Finite Group Databasebeta

← D3×C5⋊#11925895 #49137508

Subgroups — D3×C5⋊#11925895 #49137508

Order 36300.

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

normal subgroups only

This group has 352 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×D3×#10597243C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925895C211yesmaximal, characteristic, complemented
4C2×C5⋊#11925895—31nomaximal, Hall
5C3×C5×#10597243C2211yescharacteristic, complemented, Hall
6D3×C11×D55C511yesmaximal, characteristic, complemented
7D3×#11925895—51nomaximal
8C2×C5×#10597243—31no—
9C5⋊#11925895—31no—
10C5⋊#11925895D311yescharacteristic, direct product factor
11C11×D165C2×C511yescharacteristic, complemented
12C5×D3×C112C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14D3×#10597243—22no—
15D3×#10597243D511yescharacteristic, complemented
16C3⋊#11925895—51no—
17C3×#11925895—51no—
18D3×D5×C11⋊C5—111nomaximal
19D3×C5⋊AGL(1,𝔽11)—111nomaximal
20C5×#10597243C2×D311yescharacteristic, complemented, Hall
21C2×C11×D55—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×D3×C11⋊C5—111no—
29C5×D3×C11⋊C5—225no—
30C5×D3×C11⋊C5—221no—
31C3×C5⋊AGL(1,𝔽11)—111no—
32C3×D5×C11⋊C5—111no—
33D3×C11×D11—51noHall
34C2×C5×C112—31no—
35C11×D55—31no—
36C11×D55C5×D311yescharacteristic, complemented
37C2×#10597243—31no—
38C2×#10597243—62no—
39#11925895—51no—
40#11925895—151no—
41C2×C5⋊AGL(1,𝔽11)—331no—
42C2×D5×C11⋊C5—331no—
43C3×C5×C11⋊C5—111no—
44C3×C5×C11⋊C5—225no—
45C3×C5×C11⋊C5—221no—
46C11×D33—51no—
47D3×C112C5×D511yescharacteristic, complemented
48C3×C11×D11—51no—
49D3×D55C11⋊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—
57C2×C5×C11⋊C5—665no—
58C2×C5×C11⋊C5—661no—
59C5⋊AGL(1,𝔽11)—111no—
60C5⋊AGL(1,𝔽11)—331no—
61D5×C11⋊C5—111no—
62D5×C11⋊C5—331no—
63C2×C11×D11—151noHall
64C3×C112C2×C5×D511yescharacteristic, complemented, Hall
65D165C2×C11⋊C511yescharacteristic, complemented
66C11×D15—111no—
67C5×D3×C11—25no—
68C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
69C5×D3×C11C2×C11⋊C511yescharacteristic, complemented
70C3×D55C2×C11⋊C511yescharacteristic, complemented
71C3×D5×C11—111no—
72C2×C3×C11⋊C5—551no—
73C3⋊AGL(1,𝔽11)—551no—
74D3×C11⋊C5—111no—
75D3×C11⋊C5—2220no—
76D3×C11⋊C5—225no—
77D3×C11⋊C5—222no—
78D3×C11⋊C5—221no—
79D3×C11⋊C5—222no—
80D3×C11⋊C5—551no—
81C3×AGL(1,𝔽11)—551no—
82C5×D3×D5—1211noHall
83C5×C11⋊C5—111no—
84C5×C11⋊C5—225no—
85C5×C11⋊C5—221no—
86C2×C112—31no—
87C11×D11—51no—
88C11×D11—151no—
89C2×D55—31no—
90C2×D5×C11—331no—
91C22×C11⋊C5—1651no—
92C2×AGL(1,𝔽11)—1651no—
93C3×C5×C11—25no—
94C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
95C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
96C3×C11⋊C5—111no—
97C3×C11⋊C5—2220no—
98C3×C11⋊C5—225no—
99C3×C11⋊C5—222no—
100C3×C11⋊C5—222no—
101C3×C11⋊C5—221no—
102C5×D15—1211no—
103C52×D3—2421no—
104C3×C5×D5—1211no—
105C2×D3×C11—551no—
106D3×D11—51no—
107C112C5×D3×D511yescharacteristic, complemented, Sylow
108C2×C5×C11—31no—
109C2×C5×C11—31no—
110C2×C5×C11—65no—
111D55—31no—
112D55D3×C11⋊C511yescharacteristic, complemented
113D5×C11—111no—
114D5×C11—331no—
115C2×C11⋊C5—331no—
116C2×C11⋊C5—551no—
117C2×C11⋊C5—662no—
118C2×C11⋊C5—661no—
119C2×C11⋊C5—662no—
120C2×C11⋊C5—665no—
