Finite Group Databasebeta

← #11753973

Subgroups — #11753973

Order 960.

536 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 136 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
1#92019C212yesmaximal, complemented
2C2×D120C211yesmaximal, characteristic, complemented
3C5×#901C211yesmaximal, characteristic, complemented
4C3×#4050C211yesmaximal, characteristic, complemented
5#91301C212yesmaximal, complemented
6#91275C212yesmaximal, complemented
7#91253C214yesmaximal, complemented
8D3×D40C212yesmaximal, complemented
9#66086—31nomaximal, Hall
10C2×D60C2212yescomplemented
11C5×#235C2211yescharacteristic
12C3×#709C2212yescomplemented
13#6790—24no—
14D3×D20C2214yescomplemented
15D5×D12—22no—
16#6773—22no—
17#6769C2214yescomplemented
18C2×C3×C5×C8C2211yescharacteristic, complemented
19D120C2212yescomplemented
20D120C2212yescomplemented
21C5×#208C2211yescharacteristic, complemented
22C5×ΓL(1,𝔽25)C2212yescomplemented
23C5×D3×C8C2212yescomplemented
24C3×Dic20C2211yescharacteristic, complemented
25C3×D40C2211yescharacteristic, complemented
26C3×#677C2212yescomplemented
27#6658C2214yescomplemented
28#6653C2214yescomplemented
29#5769—51nomaximal, Hall
30#4149—32no—
31C5×#131—31no—
32#4054—32no—
33#4054—34no—
34#4050—32no—
35#4050D311yescharacteristic, complemented
36C2×D40—31no—
37C2×D40—32no—
38C22×D15—22no—
39C2×D3×D5—24no—
40C2×C3×C4×C5C2311yescharacteristic
41D60—22no—
42D60C2314yes—
43C5×#67D412yes—
44C5×D12D411yescharacteristic
45C4×C5×D3C2312yes—
46C5×Dic6D411yescharacteristic
47C3×C22⋊D5—22no—
48C3×D20C2312yes—
49C3×C4×D5—22no—
50C3×Dic10C2312yes—
51#1203—24no—
52#1202—24no—
53#1200—24no—
54C3×C5×C8C2311yescharacteristic
55C3×C5×C8C2311yescharacteristic
56C5×C3⋊C8C2312yes—
57#1009—52no—
58C3×#135—51no—
59#949—52no—
60#919—52no—
61#914—54no—
62D3×D8—52no—
63C2×D24—51no—
64#901D511yescharacteristic, complemented
65C5×#41—31no—
66#713—62no—
67D4×D5—62no—
68D4×D5—64no—
69#709—34no—
70#709C2×D312yescomplemented
71C2×D20—32no—
72C2×D20—34no—
73C5×M16—31no—
74C5×M16—32no—
75C2×C5×C8—32no—
76C2×C5×C8C2×D311yescharacteristic, complemented
77Dic20C2×D311yescharacteristic, complemented
78D40—34no—
79D40—32no—
80D40—32no—
81D40C2×D311yescharacteristic, complemented
82#677—34no—
83#677C2×D312yescomplemented
84#576—151noSylow
85C22×C3×C5C2×D411yescharacteristic
86C2×D15—24no—
87C2×D15—82no—
88C2×C5×D3C2×D412yes—
89C2×C3×D5—22no—
90D3×D5—84no—
91C3×C4×C5C2×D411yescharacteristic
92C3×C4×C5C2411yescharacteristic
93C3×Dic5—22no—
94C5×Dic3C2×D412yes—
95C3×#41—52no—
96#239—54no—
97D3×D4—54no—
98D3×D4—104no—
99#235—102no—
100#235C2×D511yescharacteristic
101C2×D12—52no—
102C2×D12—102no—
103C3×Q16—51no—
104C3×SD16—52no—
105C3×D8—51no—
106C2×C3×C8C2×D511yescharacteristic, complemented
107#215—54no—
108#213—54no—
109#208C2×D511yescharacteristic, complemented
110D24—52no—
111D24—52no—
112ΓL(1,𝔽25)C2×D512yescomplemented
113D3×C8C2×D512yescomplemented
114C22×D5—64no—
115C22×D5—62no—
116C5×Q8—31no—
117C5×D4—32no—
118C5×D4—31no—
119C2×C4×C5—32no—
120C2×C4×C5C22×D311yescharacteristic
121C22⋊D5—22no—
122C22⋊D5—64no—
123D20—34no—
124D20—64no—
125D20—62no—
126D20C22×D312yes—
127C4×D5—22no—
128C4×D5—64no—
129Dic10C22×D312yes—
130C5×C8—32no—
131C5×C8C22×D311yescharacteristic
132C5×C8C22×D311yescharacteristic
133H(5,𝔽2)—152no—
134AGL(1,ℤ/8)—154no—
135AGL(1,ℤ/8)—152no—
136#135—51no—
137#135—152no—
138C2×D8—152no—
139C2×D8—151no—
140#131—31no—
141C2×C3×C5—21no—
142C2×C3×C5C22×D411yescharacteristic
