Finite Group Databasebeta

← D15⋊#11925898 #49137513

Subgroups — D15⋊#11925898 #49137513

Order 36300.

200 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D15×#10597244C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925898C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925898C211yesmaximal, characteristic, complemented
4D5×#11925898—31nomaximal, Hall
5C3×C5×#10597244C2211yescharacteristic, complemented, Hall
6C11×D15⋊D11C511yesmaximal, characteristic, complemented
7D3×#11925898—51nomaximal
8D5×#10597244—31no—
9C5⋊#11925898D311yescharacteristic, complemented
10C5×#11925898—31no—
11C112×D15C2×C511yescharacteristic, complemented
12C5×C11×D33C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14D3×#10597244—51no—
15C3⋊#11925898—22no—
16C3⋊#11925898D511yescharacteristic, complemented
17C3×#11925898—51no—
18D3×D5×C11⋊C5—111nomaximal
19D15⋊AGL(1,𝔽11)—111nomaximal
20C5×#10597244C2×D311yescharacteristic, complemented, Hall
21D5×C11×D11—31no—
22C2×#11925898—151no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×#10597244—22no—
25C3×#10597244C2×D511yescharacteristic, complemented
26D15×C11⋊C5—111no—
27D15×C11⋊C5—221no—
28C5×C3⋊AGL(1,𝔽11)—111no—
29C5×D3×C11⋊C5—111no—
30C3×C5⋊AGL(1,𝔽11)—111no—
31C3×D5×C11⋊C5—111no—
32D3×C11×D11—51noHall
33C11×D55C5×D311yescharacteristic, complemented
34D5×C112—31no—
35C5×C11×D11—31no—
36C2×#10597244—151no—
37#11925898—31no—
38#11925898—51no—
39#11925898—62no—
40C2×D5×C11⋊C5—331no—
41D5×AGL(1,𝔽11)—331no—
42C3×C5×C11⋊C5—111no—
43C3×C5×C11⋊C5—221no—
44C11×D33C5×D511yescharacteristic, complemented
45D3×C112—51no—
46C3×C11×D11—51no—
47D15⋊D11C11⋊C511yescharacteristic, complemented
48D3×D5×C11—111no—
49C2×D3×C11⋊C5—551no—
50D3×AGL(1,𝔽11)—551no—
51C5×C112C2×C5×D311yescharacteristic, complemented
52#10597244—22no—
53#10597244D3×D511yescharacteristic, complemented
54C2×C5×C11⋊C5—331no—
55C5⋊AGL(1,𝔽11)—111no—
56D5×C11⋊C5—111no—
57D5×C11⋊C5—331no—
58D5×C11⋊C5—661no—
59C5×AGL(1,𝔽11)—331no—
60C2×C11×D11—151noHall
61C3×C112C2×C5×D511yescharacteristic, complemented, Hall
62C11×D15—101no—
63C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
64C11×D15C2×C11⋊C511yescharacteristic, complemented
65C5×D33C2×C11⋊C511yescharacteristic, complemented
66C5×D3×C11—111no—
67C3×D55C2×C11⋊C511yescharacteristic, complemented
68C3×D5×C11—111no—
69C2×C3×C11⋊C5—551no—
70C3⋊AGL(1,𝔽11)—111no—
71C3⋊AGL(1,𝔽11)—222no—
72D3×C11⋊C5—111no—
73D3×C11⋊C5—222no—
74D3×C11⋊C5—551no—
75D3×C11⋊C5—1101no—
76C3×AGL(1,𝔽11)—551no—
77C5×D3×D5—1211noHall
78C5×C11⋊C5—111no—
79C5×C11⋊C5—221no—
80C2×C112—151no—
81C11×D11—31no—
82C11×D11—51no—
83C2×D5×C11—331no—
84D5×D11—31no—
85C22×C11⋊C5—1651no—
86C2×AGL(1,𝔽11)—1651no—
87C3×C5×C11—101no—
88C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
89C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
90C3×C11⋊C5—111no—
91C3×C11⋊C5—222no—
92C3×C11⋊C5—221no—
93C3×C11⋊C5—442no—
94C5×D15—2421no—
95C52×D3—1211no—
96C3×C5×D5—1211no—
97C2×D3×C11—551no—
98D3×D11—51no—
99C112C5×D3×D511yescharacteristic, complemented, Sylow
100C2×C5×C11—331no—
101D55D3×C11⋊C511yescharacteristic, complemented
102C5×D11—31no—
103D5×C11—31no—
104D5×C11—31no—
105D5×C11—111no—
