Finite Group Databasebeta

← #14458175

Subgroups — #14458175

Order 1920.

952 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 167 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#11756516C214yesmaximal, complemented
2C3×C5×#493C211yesmaximal, characteristic, complemented
3#11751261C214yesmaximal, complemented
4#11751178C214yesmaximal, complemented
5#11750801C212yesmaximal, complemented
6#10613522—31nomaximal, Hall
7#92095C2214yescomplemented
8C2×C3×C5×D8C2214yescomplemented
9C3×C5×#127C2212yescomplemented
10#91821C2218yescomplemented
11#91801—24no—
12#91800—28no—
13D8×D15—24no—
14#91793C2212yes—
15#91790C2214yescomplemented
16C3×C4×C5×C8C2211yescharacteristic, complemented
17#91117C2214yescomplemented
18#91103C2212yescomplemented
19#91089C2214yescomplemented
20#81791—51nomaximal, Hall
21#66091—34no—
22C5×#493D311yescharacteristic, complemented
23#65449—34no—
24#65366—34no—
25#64989—32no—
26C2×C3×C5×D4—42no—
27C2×C3×C5×D4C2314yes—
28C2×#1220—44no—
29#6819—28no—
30D4×D15—28no—
31#6817C2314yes—
32C3×C5×D8—24no—
33C3×C5×D8—24no—
34C2×C3×C5×C8C2312yes—
35C3×C42×C5C2311yescharacteristic
36#6716—28no—
37#6715—28no—
38#6710C2314yes—
39Dic60D412yescomplemented
40D120D412yescomplemented
41#6706D414yescomplemented
42#6705—24no—
43C8×D15—24no—
44#5757—54no—
45C3×#493D511yescharacteristic, complemented
46#5160—54no—
47#5077—54no—
48#4700—52no—
49#4144—34no—
50C2×C5×D8C2×D314yescomplemented
51C5×#127C2×D312yescomplemented
52#4078—38no—
53#4058—64no—
54#4057—68no—
55D5×D8—64no—
56#4050—32no—
57#4047—34no—
58C4×C5×C8C2×D311yescharacteristic, complemented
59#3965—34no—
60#3951—32no—
61#3937—34no—
62#3292—151noSylow
63C23×C3×C5—24no—
64C22×D15—44no—
65C3×C5×D4—28no—
66C3×C5×D4—84no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5C2411yescharacteristic
69#1220—24no—
70#1220—48no—
71C2×Dic15—44no—
72D60C2×D414yes—
73C4×D15—24no—
74Dic30C2×D414yes—
75C3×C5×C8C2×D412yes—
76C3×C5×C8C2×D412yes—
77C3⋊#168—24no—
78#1004—54no—
79C2×C3×D8C2×D514yescomplemented
80C3×#127C2×D512yescomplemented
81#932—58no—
82#912—104no—
83#911—108no—
84D3×D8—104no—
85#904—52no—
86#901—54no—
87C3×C4×C8C2×D511yescharacteristic, complemented
88#833—54no—
89#819—52no—
90#805—54no—
91C2×C5×D4—42no—
92C2×C5×D4C22×D314yes—
93C2×C22⋊D5—124no—
94#711—68no—
95D4×D5—68no—
96#709—34no—
97C5×D8—24no—
98C5×D8—24no—
99C2×C5×C8C22×D312yes—
100C42×C5C22×D311yescharacteristic
101#687—68no—
102#686—68no—
103#681—34no—
104Dic20—32no—
105D40—32no—
106#677—34no—
107#676—64no—
108C8×D5—64no—
109#576—154no—
110#493D1511yescharacteristic, complemented
111#472—154no—
112#453—154no—
113#443—152no—
114C22×C3×C5—44no—
115C22×C3×C5—84no—
116C22×C3×C5H(5,𝔽2)11yescharacteristic
117C2×D15—24no—
118C2×D15—164no—
119C3×C4×C5—22no—
120C3×C4×C5C22×D412yes—
121Dic15—24no—
122C2×C3×D4—42no—
123C2×C3×D4C22×D514yes—
124C2×#67—204no—
125#237—108no—
126D3×D4—108no—
127#235—54no—
128C3×D8—24no—
129C3×D8—24no—
130C2×C3×C8C22×D512yes—
131C3×C42C22×D511yescharacteristic
132#214—108no—
133#213—108no—
134#208—54no—
135Dic12—52no—
136D24—52no—
137#204—54no—
138ΓL(1,𝔽25)—104no—
139D3×C8—104no—
140C23×C5—24no—
141C22×D5—124no—
142C5×D4—28no—
143C5×D4—84no—
144C2×C4×C5—21no—
145C2×C4×C5C23×D311yescharacteristic
146C22⋊D5—64no—
147C22⋊D5—128no—
148C2×Dic5—124no—
