Finite Group Databasebeta

← D15⋊#11925896 #49137531

Subgroups — D15⋊#11925896 #49137531

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×#10597245C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925896C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925896C211yesmaximal, characteristic, complemented
4D5×#11925896—31nomaximal, Hall
5C3×C5×#10597245C2211yescharacteristic, complemented, Hall
6C11×D15⋊D11C511yesmaximal, characteristic, complemented
7D3×#11925896—51nomaximal
8D5×#10597245—31no—
9C5⋊#11925896D311yescharacteristic, complemented
10C5×#11925896—31no—
11C112×D15C2×C511yescharacteristic, complemented
12C5×C11×D33C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14D3×#10597245—51no—
15C3⋊#11925896—21no—
16C3⋊#11925896—21no—
17C3⋊#11925896D511yescharacteristic, complemented
18C3×#11925896—51no—
19D3×D5×C11⋊C5—111nomaximal
20D15⋊AGL(1,𝔽11)—111nomaximal
21C5×#10597245C2×D311yescharacteristic, complemented, Hall
22D5×C11×D11—31no—
23C2×#11925896—151no—
24C3×C5×C112C22×C511yescharacteristic, complemented
25C3×#10597245—21no—
26C3×#10597245—21no—
27C3×#10597245C2×D511yescharacteristic, complemented
28D15×C11⋊C5—111no—
29D15×C11⋊C5—221no—
30C5×C3⋊AGL(1,𝔽11)—111no—
31C5×D3×C11⋊C5—111no—
32C3×C5⋊AGL(1,𝔽11)—111no—
33C3×D5×C11⋊C5—111no—
34D3×C11×D11—51noHall
35C11×D55C5×D311yescharacteristic, complemented
36D5×C112—31no—
37C5×C11×D11—31no—
38C2×#10597245—151no—
39#11925896—31no—
40#11925896—51no—
41#11925896—61no—
42#11925896—61no—
43C2×D5×C11⋊C5—331no—
44D5×AGL(1,𝔽11)—331no—
45C3×C5×C11⋊C5—111no—
46C3×C5×C11⋊C5—221no—
47C11×D33C5×D511yescharacteristic, complemented
48D3×C112—51no—
49C3×C11×D11—51no—
50D15⋊D11C11⋊C511yescharacteristic, complemented
51D3×D5×C11—111no—
52C2×D3×C11⋊C5—551no—
53D3×AGL(1,𝔽11)—551no—
54C5×C112C2×C5×D311yescharacteristic, complemented
55#10597245—21no—
56#10597245—21no—
57#10597245D3×D511yescharacteristic, complemented
58C2×C5×C11⋊C5—331no—
59C5⋊AGL(1,𝔽11)—111no—
60D5×C11⋊C5—111no—
61D5×C11⋊C5—331no—
62D5×C11⋊C5—661no—
63C5×AGL(1,𝔽11)—331no—
64C2×C11×D11—151noHall
65C3×C112C2×C5×D511yescharacteristic, complemented, Hall
66C11×D15—101no—
67C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
68C11×D15C2×C11⋊C511yescharacteristic, complemented
69C5×D33C2×C11⋊C511yescharacteristic, complemented
70C5×D3×C11—111no—
71C3×D55C2×C11⋊C511yescharacteristic, complemented
72C3×D5×C11—111no—
73C2×C3×C11⋊C5—551no—
74C3⋊AGL(1,𝔽11)—111no—
75C3⋊AGL(1,𝔽11)—221no—
76C3⋊AGL(1,𝔽11)—221no—
77D3×C11⋊C5—111no—
78D3×C11⋊C5—221no—
79D3×C11⋊C5—221no—
80D3×C11⋊C5—551no—
81D3×C11⋊C5—1101no—
82C3×AGL(1,𝔽11)—551no—
83C5×D3×D5—1211noHall
84C5×C11⋊C5—111no—
85C5×C11⋊C5—221no—
86C2×C112—151no—
87C11×D11—31no—
88C11×D11—51no—
89C2×D5×C11—331no—
90D5×D11—31no—
91C22×C11⋊C5—1651no—
92C2×AGL(1,𝔽11)—1651no—
93C3×C5×C11—101no—
94C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
95C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
96C3×C11⋊C5—111no—
97C3×C11⋊C5—221no—
98C3×C11⋊C5—221no—
99C3×C11⋊C5—221no—
100C3×C11⋊C5—221no—
101C3×C11⋊C5—441no—
102C5×D15—2421no—
103C52×D3—1211no—
104C3×C5×D5—1211no—
105C2×D3×C11—551no—
106D3×D11—51no—
107C112C5×D3×D511yescharacteristic, complemented, Sylow
108C2×C5×C11—331no—
109D55D3×C11⋊C511yescharacteristic, complemented
110C5×D11—31no—
111D5×C11—31no—
112D5×C11—31no—
113D5×C11—111no—
