Finite Group Databasebeta

← D15⋊#11925895 #49137509

Subgroups — D15⋊#11925895 #49137509

Order 36300.

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

normal subgroups only

This group has 292 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×#10597243C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925895C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925895C211yesmaximal, characteristic, complemented
4D5×#11925895—31nomaximal, Hall
5C3×C5×#10597243C2211yescharacteristic, complemented, Hall
6C11×D15⋊D11C511yesmaximal, characteristic, complemented
7D3×#11925895—51nomaximal
8D5×#10597243—31no—
9C5⋊#11925895D311yescharacteristic, complemented
10C5×#11925895—31no—
11C112×D15C2×C511yescharacteristic, complemented
12C5×C11×D33C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14D3×#10597243—51no—
15C3⋊#11925895—22no—
16C3⋊#11925895D511yescharacteristic, complemented
17C3×#11925895—51no—
18D3×D5×C11⋊C5—111nomaximal
19D15⋊AGL(1,𝔽11)—111nomaximal
20C5×#10597243C2×D311yescharacteristic, complemented, Hall
21D5×C11×D11—31no—
22C2×#11925895—151no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×#10597243—22no—
25C3×#10597243C2×D511yescharacteristic, complemented
26D15×C11⋊C5—111no—
27D15×C11⋊C5—111no—
28D15×C11⋊C5—225no—
29C5×C3⋊AGL(1,𝔽11)—111no—
30C5×D3×C11⋊C5—111no—
31C3×C5⋊AGL(1,𝔽11)—111no—
32C3×D5×C11⋊C5—111no—
33D3×C11×D11—51noHall
34C11×D55C5×D311yescharacteristic, complemented
35D5×C112—31no—
36C5×C11×D11—31no—
37C2×#10597243—151no—
38#11925895—31no—
39#11925895—51no—
40#11925895—62no—
41C2×D5×C11⋊C5—331no—
42D5×AGL(1,𝔽11)—331no—
43C3×C5×C11⋊C5—111no—
44C3×C5×C11⋊C5—111no—
45C3×C5×C11⋊C5—225no—
46C11×D33C5×D511yescharacteristic, complemented
47D3×C112—51no—
48C3×C11×D11—51no—
49D15⋊D11C11⋊C511yescharacteristic, complemented
50D3×D5×C11—111no—
51C2×D3×C11⋊C5—551no—
52D3×AGL(1,𝔽11)—551no—
53C5×C112C2×C5×D311yescharacteristic, complemented
54#10597243—22no—
55#10597243D3×D511yescharacteristic, complemented
56C2×C5×C11⋊C5—331no—
57C5⋊AGL(1,𝔽11)—111no—
58D5×C11⋊C5—111no—
59D5×C11⋊C5—331no—
60D5×C11⋊C5—661no—
61D5×C11⋊C5—665no—
62C5×AGL(1,𝔽11)—331no—
63C2×C11×D11—151noHall
64C3×C112C2×C5×D511yescharacteristic, complemented, Hall
65C11×D15—25no—
66C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
67C11×D15C2×C11⋊C511yescharacteristic, complemented
68C5×D33C2×C11⋊C511yescharacteristic, complemented
69C5×D3×C11—111no—
70C3×D55C2×C11⋊C511yescharacteristic, complemented
71C3×D5×C11—111no—
72C2×C3×C11⋊C5—551no—
73C3⋊AGL(1,𝔽11)—111no—
74C3⋊AGL(1,𝔽11)—222no—
75D3×C11⋊C5—111no—
76D3×C11⋊C5—222no—
77D3×C11⋊C5—551no—
78D3×C11⋊C5—1101no—
79D3×C11⋊C5—1105no—
80C3×AGL(1,𝔽11)—551no—
81C5×D3×D5—1211noHall
82C5×C11⋊C5—111no—
83C5×C11⋊C5—225no—
84C5×C11⋊C5—221no—
85C2×C112—151no—
86C11×D11—31no—
87C11×D11—51no—
88C2×D5×C11—331no—
89D5×D11—31no—
90C22×C11⋊C5—1651no—
91C2×AGL(1,𝔽11)—1651no—
92C3×C5×C11—25no—
93C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
94C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
95C3×C11⋊C5—111no—
96C3×C11⋊C5—222no—
97C3×C11⋊C5—225no—
98C3×C11⋊C5—221no—
99C3×C11⋊C5—4410no—
100C3×C11⋊C5—442no—
101C5×D15—2421no—
102C52×D3—1211no—
103C3×C5×D5—1211no—
104C2×D3×C11—551no—
105D3×D11—51no—
106C112C5×D3×D511yescharacteristic, complemented, Sylow
107C2×C5×C11—331no—
108D55D3×C11⋊C511yescharacteristic, complemented