149D20—34no—
150C4×D5—64no—
151Dic10—34no—
152C5×C8D3×D412yes—
153C5×C8D3×D412yes—
154#168—64no—
155H(5,𝔽2)—154no—
156AGL(1,ℤ/8)—158no—
157AGL(1,ℤ/8)—308no—
158#135—152no—
159#135—304no—
160C2×D8—304no—
161C2×D8C2×D1514yescomplemented
162#131—154no—
163#127C2×D1512yescomplemented
164#108—152no—
165#104—154no—
166#100—154no—
167C4×C8C2×D1511yescharacteristic, complemented
168C2×C3×C5—21no—
169C2×C3×C5—84no—
170C2×C3×C5D4211yescharacteristic
171D15—44no—
172C23×C3—24no—
173C22×D3—204no—
174C3×D4—28no—
175C3×D4—84no—
176C2×C3×C4—21no—
177C2×C3×C4C23×D511yescharacteristic
178#67—104no—
179#67—208no—
180C2×Dic3—204no—
181D12—54no—
182C4×D3—104no—
183Dic6—54no—
184C3×C8D4×D512yes—
185C3×C8D4×D512yes—
186C3⋊C8—104no—
187C22×C5—44no—
188C22×C5—84no—
189C22×C5#100411yescharacteristic
190C2×D5—64no—
191C2×D5—484no—
192C4×C5—22no—
193C4×C5C2×D3×D412yes—
194Dic5—64no—
195#41—154no—
196#41—308no—
197C2×D4—42no—
198C2×D4—308no—
199C2×D4—604no—
200C2×D4C22×D1514yes—
201Q16—152no—
202SD16—154no—
203SD16—308no—
204D8—24no—
205D8—24no—
206D8—152no—
207D8—308no—
208M16—154no—
209M16—304no—
210C2×C8—304no—
211C2×C8C22×D1512yes—
212C42C22×D1511yescharacteristic
213C3×C5#329211yescharacteristic, complemented, Hall
214C22×C3—44no—
215C22×C3—84no—
216C22×C3#414411yescharacteristic
217C2×D3—104no—
218C2×D3—804no—
219C3×C4—22no—
220C3×C4C2×D4×D512yes—
221Dic3—104no—
222C2×C5—21no—
223C2×C5—84no—
224C2×C5#571711yescharacteristic
225D5—124no—
226C23—24no—
227C23—604no—
228Q8—154no—
229D4—28no—
230D4—84no—
231D4—154no—
232D4—304no—
233D4—608no—
234C2×C4—21no—
235C2×C4—304no—
236C2×C4—604no—
237C2×C4C23×D1511yescharacteristic
238C8—304no—
239C8D4×D1512yes—
240C8D4×D1512yes—
241C2×C3—21no—
242C2×C3—84no—
243C2×C3#6605111yescharacteristic
244D3—204no—
245C5#8179111yescharacteristic, complemented, Sylow
246C22—44no—
247C22—84no—
248C22—304no—
249C22—2404no—
250C22#9209511yescharacteristic
251C4—22no—
252C4—304no—
253C4C2×D4×D1512yes—
254C3#1061352211yescharacteristic, complemented, Sylow
255C2—21no—
256C2—84no—
257C2—604no—
258C2#1175647611yescharacteristic
subgroupG/H
centerC2#11756476
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#493C2
socleC2×C3×C5D42
hypercenter#493D15
hypocenterC3×C5#3292
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #11756516C2semidirect
2. C3×C5×#493C2semidirect
3. #11751261C2semidirect
4. #11751178C2semidirect
5. #11750801C2semidirect
7. #92095C22semidirect
8. C2×C3×C5×D8C22semidirect
9. C3×C5×#127C22semidirect
10. #91821C22semidirect
15. #91790C22semidirect
16. C3×C4×C5×C8C22semidirect
17. #91117C22semidirect
18. #91103C22semidirect
19. #91089C22semidirect
22. C5×#493D3semidirect
39. Dic60D4semidirect
40. D120D4semidirect
41. #6706D4semidirect
45. C3×#493D5semidirect
50. C2×C5×D8C2×D3semidirect
51. C5×#127C2×D3semidirect
58. C4×C5×C8C2×D3semidirect
79. C2×C3×D8C2×D5semidirect
80. C3×#127C2×D5semidirect
87. C3×C4×C8C2×D5semidirect
110. #493D15semidirect
161. C2×D8C2×D15semidirect
163. #127C2×D15semidirect
167. C4×C8C2×D15semidirect
213. C3×C5#3292semidirect
245. C5#81791semidirect
254. C3#10613522semidirect

Maximal subgroups

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

subgroupindex
#117565162
C3×C5×#4932
#117512612
#117511782
#117508012
#106135223
#817915