114D5×C11—301no—
115C2×C11⋊C5—331no—
116C2×C11⋊C5—551no—
117C2×C11⋊C5—661no—
118C2×C11⋊C5—661no—
119C2×C11⋊C5—3301no—
120C2×C11⋊C5—1651no—
121AGL(1,𝔽11)—331no—
122AGL(1,𝔽11)—551no—
123AGL(1,𝔽11)—661no—
124AGL(1,𝔽11)—661no—
125C2×C5×D5—3631noHall
126C3×C52—2421noHall
127C2×C3×C11—551no—
128D33D5×C11⋊C511yescharacteristic, complemented
129C3×D11—51no—
130D3×C11—51no—
131D3×C11—51no—
132D3×C11—111no—
133D3×C11—501no—
134C2×C5×D3—6051no—
135D3×D5—111no—
136C5×C11—101no—
137C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
138C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
139C11⋊C5—111no—
140C11⋊C5—221no—
141C11⋊C5—221no—
142C11⋊C5—221no—
143C11⋊C5—221no—
144C11⋊C5—441no—
145C2×C52—3631no—
146C5×D5—1211no—
147C5×D5—7261no—
148C22×C11—1651no—
149C2×D11—151no—
150C3×C11—101no—
151C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
152C3×C11C2×D5×C11⋊C511yescharacteristic, complemented
153C2×C3×C5—6051no—
154D15#1192589611yescharacteristic, complemented
155C3×D5—111no—
156C5×D3—111no—
157C5×D3—6051no—
158C5×D3—1211no—
159C5×D3—2421no—
160C5×D3—2421no—
161C52—2421noSylow
162C2×C11—151no—
163C2×C11—151no—
164C2×C11—331no—
165C2×C11—551no—
166C2×C11—1501no—
167D11—31no—
168D11—51no—
169C22×C5—18151no—
170C2×D5—331no—
171C3×C5—1211no—
172C3×C5—4841no—
173C3×C5—4841no—
174C3×C5C2×#1192589611yescharacteristic, complemented
175C2×D3—551noHall
176C11—101no—
177C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
178C11D3×D5×C11⋊C511yescharacteristic, complemented
179C2×C5—331no—
180C2×C5—36301no—
181C2×C5—6051no—
182C2×C5—3631no—
183C2×C5—7261no—
184C2×C5—7261no—
185D5—31no—
186D5—111no—
187C2×C3—551no—
188D3—51no—
189D3—111no—
190C5—4841no—
191C5—4841no—
192C5—2421no—
193C5D3×#1192589611yescharacteristic, complemented
194C22—1651noSylow
195C3D5×#1192589611yescharacteristic, complemented, Sylow
196C2—151no—
197C2—331no—
198C2—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×#10597245C2semidirect
2. C5×C3⋊#11925896C2semidirect
3. C3×C5⋊#11925896C2semidirect
5. C3×C5×#10597245C22semidirect
6. C11×D15⋊D11C5semidirect
9. C5⋊#11925896D3semidirect
11. C112×D15C2×C5semidirect
12. C5×C11×D33C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
17. C3⋊#11925896D5semidirect
21. C5×#10597245C2×D3semidirect
24. C3×C5×C112C22×C5semidirect
27. C3×#10597245C2×D5semidirect
35. C11×D55C5×D3semidirect
47. C11×D33C5×D5semidirect
50. D15⋊D11C11⋊C5semidirect
54. C5×C112C2×C5×D3semidirect
57. #10597245D3×D5semidirect
65. C3×C112C2×C5×D5semidirect
67. C11×D15AGL(1,𝔽11)semidirect
68. C11×D15C2×C11⋊C5semidirect
69. C5×D33C2×C11⋊C5semidirect
71. C3×D55C2×C11⋊C5semidirect
94. C3×C5×C11C2×AGL(1,𝔽11)semidirect
95. C3×C5×C11C22×C11⋊C5semidirect
107. C112C5×D3×D5semidirect
109. D55D3×C11⋊C5semidirect
128. D33D5×C11⋊C5semidirect
137. C5×C11D3×AGL(1,𝔽11)semidirect
138. C5×C11C2×D3×C11⋊C5semidirect
151. C3×C11D5×AGL(1,𝔽11)semidirect
152. C3×C11C2×D5×C11⋊C5semidirect
154. D15#11925896semidirect
174. C3×C5C2×#11925896semidirect
177. C11D15⋊AGL(1,𝔽11)semidirect
178. C11D3×D5×C11⋊C5semidirect
193. C5D3×#11925896semidirect
195. C3D5×#11925896semidirect

Maximal subgroups

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

subgroupindex
D15×#105972452
C5×C3⋊#119258962
C3×C5⋊#119258962
D5×#119258963
C11×D15⋊D115
D3×#119258965
D3×D5×C11⋊C511
D15⋊AGL(1,𝔽11)11