Finite Group Databasebeta

← C3×D11×C5⋊D55 #49137730

Subgroups — C3×D11×C5⋊D55 #49137730

Order 36300.

480 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 104 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×C11×D11C211yesmaximal, characteristic, complemented
2C3×C11×C5⋊D55C211yesmaximal, characteristic, complemented
3C3×C5⋊(C5⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4D11×C5⋊D55C311yesmaximal, characteristic, direct product factor, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6C3×D11×D55—56nomaximal
7C5⋊(C5⋊(C11⋊D11))C2×C311yescharacteristic, complemented
8C11×C5⋊D55C2×C311yescharacteristic, complemented
9C52×C11×D11C2×C311yescharacteristic, complemented
10C3×C5⋊(C11⋊D11)—56no—
11C3×C11×D55—56no—
12C3×C5×C11×D11D516yescomplemented
13C2×C3×C5⋊D55—111nomaximal
14C3×D11×C5⋊D5—111nomaximal
15C52×C112C22×C311yescharacteristic, complemented, Hall
16D11×D55—56no—
17C3×C5×C112C2×D516yescomplemented
18C2×C3×C52×C11—111no—
19C3×C5⋊D55—111no—
20C3×C5⋊D55—111no—
21C3×C5⋊D55—225no—
22C3×C5⋊D55D1111yescharacteristic, direct product factor
23C3×C11×C5⋊D5—111no—
24C3×C52×D11D1111yescharacteristic, complemented
25C3×D112—251noHall
26C5⋊(C11⋊D11)—56no—
27C11×D55—56no—
28C5×C11×D11C3×D516yescomplemented
29C2×C5⋊D55—111no—
30D11×C5⋊D5—111no—
31C3×C52×C11—25no—
32C3×C52×C11C2×D1111yescharacteristic, complemented
33C3×C52×C11C2×D1111yescharacteristic, complemented
34C3×C11⋊D11—251no—
35C3×C11×D11—251no—
36C3×C11×D11C5⋊D511yescharacteristic, complemented
37C2×C3×D55—556no—
38C3×D5×D11—556no—
39C5×C112C2×C3×D516yescomplemented
40C2×C52×C11—111no—
41C5⋊D55—111no—
42C5⋊D55—111no—
43C5⋊D55—225no—
44C5⋊D55C3×D1111yescharacteristic, direct product factor
45C11×C5⋊D5—111no—
46C52×D11C3×D1111yescharacteristic, complemented
47D112—251noHall
48C3×C112C2×C5⋊D511yescharacteristic, complemented, Hall
49C2×C3×C5×C11—116no—
50C3×D55—56no—
51C3×D55—556no—
52C3×D55—556no—
53C3×D55—11030no—
54C3×D5×C11—556no—
55C3×C5×D11D5516yescomplemented
56C2×C3×C5⋊D5—1211noHall
57C52×C11—25no—
58C52×C11C2×C3×D1111yescharacteristic, complemented
59C52×C11C2×C3×D1111yescharacteristic, complemented
60C11⋊D11—251no—
61C11×D11—251no—
62C11×D11C3×C5⋊D511yescharacteristic, complemented
63C2×D55—556no—
64D5×D11—556no—
65C3×C5×C11—230no—
66C3×C5×C11D5×D1116yescomplemented
67C3×C5×C11C2×D5516yescomplemented
68C2×C3×C52—111no—
69C3×C5⋊D5—111no—
70C3×C5⋊D5—1211no—
71C2×C3×D11—2751no—
72C2×C3×D11—2751no—
73C112C2×C3×C5⋊D511yescharacteristic, complemented, Sylow
74C2×C5×C11—116no—
75D55—56no—
76D55—556no—
77D55—556no—
78D55—11030no—
79C5×D11C3×D5516yescomplemented
80D5×C11—556no—
81C2×C5⋊D5—1211noHall
82C3×C52D11211yescharacteristic, complemented, Hall
83C2×C3×C11—111no—
84C2×C3×C11—2751no—
