Finite Group Databasebeta

← #10617728⋊C3 #14514036

Subgroups — #10617728⋊C3 #14514036

Order 1920.

762 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#4150⋊C3C212yesmaximal, complemented
2C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
3SL(2,𝔽3)×D20C214yesmaximal, complemented
4#10617728C311yesmaximal, characteristic, complemented, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6#4150⋊C3—24no—
7C2×D5×SL(2,𝔽3)C2214yes—
8C3×#4020—41nomaximal
9C4×C5×SL(2,𝔽3)C2212yes—
10#3499⋊C3—51nomaximal, Hall
11C2×#4150C2×C312yescomplemented
12C4×C5×#41C2×C311yescharacteristic, complemented
13Q8×D20C2×C314yescomplemented
14#65889—34no—
15#65860—32no—
16#65811—31no—
17C2×#4015—31no—
18C2×C3×D20—42no—
19C2×C3×D20—44no—
20C5×#41⋊C3D412yescomplemented
21C2×C5×SL(2,𝔽3)C2311yescharacteristic
22D5×SL(2,𝔽3)—24no—
23C3×C42×C5—41no—
24C2×2−1+4⋊C3—52no—
25D4×SL(2,𝔽3)—54no—
26C4×#41⋊C3D511yescharacteristic, complemented
27C2×C5×#41C22×C311yescharacteristic
28#4150—24no—
29#4150—64no—
30C2×Q8×D5C22×C314yes—
31C2×#711—34no—
32C2×#709—32no—
33C22×Dic10—32no—
34C4×C5×Q8C22×C312yes—
35C4×C5×D4—32no—
36C5×#117—31no—
37C2×C42×C5—31no—
38#4076—34no—
39C2×C4⋊Dic5—34no—
40#4043—38no—
41#4032—38no—
42#4021—32no—
43#4020A411yescharacteristic
44C4×D20—34no—
45#4015—32no—
46#4015—31no—
47#4015—34no—
48#3499—51noSylow
49C22×C3×D5—44no—
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5—42no—
52C3×D20—84no—
53C3×D20—88no—
54C5×SL(2,𝔽3)C2×D411yescharacteristic
552−1+4⋊C3—104no—
56C2×#41⋊C3C2×D511yescharacteristic
57C22×SL(2,𝔽3)—54no—
58C3×#127—201no—
59C4×SL(2,𝔽3)C2×D512yes—
60C5×#41—32no—
61C5×#41C3×D412yescomplemented
62C2×C5×Q8C23×C311yescharacteristic
63C2×C5×D4—31no—
64C22×C4×C5—31no—
65C22×C4×C5—32no—
66C2×C22⋊D5—34no—
67C22×Dic5—34no—
68Q8×D5—24no—
69Q8×D5—64no—
70#711—68no—
71#711—68no—
72#709—64no—
73#709—64no—
74C2×D20C2×A412yes—
75C2×D20C2×A414yes—
76C2×C4×D5—34no—
77C2×Dic10—32no—
78C2×Dic10—34no—
79C2×Dic10—64no—
80C2×Dic10—64no—
81C5×C4⋊C4—32no—
82C5×C22⋊C4—32no—
83C42×C5—31no—
84C42×C5—32no—
85C42×C5C2×A411yescharacteristic
86#685—38no—
87C4⋊Dic5—38no—
88C4⋊Dic5—34no—
89C2×2−1+4—52no—
90D4×Q8—54no—
91#547—154no—
92#536—152no—
93#532—151no—
94C2×C4⋊Q8—151no—
95C4×#41C3×D511yescharacteristic, complemented
96C22×C3×C5—41no—
97C2×C3×D5—84no—
98C2×C3×D5—88no—
99C3×C4×C5—42no—
100C3×C4×C5—44no—
101C2×C3×D4—202no—
102C2×C3×D4—204no—
103#41⋊C3D2012yescomplemented
104C2×SL(2,𝔽3)—104no—
105C2×SL(2,𝔽3)C22×D511yescharacteristic
106C3×C42—41no—
107C23×C5—31no—
108C22×D5C22×A414yes—
109C5×Q8—31no—
110C5×Q8C2×C3×D411yescharacteristic
111C5×D4—32no—
112C5×D4—32no—
113C2×C4×C5—31no—
114C2×C4×C5—32no—
115C2×C4×C5—32no—
116C2×C4×C5—32no—
117C2×C4×C5—64no—
118C2×C4×C5C22×A411yescharacteristic
119C2×C4×C5C22×A412yes—
120C22⋊D5—68no—
121C2×Dic5—34no—
122C2×Dic5—68no—
123D20—24no—
124D20—28no—
125C4×D5—64no—
126C4×D5—64no—
127Dic10—64no—
128Dic10—64no—