109C5×D11—31no—
110D5×C11—31no—
111D5×C11—31no—
112D5×C11—65no—
113D5×C11—111no—
114C2×C11⋊C5—331no—
115C2×C11⋊C5—551no—
116C2×C11⋊C5—662no—
117C2×C11⋊C5—3301no—
118C2×C11⋊C5—3305no—
119C2×C11⋊C5—1651no—
120AGL(1,𝔽11)—331no—
121AGL(1,𝔽11)—551no—
122AGL(1,𝔽11)—662no—
123C2×C5×D5—3631noHall
124C3×C52—2421noHall
125C2×C3×C11—551no—
126D33D5×C11⋊C511yescharacteristic, complemented
127C3×D11—51no—
128D3×C11—51no—
129D3×C11—51no—
130D3×C11—105no—
131D3×C11—111no—
132C2×C5×D3—6051no—
133D3×D5—111no—
134C5×C11—25no—
135C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
136C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
137C11⋊C5—111no—
138C11⋊C5—222no—
139C11⋊C5—225no—
140C11⋊C5—221no—
141C11⋊C5—4410no—
142C11⋊C5—442no—
143C2×C52—3631no—
144C5×D5—1211no—
145C5×D5—7261no—
146C22×C11—1651no—
147C2×D11—151no—
148C3×C11—25no—
149C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
150C3×C11C2×D5×C11⋊C511yescharacteristic, complemented
151C2×C3×C5—6051no—
152D15#1192589511yescharacteristic, complemented
153C3×D5—111no—
154C5×D3—111no—
155C5×D3—1211no—
156C5×D3—12101no—
157C5×D3—2422no—
158C52—2421noSylow
159C2×C11—151no—
160C2×C11—151no—
161C2×C11—305no—
162C2×C11—331no—
163C2×C11—551no—
164D11—31no—
165D11—51no—
166C22×C5—18151no—
167C2×D5—331no—
168C3×C5—4842no—
169C3×C5—2421no—
170C3×C5C2×#1192589511yescharacteristic, complemented
171C2×D3—551noHall
172C11—25no—
173C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
174C11D3×D5×C11⋊C511yescharacteristic, complemented
175C2×C5—331no—
176C2×C5—36301no—
177C2×C5—6051no—
178C2×C5—3631no—
179C2×C5—7262no—
180D5—31no—
181D5—111no—
182C2×C3—551no—
183D3—51no—
184D3—111no—
185C5—4842no—
186C5—2421no—
187C5D3×#1192589511yescharacteristic, complemented
188C22—1651noSylow
189C3D5×#1192589511yescharacteristic, complemented, Sylow
190C2—151no—
191C2—331no—
192C2—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×#10597243C2semidirect
2. C5×C3⋊#11925895C2semidirect
3. C3×C5⋊#11925895C2semidirect
5. C3×C5×#10597243C22semidirect
6. C11×D15⋊D11C5semidirect
9. C5⋊#11925895D3semidirect
11. C112×D15C2×C5semidirect
12. C5×C11×D33C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
16. C3⋊#11925895D5semidirect
20. C5×#10597243C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×#10597243C2×D5semidirect
34. C11×D55C5×D3semidirect
46. C11×D33C5×D5semidirect
49. D15⋊D11C11⋊C5semidirect
53. C5×C112C2×C5×D3semidirect
55. #10597243D3×D5semidirect
64. C3×C112C2×C5×D5semidirect
66. C11×D15AGL(1,𝔽11)semidirect
67. C11×D15C2×C11⋊C5semidirect
68. C5×D33C2×C11⋊C5semidirect
70. C3×D55C2×C11⋊C5semidirect
93. C3×C5×C11C2×AGL(1,𝔽11)semidirect
94. C3×C5×C11C22×C11⋊C5semidirect
106. C112C5×D3×D5semidirect
108. D55D3×C11⋊C5semidirect
126. D33D5×C11⋊C5semidirect
135. C5×C11D3×AGL(1,𝔽11)semidirect
136. C5×C11C2×D3×C11⋊C5semidirect
149. C3×C11D5×AGL(1,𝔽11)semidirect
150. C3×C11C2×D5×C11⋊C5semidirect
152. D15#11925895semidirect
170. C3×C5C2×#11925895semidirect
173. C11D15⋊AGL(1,𝔽11)semidirect
174. C11D3×D5×C11⋊C5semidirect
187. C5D3×#11925895semidirect
189. C3D5×#11925895semidirect

Maximal subgroups

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

subgroupindex
D15×#105972432
C5×C3⋊#119258952
C3×C5⋊#119258952
D5×#119258953
C11×D15⋊D115
D3×#119258955
D3×D5×C11⋊C511
D15⋊AGL(1,𝔽11)11