143D15—44no—
144C3×D5—42no—
145C5×D3—22no—
146C22×D3—102no—
147C22×D3—104no—
148C3×Q8—52no—
149C3×D4—52no—
150C3×D4—102no—
151C2×C3×C4—102no—
152C2×C3×C4C22×D511yescharacteristic
153#67—104no—
154#67D2012yes—
155D12—54no—
156D12—104no—
157D12—102no—
158D12D2011yescharacteristic
159C4×D3—104no—
160C4×D3C22×D512yes—
161Dic6D2011yescharacteristic
162C3×C8C22×D511yescharacteristic
163C3×C8C22×D511yescharacteristic
164C3⋊C8C22×D512yes—
165C22×C5—32no—
166C22×C5D3×D411yescharacteristic
167C2×D5—22no—
168C2×D5—64no—
169C2×D5—244no—
170C2×D5—242no—
171C4×C5—32no—
172C4×C5D3×D411yescharacteristic
173C4×C5C23×D311yescharacteristic
174Dic5—22no—
175#41—31no—
176#41—52no—
177#41—154no—
178#41—302no—
179C2×D4—154no—
180C2×D4—152no—
181C2×D4—302no—
182C2×D4—304no—
183Q16—51no—
184SD16—52no—
185SD16—154no—
186D8—51no—
187D8—154no—
188D8—152no—
189D8—152no—
190M16—31no—
191M16—32no—
192C2×C8—32no—
193C2×C8D3×D511yescharacteristic, complemented
194C3×C5#57611yescharacteristic, complemented, Hall
195C22×C3—102no—
196C22×C3C2×D2011yescharacteristic
197C2×D3—104no—
198C2×D3—404no—
199C2×D3—402no—
200C2×D3C2×D2012yes—
201C3×C4—102no—
202C3×C4C2×D2011yescharacteristic
203C3×C4C23×D511yescharacteristic
204Dic3C2×D2012yes—
205C2×C5—21no—
206C2×C5—62no—
207C2×C5C2×D3×D411yescharacteristic
208D5—42no—
209D5—124no—
210C23—304no—
211C23—302no—
212Q8—31no—
213Q8—52no—
214D4—32no—
215D4—31no—
216D4—52no—
217D4—102no—
218D4—154no—
219D4—304no—
220D4—304no—
221D4—302no—
222C2×C4—32no—
223C2×C4—102no—
224C2×C4—304no—
225C2×C4C2×D3×D511yescharacteristic
226C8—32no—
227C8C2×D3×D511yescharacteristic
228C8C2×D3×D511yescharacteristic
229C2×C3—21no—
230C2×C3—202no—
231C2×C3C22×D2011yescharacteristic
232D3—22no—
233D3—204no—
234C5#576911yescharacteristic, complemented, Sylow
235C22—32no—
236C22—102no—
237C22—304no—
238C22—1202no—
239C22—1204no—
240C22D3×D2011yescharacteristic
241C4—32no—
242C4—102no—
243C4D3×D2011yescharacteristic
244C4C22×D3×D511yescharacteristic
245C3#6608611yescharacteristic, complemented, Sylow
246C2—21no—
247C2—62no—
248C2—202no—
249C2—604no—
250C2C2×D3×D2011yescharacteristic
subgroupG/H
centerC2C2×D3×D20
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC2×C3×C5×C8C22
socleC2×C3×C5C22×D4
hypercenterC2×C8D3×D5
hypocenterC3×C5#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #92019C2semidirect
2. C2×D120C2semidirect
3. C5×#901C2semidirect
4. C3×#4050C2semidirect
5. #91301C2semidirect
6. #91275C2semidirect
7. #91253C2semidirect
8. D3×D40C2semidirect
10. C2×D60C22semidirect
12. C3×#709C22semidirect
14. D3×D20C22semidirect
17. #6769C22semidirect
18. C2×C3×C5×C8C22semidirect
19. D120C22semidirect
20. D120C22semidirect
21. C5×#208C22semidirect
22. C5×ΓL(1,𝔽25)C22semidirect
23. C5×D3×C8C22semidirect
24. C3×Dic20C22semidirect
25. C3×D40C22semidirect
26. C3×#677C22semidirect
27. #6658C22semidirect
28. #6653C22semidirect
35. #4050D3semidirect
64. #901D5semidirect
70. #709C2×D3semidirect
76. C2×C5×C8C2×D3semidirect
77. Dic20C2×D3semidirect
81. D40C2×D3semidirect
83. #677C2×D3semidirect
106. C2×C3×C8C2×D5semidirect
109. #208C2×D5semidirect
112. ΓL(1,𝔽25)C2×D5semidirect
113. D3×C8C2×D5semidirect
193. C2×C8D3×D5semidirect
194. C3×C5#576semidirect
234. C5#5769semidirect
245. C3#66086semidirect

Maximal subgroups

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

subgroupindex
#920192
C2×D1202
C5×#9012
C3×#40502
#913012
#912752
#912532
D3×D402
#660863
#57695