Finite Group Databasebeta

← #14513748

Subgroups — #14513748

Order 1920.

658 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 73 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×#91956C212yesmaximal, complemented
2C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
3C4⋊(C5⋊GL(2,𝔽3))C214yesmaximal, complemented
4#10614257—31nomaximal, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6#91956—24no—
7C2×C5⋊GL(2,𝔽3)C2214yescomplemented
8#91763—41nomaximal
9C4×C5×SL(2,𝔽3)C2212yescomplemented
10#85346—51nomaximal, Hall
11C4×C5×#41D311yescharacteristic, complemented
12C2×#4095—32no—
13C2×#4020—31no—
14#65316—34no—
15#65304—34no—
16#65290—32no—
17#65213—31no—
18C2×D60—42no—
19C2×D60—44no—
20C5×#41⋊C3D412yescomplemented
21C2×C5×SL(2,𝔽3)C2311yescharacteristic
22C5⋊GL(2,𝔽3)—24no—
23C3×C42×C5—41no—
24C2×#986—52no—
25C4×#41⋊C3D511yescharacteristic, complemented
26C4⋊GL(2,𝔽3)—54no—
27C2×C5×#41C2×D311yescharacteristic
28C22×D20—32no—
29C22×D20—62no—
30C4×C5×Q8C2×D312yes—
31C4×C5×D4—32no—
32C5×#117—31no—
33C2×C42×C5—31no—
34#4095—64no—
35#4095—64no—
36C2×#688—34no—
37C2×#686—34no—
38C2×#681—32no—
39#4020—34no—
40#4020—61no—
41#4020—61no—
42#3941—38no—
43C4⋊#168—34no—
44#3038—151noSylow
45C22×D15—44no—
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5—42no—
48D60—84no—
49D60—88no—
50C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
51C2×#41⋊C3C2×D511yescharacteristic
52#986—104no—
53C2×GL(2,𝔽3)—54no—
54#874—201no—
55C4×SL(2,𝔽3)C2×D512yescomplemented
56C23×D5—62no—
57C5×#41—32no—
58C5×#41D1212yescomplemented
59C2×C5×Q8C22×D311yescharacteristic
60C2×C5×D4—31no—
61C22×C4×C5—31no—
62C22×C4×C5—32no—
63C2×D20—34no—
64C2×D20—64no—
65C2×D20—64no—
66C2×D20—64no—
67C2×D20—62no—
68C2×D20—64no—
69C2×D20—128no—
70C5×C4⋊C4—32no—
71C5×C22⋊C4—61no—
72C42×C5—31no—
73C42×C5—32no—
74C42×C5S411yescharacteristic
75#688—64no—
76#688—64no—
77#686—68no—
78#681—64no—
79C2×#168—34no—
80C2×AGL(1,ℤ/8)—152no—
81C2×#127—151no—
82C4×#41D1511yescharacteristic, complemented
83#460—154no—
84#459—154no—
85#423—151no—
86#418—152no—
87C22×C3×C5—41no—
88C2×D15—84no—
89C2×D15—88no—
90C3×C4×C5—42no—
91C3×C4×C5—44no—
92C2×D12—204no—
93C2×D12—202no—
94#41⋊C3D2012yescomplemented
95C2×SL(2,𝔽3)C22×D511yescharacteristic
96GL(2,𝔽3)—104no—
97C3×C42—41no—
98C23×C5—31no—
99C22×D5—64no—
100C22×D5—124no—
101C22×D5—128no—
102C5×Q8—31no—
103C5×Q8C2×D1211yescharacteristic
104C5×D4—32no—
105C5×D4—61no—
106C2×C4×C5—31no—
107C2×C4×C5—32no—
108C2×C4×C5—32no—
109C2×C4×C5—32no—
110C2×C4×C5—64no—
111C2×C4×C5C2×S411yescharacteristic
112C2×C4×C5C2×S412yes—
113D20—64no—
114D20—64no—
115D20—128no—
116D20—124no—
117D20—128no—
118#168—64no—
119C2×#41C2×D1511yescharacteristic
120C22×D4—152no—
121C22×D4—302no—
