Finite Group Databasebeta

← D5×C3⋊#11925895 #49137507

Subgroups — D5×C3⋊#11925895 #49137507

Order 36300.

292 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊#11925895)C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925895C211yesmaximal, characteristic, complemented
3C3×D5×#10597243C211yesmaximal, characteristic, complemented
4D5×#11925895—31nomaximal, Hall
5C3×C5×#10597243C2211yescharacteristic, complemented, Hall
6D5×C11×D33C511yesmaximal, characteristic, complemented
7C2×C3⋊#11925895—51nomaximal
8D5×#10597243D311yescharacteristic, complemented
9C5⋊#11925895—31no—
10C5×#11925895—31no—
11C11×D165C2×C511yescharacteristic, complemented
12C5×C11×D33C2×C511yescharacteristic, complemented
13C3×D5×C112C2×C511yescharacteristic, complemented
14C2×C3×#10597243—51no—
15C3⋊#11925895—22no—
16C3⋊#11925895—51no—
17C3⋊#11925895D511yescharacteristic, direct product factor
18D3×D5×C11⋊C5—111nomaximal
19D5×C3⋊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
26C3⋊(C5⋊AGL(1,𝔽11))—111no—
27D15×C11⋊C5—111no—
28C5×C3⋊AGL(1,𝔽11)—111no—
29C5×D3×C11⋊C5—111no—
30C3×D5×C11⋊C5—111no—
31C3×D5×C11⋊C5—225no—
32C3×D5×C11⋊C5—221no—
33C2×C11×D33—51noHall
34C11×D55—31no—
35D5×C112C5×D311yescharacteristic, complemented
36C5×C11×D11—31no—
37C2×#10597243—51no—
38#11925895—31no—
39#11925895—62no—
40#11925895—151no—
41C2×D5×C11⋊C5—331no—
42D5×AGL(1,𝔽11)—331no—
43C3×C5×C11⋊C5—111no—
44C3×C5×C11⋊C5—225no—
45C3×C5×C11⋊C5—221no—
46C2×C3×C112—51no—
47C11×D33—51no—
48C11×D33C5×D511yescharacteristic, complemented
49D5×D33C11⋊C511yescharacteristic, complemented
50D3×D5×C11—111no—
51C2×C3⋊AGL(1,𝔽11)—551no—
52C2×D3×C11⋊C5—551no—
53C5×C112C2×C5×D311yescharacteristic, complemented
54#10597243—22no—
55#10597243D3×D511yescharacteristic, complemented
56C2×C5×C11⋊C5—331no—
57C5⋊AGL(1,𝔽11)—331no—
58D5×C11⋊C5—111no—
59D5×C11⋊C5—225no—
60D5×C11⋊C5—221no—
61D5×C11⋊C5—331no—
62C5×AGL(1,𝔽11)—331no—
63C2×C11×D11—151noHall
64C3×C112C2×C5×D511yescharacteristic, complemented, Hall
65D165C2×C11⋊C511yescharacteristic, complemented
66C11×D15—111no—
67C5×D33C2×C11⋊C511yescharacteristic, complemented
68C5×D3×C11—111no—
69C3×D5×C11—25no—
70C3×D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
71C3×D5×C11C2×C11⋊C511yescharacteristic, complemented
72C2×C3×C11⋊C5—551no—
73C2×C3×C11⋊C5—1101no—
74C2×C3×C11⋊C5—1105no—
75C3⋊AGL(1,𝔽11)—111no—
76C3⋊AGL(1,𝔽11)—222no—
77C3⋊AGL(1,𝔽11)—551no—
78D3×C11⋊C5—111no—
79D3×C11⋊C5—222no—
80D3×C11⋊C5—551no—
81C5×D3×D5—1211noHall
82C5×C11⋊C5—111no—
83C5×C11⋊C5—225no—
84C5×C11⋊C5—221no—
85C2×C112—51no—
86C11×D11—31no—
87C11×D11—151no—
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—1211no—
102C52×D3—1211no—
103C3×C5×D5—2421no—
104C2×D33—51no—
105C2×D3×C11—551no—
106C112C5×D3×D511yescharacteristic, complemented, Sylow
107C2×C5×C11—331no—
108D55—31no—
109C5×D11—31no—
110D5×C11—25no—
111D5×C11—331no—
112D5×C11D3×C11⋊C511yescharacteristic, complemented
113D5×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
114C2×C11⋊C5—331no—
115C2×C11⋊C5—551no—
116C2×C11⋊C5—662no—
117C2×C11⋊C5—1101no—
118C2×C11⋊C5—1105no—
119C2×C11⋊C5—1651no—