121C2×C11⋊C5—6620no—
122C2×C11⋊C5—1651no—
123AGL(1,𝔽11)—551no—
124AGL(1,𝔽11)—1651no—
125C2×C5×D5—3631noHall
126C3×C52—2421noHall
127C2×C3×C11—551no—
128D33—51no—
129C3×D11—51no—
130D3×C11—25no—
131D3×C11—551no—
132D3×C11D5×C11⋊C511yescharacteristic, complemented
133D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
134C2×C5×D3—6051no—
135D3×D5—111no—
136C5×C11—25no—
137C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
138C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
139C11⋊C5—111no—
140C11⋊C5—2220no—
141C11⋊C5—225no—
142C11⋊C5—221no—
143C11⋊C5—222no—
144C11⋊C5—222no—
145C2×C52—7261no—
146C5×D5—3631no—
147C5×D5—1211no—
148C22×C11—1651no—
149C2×D11—151no—
150C3×C11—25no—
151C3×C11C2×D5×C11⋊C511yescharacteristic, complemented
152C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
153C2×C3×C5—6051no—
154D15—111no—
155C3×D5—111no—
156C5×D3—6051no—
157C5×D3—2421no—
158C5×D3—2422no—
159C5×D3#1192589511yescharacteristic, complemented
160C52—2421noSylow
161C2×C11—31no—
162C2×C11—31no—
163C2×C11—65no—
164C2×C11—551no—
165C2×C11—1651no—
166D11—51no—
167D11—151no—
168C22×C5—18151no—
169C2×D5—331no—
170C3×C5—2421no—
171C3×C5—2422no—
172C3×C5C2×#1192589511yescharacteristic, complemented
173C2×D3—551noHall
174C11—25no—
175C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
176C11D3×D5×C11⋊C511yescharacteristic, complemented
177C2×C5—31no—
178C2×C5—18151no—
179C2×C5—6051no—
180C2×C5—7261no—
181C2×C5—7262no—
182D5—111no—
183D5—331no—
184C2×C3—551no—
185D3—551no—
186D3C5⋊#1192589511yescharacteristic, direct product factor
187C5—2421no—
188C5—2422no—
189C5D3×#1192589511yescharacteristic, complemented
190C22—1651noSylow
191C3C2×C5⋊#1192589511yescharacteristic, complemented, Sylow
192C2—31no—
193C2—551no—
194C2—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×D3×#10597243C2semidirect
3. C3×C5⋊#11925895C2semidirect
5. C3×C5×#10597243C22semidirect
6. D3×C11×D55C5semidirect
10. C5⋊#11925895D3direct (N × H)
11. C11×D165C2×C5semidirect
12. C5×D3×C112C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
15. D3×#10597243D5semidirect
20. C5×#10597243C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×#10597243C2×D5semidirect
36. C11×D55C5×D3semidirect
47. D3×C112C5×D5semidirect
49. D3×D55C11⋊C5semidirect
53. C5×C112C2×C5×D3semidirect
55. #10597243D3×D5semidirect
64. C3×C112C2×C5×D5semidirect
65. D165C2×C11⋊C5semidirect
68. C5×D3×C11AGL(1,𝔽11)semidirect
69. C5×D3×C11C2×C11⋊C5semidirect
70. C3×D55C2×C11⋊C5semidirect
94. C3×C5×C11C2×AGL(1,𝔽11)semidirect
95. C3×C5×C11C22×C11⋊C5semidirect
107. C112C5×D3×D5semidirect
112. D55D3×C11⋊C5semidirect
132. D3×C11D5×C11⋊C5semidirect
133. D3×C11C5⋊AGL(1,𝔽11)semidirect
137. C5×C11D3×AGL(1,𝔽11)semidirect
138. C5×C11C2×D3×C11⋊C5semidirect
151. C3×C11C2×D5×C11⋊C5semidirect
152. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
159. C5×D3#11925895semidirect
172. C3×C5C2×#11925895semidirect
175. C11D3×C5⋊AGL(1,𝔽11)semidirect
176. C11D3×D5×C11⋊C5semidirect
186. D3C5⋊#11925895direct (N × H)
189. C5D3×#11925895semidirect
191. C3C2×C5⋊#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×D3×#105972432
C3×C5⋊#119258952
C2×C5⋊#119258953
D3×C11×D555
D3×#119258955
D3×D5×C11⋊C511
D3×C5⋊AGL(1,𝔽11)11