106D5×C11—301no—
107C2×C11⋊C5—331no—
108C2×C11⋊C5—551no—
109C2×C11⋊C5—662no—
110C2×C11⋊C5—3301no—
111C2×C11⋊C5—1651no—
112AGL(1,𝔽11)—331no—
113AGL(1,𝔽11)—551no—
114AGL(1,𝔽11)—662no—
115C2×C5×D5—3631noHall
116C3×C52—2421noHall
117C2×C3×C11—551no—
118D33D5×C11⋊C511yescharacteristic, complemented
119C3×D11—51no—
120D3×C11—51no—
121D3×C11—51no—
122D3×C11—111no—
123D3×C11—501no—
124C2×C5×D3—6051no—
125D3×D5—111no—
126C5×C11—101no—
127C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
128C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
129C11⋊C5—111no—
130C11⋊C5—221no—
131C11⋊C5—222no—
132C11⋊C5—442no—
133C2×C52—3631no—
134C5×D5—1211no—
135C5×D5—7261no—
136C22×C11—1651no—
137C2×D11—151no—
138C3×C11—101no—
139C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
140C3×C11C2×D5×C11⋊C511yescharacteristic, complemented
141C2×C3×C5—6051no—
142D15#1192589811yescharacteristic, complemented
143C3×D5—111no—
144C5×D3—111no—
145C5×D3—1211no—
146C5×D3—12101no—
147C5×D3—2422no—
148C52—2421noSylow
149C2×C11—151no—
150C2×C11—151no—
151C2×C11—331no—
152C2×C11—551no—
153C2×C11—1501no—
154D11—31no—
155D11—51no—
156C22×C5—18151no—
157C2×D5—331no—
158C3×C5—4842no—
159C3×C5—2421no—
160C3×C5C2×#1192589811yescharacteristic, complemented
161C2×D3—551noHall
162C11—101no—
163C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
164C11D3×D5×C11⋊C511yescharacteristic, complemented
165C2×C5—18151no—
166C2×C5—331no—
167C2×C5—6051no—
168C2×C5—3631no—
169C2×C5—7262no—
170D5—31no—
171D5—111no—
172C2×C3—551no—
173D3—51no—
174D3—111no—
175C5—1211no—
176C5—4842no—
177C5D3×#1192589811yescharacteristic, complemented
178C22—1651noSylow
179C3D5×#1192589811yescharacteristic, complemented, Sylow
180C2—151no—
181C2—331no—
182C2—551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. D15×#10597244C2semidirect
2. C5×C3⋊#11925898C2semidirect
3. C3×C5⋊#11925898C2semidirect
5. C3×C5×#10597244C22semidirect
6. C11×D15⋊D11C5semidirect
9. C5⋊#11925898D3semidirect
11. C112×D15C2×C5semidirect
12. C5×C11×D33C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
16. C3⋊#11925898D5semidirect
20. C5×#10597244C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×#10597244C2×D5semidirect
33. C11×D55C5×D3semidirect
44. C11×D33C5×D5semidirect
47. D15⋊D11C11⋊C5semidirect
51. C5×C112C2×C5×D3semidirect
53. #10597244D3×D5semidirect
61. C3×C112C2×C5×D5semidirect
63. C11×D15AGL(1,𝔽11)semidirect
64. C11×D15C2×C11⋊C5semidirect
65. C5×D33C2×C11⋊C5semidirect
67. C3×D55C2×C11⋊C5semidirect
88. C3×C5×C11C2×AGL(1,𝔽11)semidirect
89. C3×C5×C11C22×C11⋊C5semidirect
99. C112C5×D3×D5semidirect
101. D55D3×C11⋊C5semidirect
118. D33D5×C11⋊C5semidirect
127. C5×C11D3×AGL(1,𝔽11)semidirect
128. C5×C11C2×D3×C11⋊C5semidirect
139. C3×C11D5×AGL(1,𝔽11)semidirect
140. C3×C11C2×D5×C11⋊C5semidirect
142. D15#11925898semidirect
160. C3×C5C2×#11925898semidirect
163. C11D15⋊AGL(1,𝔽11)semidirect
164. C11D3×D5×C11⋊C5semidirect
177. C5D3×#11925898semidirect
179. C3D5×#11925898semidirect

Maximal subgroups

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

subgroupindex
D15×#105972442
C5×C3⋊#119258982
C3×C5⋊#119258982
D5×#119258983
C11×D15⋊D115
D3×#119258985
D3×D5×C11⋊C511
D15⋊AGL(1,𝔽11)11