85C3×D11—2751no—
86C3×D11—2751no—
87C3×D11—251no—
88C3×D11—5505no—
89C3×D11C5⋊D5511yescharacteristic, direct product factor
90C2×C3×D5—6056no—
91C5×C11—230no—
92C5×C11C3×D5×D1116yescomplemented
93C5×C11C2×C3×D5516yescomplemented
94C2×C52—111no—
95C5⋊D5—111no—
96C5⋊D5—1211no—
97C2×D11—2751no—
98C2×D11—2751no—
99C3×C11—25no—
100C3×C11D11×C5⋊D511yescharacteristic, complemented
101C3×C11C2×C5⋊D5511yescharacteristic, complemented
102C2×C3×C5—116no—
103C3×D5—556no—
104C3×D5—6056no—
105C52C3×D11211yescharacteristic, complemented, Sylow
106C2×C11—111no—
107C2×C11—2751no—
108D11—2751no—
109D11—2751no—
110D11—251no—
111D11—5505no—
112D11C3×C5⋊D5511yescharacteristic, direct product factor
113C2×D5—6056no—
114C3×C5D11×D5516yescomplemented
115C22×C3—30251noHall
116C11—25no—
117C11C3×D11×C5⋊D511yescharacteristic, complemented
118C11C2×C3×C5⋊D5511yescharacteristic, complemented
119C2×C5—116no—
120D5—556no—
121D5—6056no—
122C2×C3—111no—
123C2×C3—2751no—
124C2×C3—30251no—
125C5C3×D11×D5516yescomplemented
126C22—30251noSylow
127C3D11×C5⋊D5511yescharacteristic, direct product factor, Sylow
128C2—111no—
129C2—2751no—
130C2—30251no—
subgroupG/H
center, hypercenterC3D11×C5⋊D55
commutator, cosocle, hypocenterC52×C112C22×C3
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C52×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D11C2semidirect
2. C3×C11×C5⋊D55C2semidirect
3. C3×C5⋊(C5⋊(C11⋊D11))C2semidirect
4. D11×C5⋊D55C3direct (N × H)
5. C3×C52×C112C22semidirect
7. C5⋊(C5⋊(C11⋊D11))C2×C3semidirect
8. C11×C5⋊D55C2×C3semidirect
9. C52×C11×D11C2×C3semidirect
12. C3×C5×C11×D11D5semidirect
15. C52×C112C22×C3semidirect
17. C3×C5×C112C2×D5semidirect
22. C3×C5⋊D55D11direct (N × H)
24. C3×C52×D11D11semidirect
28. C5×C11×D11C3×D5semidirect
32. C3×C52×C11C2×D11semidirect
33. C3×C52×C11C2×D11semidirect
36. C3×C11×D11C5⋊D5semidirect
39. C5×C112C2×C3×D5semidirect
44. C5⋊D55C3×D11direct (N × H)
46. C52×D11C3×D11semidirect
48. C3×C112C2×C5⋊D5semidirect
55. C3×C5×D11D55semidirect
58. C52×C11C2×C3×D11semidirect
59. C52×C11C2×C3×D11semidirect
62. C11×D11C3×C5⋊D5semidirect
66. C3×C5×C11D5×D11semidirect
67. C3×C5×C11C2×D55semidirect
73. C112C2×C3×C5⋊D5semidirect
79. C5×D11C3×D55semidirect
82. C3×C52D112semidirect
89. C3×D11C5⋊D55direct (N × H)
92. C5×C11C3×D5×D11semidirect
93. C5×C11C2×C3×D55semidirect
100. C3×C11D11×C5⋊D5semidirect
101. C3×C11C2×C5⋊D55semidirect
105. C52C3×D112semidirect
112. D11C3×C5⋊D55direct (N × H)
114. C3×C5D11×D55semidirect
117. C11C3×D11×C5⋊D5semidirect
118. C11C2×C3×C5⋊D55semidirect
125. C5C3×D11×D55semidirect
127. C3D11×C5⋊D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×C11×D112
C3×C11×C5⋊D552
C3×C5⋊(C5⋊(C11⋊D11))2
D11×C5⋊D553
C3×D11×D555
C2×C3×C5⋊D5511
C3×D11×C5⋊D511