Finite Group Databasebeta

← D15⋊(C5⋊(C11⋊D11)) #49137785

Subgroups — D15⋊(C5⋊(C11⋊D11)) #49137785

Order 36300.

672 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 145 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×C5⋊(C5⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
2C5×C112×D15C211yesmaximal, characteristic, complemented
3C5×C3⋊(C5⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4D5×C5⋊(C11⋊D11)—31nomaximal, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6D15⋊(C11⋊D11)—51nomaximal
7D3×C5⋊(C11⋊D11)—51nomaximal
8C5⋊(C5⋊(C11⋊D11))D311yescharacteristic, complemented
9C5×C5⋊(C11⋊D11)—31no—
10C5×D5×C112—31no—
11C3⋊(C5⋊(C11⋊D11))D511yescharacteristic, complemented
12C112×D15D511yescharacteristic, complemented
13C5×C3⋊(C11⋊D11)—51no—
14C5×D3×C112—51no—
15C3×C5⋊(C11⋊D11)—51no—
16C3×C5⋊(C11⋊D11)—51no—
17C3×C5⋊(C11⋊D11)—102no—
18D15⋊D55—1112nomaximal
19C52×C112C2×D311yescharacteristic, complemented, Hall
20C2×C5⋊(C11⋊D11)—151no—
21D5×C11⋊D11—151no—
22C3×C5×C112—22no—
23C3×C5×C112C2×D511yescharacteristic, complemented
24C3×C5×C112C2×D511yescharacteristic, complemented
25C5×D165—1112no—
26C5×C11×D15D11112yescomplemented
27C3×C5⋊D55—1112no—
28D3×C11⋊D11—251noHall
29C2×C5×C112—151no—
30C5⋊(C11⋊D11)—31no—
31C5⋊(C11⋊D11)—51no—
32C5⋊(C11⋊D11)—51no—
33C5⋊(C11⋊D11)—102no—
34D5×C112—31no—
35C5×C11⋊D11—151no—
36D5×D55—3312no—
37C3×C52×C11C2×D11112yescomplemented
38C3⋊(C11⋊D11)—51no—
39D3×C112—51no—
40C3×C11⋊D11—251no—
41D15⋊D11—5512no—
42D3×D55—5512no—
43C5×C112—22no—
44C5×C112D3×D511yescharacteristic, complemented
45C5×C112D3×D511yescharacteristic, complemented
46C5⋊D55—1112no—
47C5×D55—3312no—
48C5×D5×C11—312no—
49C2×C11⋊D11—751noHall
50C3×C112D5211yescharacteristic, complemented, Hall
51D165—1112no—
52C11×D15D55112yescomplemented
53C5×D33—5512no—
54C5×D3×C11—512no—
55C3×D55—5512no—
56C3×D55—5512no—
57C3×D55—11024no—
58D15⋊D5—1211noHall
59C52×C11D3×D11112yescomplemented
60C2×C112—151no—
61C11⋊D11—151no—
62C11⋊D11—251no—
63C2×D55—16512no—
64D5×D11—16512no—
65C3×C5×C11—224no—
66C3×C5×C11D5×D11112yescomplemented
67C3×C5×C11C2×D55112yescomplemented
68C5×D15—1211no—
69C5×D15C11⋊D1111yescharacteristic, complemented
70C3×C5⋊D5—1211no—
71D3×D11—27512no—
72C112D15⋊D511yescharacteristic, complemented, Sylow
73C2×C5×C11—1512no—
74D55—3312no—
75D55—5512no—
76D55—5512no—
77D55—11024no—
78C5×D11—16512no—
79D5×C11—312no—
80D52—3631noHall
81C3×C52C2×C11⋊D1111yescharacteristic, complemented, Hall
82D33—5512no—
83C3×D11—27512no—
84D3×C11—512no—
85D3×D5—6051no—
86D3×D5—6051no—
87C5×C11—224no—
88C5×C11D3×D55112yescomplemented
89C5×C11D15⋊D11112yescomplemented
90C5⋊D5—1211no—
91C5×D5—31no—
92C5×D5—3631no—
93C2×D11—82512no—
94C3×C11D5×D55112yescomplemented
95D15—1211no—
96D15C5⋊(C11⋊D11)11yescharacteristic, complemented
97C3×D5—6051no—
98C3×D5—6051no—
99C3×D5—12102no—
100C5×D3—51no—
101C5×D3—6051no—
102C52D3×C11⋊D1111yescharacteristic, complemented, Sylow
103C2×C11—1512no—
104D11—27512no—
105D11—16512no—
106C2×D5—18151no—
107C2×D5—18151no—
108C3×C5—22no—
109C3×C5D5×C11⋊D1111yescharacteristic, complemented
110C3×C5C2×C5⋊(C11⋊D11)11yescharacteristic, complemented
111C2×D3—30251noHall
112C11D15⋊D55112yescomplemented
113C2×C5—151no—
114C2×C5—18151no—
115D5—31no—
116D5—6051no—
117D5—6051no—
118D5—3631no—
119D5—12102no—
120C2×C3—30251no—
121D3—51no—
122D3—6051no—
123C5—22no—
124C5D3×C5⋊(C11⋊D11)11yescharacteristic, complemented
125C5D15⋊(C11⋊D11)11yescharacteristic, complemented
126C22—90751noSylow
127C3D5×C5⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
128C2—151no—
129C2—18151no—
130C2—30251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C112C22
LCSG ▷ C3×C52×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊(C5⋊(C11⋊D11))C2semidirect
2. C5×C112×D15C2semidirect
3. C5×C3⋊(C5⋊(C11⋊D11))C2semidirect
5. C3×C52×C112C22semidirect
8. C5⋊(C5⋊(C11⋊D11))D3semidirect
11. C3⋊(C5⋊(C11⋊D11))D5semidirect
12. C112×D15D5semidirect
19. C52×C112C2×D3semidirect
23. C3×C5×C112C2×D5semidirect
24. C3×C5×C112C2×D5semidirect
26. C5×C11×D15D11semidirect
37. C3×C52×C11C2×D11semidirect
44. C5×C112D3×D5semidirect
45. C5×C112D3×D5semidirect
50. C3×C112D52semidirect
52. C11×D15D55semidirect
59. C52×C11D3×D11semidirect
66. C3×C5×C11D5×D11semidirect
67. C3×C5×C11C2×D55semidirect
69. C5×D15C11⋊D11semidirect
72. C112D15⋊D5semidirect
81. C3×C52C2×C11⋊D11semidirect
88. C5×C11D3×D55semidirect
89. C5×C11D15⋊D11semidirect
94. C3×C11D5×D55semidirect
96. D15C5⋊(C11⋊D11)semidirect
102. C52D3×C11⋊D11semidirect
109. C3×C5D5×C11⋊D11semidirect
110. C3×C5C2×C5⋊(C11⋊D11)semidirect
112. C11D15⋊D55semidirect
124. C5D3×C5⋊(C11⋊D11)semidirect
125. C5D15⋊(C11⋊D11)semidirect
127. C3D5×C5⋊(C11⋊D11)semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊(C5⋊(C11⋊D11))2
C5×C112×D152
C5×C3⋊(C5⋊(C11⋊D11))2
D5×C5⋊(C11⋊D11)3
D15⋊(C11⋊D11)5
D3×C5⋊(C11⋊D11)5
D15⋊D5511