C3×C52×D31—31no—
15C5⋊D5×D31—91noHall
16C3⋊D465—56no—
17C3×D15×C31—56no—
18C3×C5×D93D516yescomplemented
19C3×C52×C31—21no—
20C3×C52×C31C2×D311yescharacteristic, complemented
21C3×C52×C31C2×D311yescharacteristic, complemented
22D5×D93—156no—
23D15×D31—156no—
24C5⋊D155—91no—
25C31×C5⋊D5—31no—
26C52×D31—31no—
27C32×C5×C31C2×D516yescomplemented
28D3×D93—251noHall
29D465—156no—
30D465—156no—
31D465—306no—
32D15×C31—56no—
33C5×D93D1516yescomplemented
34C3×D5×C31—156no—
35C3×C5×D31—36no—
36D3×C3⋊(C5⋊D5)—311nomaximal, Hall
37C52×C31D3211yescharacteristic, complemented, Hall
38D5×D31—456no—
39C3⋊D93—251no—
40C3×D93C5⋊D511yescharacteristic, complemented
41C3×D3×C31—251no—
42C3×C5×C31—26no—
43C3×C5×C31D3×D516yescomplemented
44C3×C5×C31C2×D1516yescomplemented
45C3⋊(C3⋊(C5⋊D5))—311no—
46C3×C3⋊(C5⋊D5)D3111yescharacteristic, complemented
47C3×C52×D3—311no—
48C2×D93—751no—
49D3×D31—751no—
50D155—456no—
51C5×D31—36no—
52D5×C31—156no—
53C2×C3⋊(C5⋊D5)—931no—
54D3×C5⋊D5—931no—
55C32×C31C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—751no—
58D93—751no—
59D93—751no—
60D93—1501no—
61D93C3⋊(C5⋊D5)11yescharacteristic, direct product factor
62C3×D31—31no—
63D3×C31—251no—
64D3×D15—1556no—
65C5×C31D3×D1516yescomplemented
66C2×C3×C52—931no—
67C3⋊(C5⋊D5)—931no—
68C3⋊(C5⋊D5)—931no—
69C3⋊(C5⋊D5)—1861no—
70C3⋊(C5⋊D5)D9311yescharacteristic, direct product factor
71C52×D3—311no—
72C3×C5⋊D5—31no—
73C2×D31—2251noHall
74C2×C5⋊D5—2791noHall
75C3×C31—21no—
76C3×C31D3×C5⋊D511yescharacteristic, complemented
77C3×C31C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
78C3⋊D15—1556no—
79C3×D15—56no—
80C3×C5×D3—316no—
81C3×C52—21no—
82C3×C52D3×D3111yescharacteristic, complemented
83C3×C52C2×D9311yescharacteristic, complemented
84C2×C31—751no—
85D31—31no—
86D31—2251no—
87C2×D15—4656no—
88D3×D5—4656no—
89C2×C52—931no—
90C5⋊D5—31no—
91C5⋊D5—2791no—
92C32×C5D5×D3116yescomplemented
93D32—7751noHall
94C31D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
95C2×C3×C5—936no—
96D15—56no—
97D15—9306no—
98D15—4656no—
99D15—4656no—
100C3×D5—156no—
101C5×D3—316no—
102C52D3×D9311yescharacteristic, complemented, Sylow
103C2×D5—13956no—
104C3⋊D3—7751no—
105C3×D3—251no—
106C3×D3—311no—
107C3×C5—26no—
108C3×C5D15×D3116yescomplemented
109C3×C5D5×D9316yescomplemented
110C2×D3—23251no—
111C2×D3—23251no—
112C2×C5—936no—
113D5—156no—
114D5—13956no—
115C32C5⋊D5×D3111yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—931no—
118D3—23251no—
119D3—23251no—
120D3—251no—
121D3—311no—
122D3—46501no—
123C5D15×D9316yescomplemented
124C22—69751noSylow
125C3—21no—
126C3D31×C3⋊(C5⋊D5)11yescharacteristic, complemented
127C3C5⋊D5×D9311yescharacteristic, complemented
128C2—69751no—
129C2—751no—
130C2—931no—
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×C31×C3⋊(C5⋊D5)C2semidirect
3. C3⋊(C3⋊(C5⋊D155))C2semidirect
6. C32×C52×C31C22semidirect
11. C31×C3⋊(C5⋊D5)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
40. C3×D93C5⋊D5semidirect
43. C3×C5×C31D3×D5semidirect
44. C3×C5×C31C2×D15semidirect
46. C3×C3⋊(C5⋊D5)D31semidirect
55. C32×C31C2×C5⋊D5semidirect
56. C32×C52C2×D31semidirect
61. D93C3⋊(C5⋊D5)direct (N × H)
65. C5×C31D3×D15semidirect
70. C3⋊(C5⋊D5)D93direct (N × H)
76. C3×C31D3×C5⋊D5semidirect
77. C3×C31C2×C3⋊(C5⋊D5)semidirect
82. C3×C52D3×D31semidirect
83. C3×C52C2×D93semidirect
92. C32×C5D5×D31semidirect
94. C31D3×C3⋊(C5⋊D5)semidirect
102. C52D3×D93semidirect
108. C3×C5D15×D31semidirect
109. C3×C5D5×D93semidirect
115. C32C5⋊D5×D31semidirect
123. C5D15×D93semidirect
126. C3D31×C3⋊(C5⋊D5)semidirect
127. C3C5⋊D5×D93semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D932
C3×C31×C3⋊(C5⋊D5)2
C3⋊(C3⋊(C5⋊D155))2
C5⋊D5×D933
D31×C3⋊(C5⋊D5)3
D15×D935
D3×C3⋊(C5⋊D5)31