122AGL(1,ℤ/8)—304no—
123AGL(1,ℤ/8)—304no—
124C2×SD16—154no—
125C2×D8—154no—
126C2×M16—152no—
127#127—154no—
128#127—301no—
129#127—301no—
130C4×Q8C2×D1512yes—
131C4×D4—32no—
132#117—31no—
133C2×C42—31no—
134C4⋊C8—154no—
135#102—158no—
136C2×C3×C5—41no—
137C2×C3×C5—42no—
138D15—164no—
139C22×D3—204no—
140C2×C3×C4—42no—
141C2×C3×C4—41no—
142D12—404no—
143D12—408no—
144SL(2,𝔽3)C2×D2011yescharacteristic, complemented
145C22×C5—32no—
146C22×C5—62no—
147C22×C5C22×S411yescharacteristic
148C2×D5—124no—
149C2×D5—128no—
150C2×D5—248no—
151C4×C5—31no—
152C4×C5—31no—
153C4×C5—62no—
154C4×C5C4⋊S412yes—
155C4×C5#98614yescomplemented
156C24—302no—
157#41—32no—
158#41D6012yescomplemented
159C2×Q8C22×D1511yescharacteristic
160C2×D4—31no—
161C2×D4—154no—
162C2×D4—304no—
163C2×D4—304no—
164C2×D4—304no—
165C2×D4—304no—
166C2×D4—302no—
167C2×D4—608no—
168C22×C4—31no—
169C22×C4—32no—
170SD16—304no—
171SD16—304no—
172D8—308no—
173M16—304no—
174C2×C8—154no—
175C4⋊C4—32no—
176C22⋊C4—61no—
177C42—32no—
178C42—31no—
179C42C5⋊S411yescharacteristic
180C3×C5—41noHall
181C22×C3—41no—
182C2×D3—408no—
183C2×D3—404no—
184C3×C4—42no—
185C3×C4—44no—
186C2×C5—62no—
187C2×C5C2×C4⋊S411yescharacteristic
188C2×C5C2×#98612yes—
189D5—244no—
190C23—31no—
191C23—304no—
192C23—604no—
193C23—608no—
194Q8—31no—
195Q8C2×D6011yescharacteristic
196D4—32no—
197D4—61no—
198D4—304no—
199D4—304no—
200D4—608no—
201D4—604no—
202D4—608no—
203C2×C4—31no—
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—64no—
208C2×C4C2×C5⋊S411yescharacteristic
209C2×C4C2×C5⋊S412yes—
210C8—304no—
211C2×C3—41no—
212C2×C3—42no—
213D3—804no—
214C5#8534611yescharacteristic, complemented, Sylow
215C22—32no—
216C22—62no—
217C22—604no—
218C22—608no—
219C22—1208no—
220C22C22×C5⋊S411yescharacteristic
221C4—31no—
222C4—31no—
223C4—62no—
224C4C4⋊(C5⋊S4)12yes—
225C4#9195614yescomplemented
226C3—41noSylow
227C2—62no—
228C2—1204no—
229C2C2×C4⋊(C5⋊S4)11yescharacteristic
230C2C2×#9195612yes—
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×#41D3
socleC22×C5C22×S4
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#91956C2semidirect
2. C4×C5×#41⋊C3C2semidirect
3. C4⋊(C5⋊GL(2,𝔽3))C2semidirect
7. C2×C5⋊GL(2,𝔽3)C22semidirect
9. C4×C5×SL(2,𝔽3)C22semidirect
11. C4×C5×#41D3semidirect
20. C5×#41⋊C3D4semidirect
25. C4×#41⋊C3D5semidirect
50. C5×SL(2,𝔽3)C2×D4semidirect
55. C4×SL(2,𝔽3)C2×D5semidirect
58. C5×#41D12semidirect
82. C4×#41D15semidirect
94. #41⋊C3D20semidirect
144. SL(2,𝔽3)C2×D20semidirect
155. C4×C5#986semidirect
158. #41D60semidirect
214. C5#85346semidirect
225. C4#91956semidirect

Maximal subgroups

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

subgroupindex
C2×#919562
C4×C5×#41⋊C32
C4⋊(C5⋊GL(2,𝔽3))2
#106142573
#917634
#853465