120AGL(1,𝔽11)—331no—
121AGL(1,𝔽11)—662no—
122AGL(1,𝔽11)—1651no—
123C2×C5×D5—3631noHall
124C3×C52—2421noHall
125C2×C3×C11—51no—
126C2×C3×C11—51no—
127C2×C3×C11—105no—
128D33—51no—
129D33D5×C11⋊C511yescharacteristic, complemented
130D3×C11—111no—
131D3×C11—551no—
132C2×C5×D3—6051no—
133D3×D5—111no—
134C5×C11—25no—
135C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
136C5×C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
137C11⋊C5—111no—
138C11⋊C5—222no—
139C11⋊C5—225no—
140C11⋊C5—221no—
141C11⋊C5—4410no—
142C11⋊C5—442no—
143C2×C52—3631no—
144C5×D5—3631no—
145C5×D5—1211no—
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—12101no—
152D15—111no—
153C3×D5#1192589511yescharacteristic, complemented
154C5×D3—111no—
155C5×D3—6051no—
156C5×D3—1211no—
157C5×D3—2422no—
158C52—1211noSylow
159C2×C11—51no—
160C2×C11—51no—
161C2×C11—105no—
162C2×C11—331no—
163C2×C11—1651no—
164D11—31no—
165D11—151no—
166C22×C5—18151no—
167C2×D5—331no—
168C3×C5—4842no—
169C3×C5—2421no—
170C3×C5C2×#1192589511yescharacteristic, complemented
171C2×D3—551noHall
172C11—25no—
173C11D5×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
174C11D3×D5×C11⋊C511yescharacteristic, complemented
175C2×C5—18151no—
176C2×C5—331no—
177C2×C5—3631no—
178C2×C5—12101no—
179C2×C5—7262no—
180D5—331no—
181D5C3⋊#1192589511yescharacteristic, direct product factor
182C2×C3—51no—
183D3—111no—
184D3—551no—
185C5—4842no—
186C5—2421no—
187C5C2×C3⋊#1192589511yescharacteristic, complemented
188C22—1651noSylow
189C3D5×#1192589511yescharacteristic, complemented, Sylow
190C2—51no—
191C2—331no—
192C2—1651no—
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. C3⋊(C5⋊#11925895)C2semidirect
2. C5×C3⋊#11925895C2semidirect
3. C3×D5×#10597243C2semidirect
5. C3×C5×#10597243C22semidirect
6. D5×C11×D33C5semidirect
8. D5×#10597243D3semidirect
11. C11×D165C2×C5semidirect
12. C5×C11×D33C2×C5semidirect
13. C3×D5×C112C2×C5semidirect
17. C3⋊#11925895D5direct (N × H)
20. C5×#10597243C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×#10597243C2×D5semidirect
35. D5×C112C5×D3semidirect
48. C11×D33C5×D5semidirect
49. D5×D33C11⋊C5semidirect
53. C5×C112C2×C5×D3semidirect
55. #10597243D3×D5semidirect
64. C3×C112C2×C5×D5semidirect
65. D165C2×C11⋊C5semidirect
67. C5×D33C2×C11⋊C5semidirect
70. C3×D5×C11AGL(1,𝔽11)semidirect
71. C3×D5×C11C2×C11⋊C5semidirect
93. C3×C5×C11C2×AGL(1,𝔽11)semidirect
94. C3×C5×C11C22×C11⋊C5semidirect
106. C112C5×D3×D5semidirect
112. D5×C11D3×C11⋊C5semidirect
113. D5×C11C3⋊AGL(1,𝔽11)semidirect
129. D33D5×C11⋊C5semidirect
135. C5×C11C2×D3×C11⋊C5semidirect
136. C5×C11C2×C3⋊AGL(1,𝔽11)semidirect
149. C3×C11D5×AGL(1,𝔽11)semidirect
150. C3×C11C2×D5×C11⋊C5semidirect
153. C3×D5#11925895semidirect
170. C3×C5C2×#11925895semidirect
173. C11D5×C3⋊AGL(1,𝔽11)semidirect
174. C11D3×D5×C11⋊C5semidirect
181. D5C3⋊#11925895direct (N × H)
187. C5C2×C3⋊#11925895semidirect
189. C3D5×#11925895semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11925895)2
C5×C3⋊#119258952
C3×D5×#105972432
D5×#119258953
D5×C11×D335
C2×C3⋊#119258955
D3×D5×C11⋊C511
D5×C3⋊AGL(1,𝔽11)11