129Dic10—64no—
1302−1+4—104no—
1312−1+4—304no—
132C2×#41—152no—
133C2×#41—154no—
134C2×#41C2×C3×D511yescharacteristic
135C22×Q8—54no—
136C22×Q8—152no—
137C4⋊Q8—152no—
138C4⋊Q8—154no—
139C4⋊Q8—151no—
140#127—51no—
141#124—152no—
142#123—158no—
143C22⋊Q8—158no—
144#121—154no—
145C4×Q8C2×C3×D512yes—
146C4×D4—32no—
147C4×D4—154no—
148#117—31no—
149C2×C4⋊C4—154no—
150C2×C42—31no—
151C2×C3×C5—41no—
152C2×C3×C5—42no—
153C3×D5—164no—
154C23×C3—204no—
155C3×D4—404no—
156C3×D4—408no—
157C2×C3×C4—42no—
158C2×C3×C4—41no—
159SL(2,𝔽3)C2×D2011yescharacteristic
160C22×C5—32no—
161C22×C5—62no—
162C22×C5C23×A411yescharacteristic
163C2×D5—24no—
164C2×D5—28no—
165C4×C5—31no—
166C4×C5—31no—
167C4×C5—62no—
168C4×C5D4×A412yes—
169C4×C52−1+4⋊C314yescomplemented
170Dic5—64no—
171#41—32no—
172#41—304no—
173#41—304no—
174#41—308no—
175#41—308no—
176#41C3×D2012yescomplemented
177C2×Q8—104no—
178C2×Q8—154no—
179C2×Q8—152no—
180C2×Q8—304no—
181C2×Q8—304no—
182C2×Q8—304no—
183C2×Q8C22×C3×D511yescharacteristic
184C2×D4—31no—
185C2×D4—54no—
186C2×D4—52no—
187C2×D4—154no—
188C22×C4—31no—
189C22×C4—32no—
190C22×C4—154no—
191C22×C4—154no—
192C4⋊C4—32no—
193C4⋊C4—158no—
194C4⋊C4—154no—
195C22⋊C4—32no—
196C22⋊C4—158no—
197C42—31no—
198C42—32no—
199C42D5×A411yescharacteristic
200C3×C5—41noHall
201C22×C3—41no—
202C22×C3—408no—
203C22×C3—404no—
204C3×C4—42no—
205C3×C4—44no—
206C2×C5—62no—
207C2×C5C2×D4×A411yescharacteristic
208C2×C5C2×2−1+4⋊C312yes—
209D5—44no—
210C23—31no—
211C23—54no—
212Q8—31no—
213Q8—304no—
214Q8—304no—
215Q8—304no—
216Q8C2×C3×D2011yescharacteristic
217D4—32no—
218D4—32no—
219D4—104no—
220D4—108no—
221D4—308no—
222C2×C4—31no—
223C2×C4—32no—
224C2×C4—32no—
225C2×C4—32no—
226C2×C4—64no—
227C2×C4—154no—
228C2×C4—304no—
229C2×C4—304no—
230C2×C4—308no—
231C2×C4C2×D5×A411yescharacteristic
232C2×C4C2×D5×A412yes—
233C2×C3—41no—
234C2×C3—42no—
235C2×C3—804no—
236C5#3499⋊C311yescharacteristic, complemented, Sylow
237C22—32no—
238C22—62no—
239C22—104no—
240C22—108no—
241C22C22×D5×A411yescharacteristic
242C4—31no—
243C4—31no—
244C4—62no—
245C4—304no—
246C4A4×D2012yes—
247C4#4150⋊C314yescomplemented
248C3—41noSylow
249C2—62no—
250C2—204no—
251C2C2×A4×D2011yescharacteristic
252C2C2×#4150⋊C312yes—
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC42D5×A4
hypocenterC5×Q8C2×C3×D4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#4150⋊C3C2semidirect
2. C4×C5×#41⋊C3C2semidirect
3. SL(2,𝔽3)×D20C2semidirect
4. #10617728C3semidirect
11. C2×#4150C2×C3semidirect
12. C4×C5×#41C2×C3semidirect
13. Q8×D20C2×C3semidirect
20. C5×#41⋊C3D4semidirect
26. C4×#41⋊C3D5semidirect
61. C5×#41C3×D4semidirect
95. C4×#41C3×D5semidirect
103. #41⋊C3D20semidirect
169. C4×C52−1+4⋊C3semidirect
176. #41C3×D20semidirect
236. C5#3499⋊C3semidirect
247. C4#4150⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#4150⋊C32
C4×C5×#41⋊C32
SL(2,𝔽3)×D202
#106177283
C3×#40204
#3499⋊C35