Finite Group Databasebeta

← #14305795

Subgroups — #14305795

Order 1920.

664 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 170 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
1D5×#869C211yesmaximal, characteristic
2C4×D5⋊(C3⋊C8)C211yesmaximal, characteristic
3C3×#65688C211yesmaximal, characteristic
4C2×#91153C214yesmaximal
5#10604672—31nomaximal, Hall
6C2×D5×Dic6C2212yes—
7C2×D5⋊(C3⋊C8)C2212yes—
8C2×C3×C4⋊AGL(1,𝔽5)—22no—
9C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
10#91758C411yescharacteristic, complemented
11C5×#869C411yescharacteristic, complemented
12C3×C42×D5C2211yescharacteristic
13#91468—22no—
14D5×C4⋊Dic3—22no—
15#91376C412yescomplemented
16C4×C3⋊#170—22no—
17#91153—28no—
18#69579—51nomaximal, Hall
19D5×C4⋊Q8—31no—
20C2×#4009—34no—
21#65688D311yescharacteristic
22C4×D5⋊C8—31no—
23C22×C3×AGL(1,𝔽5)—22no—
24C2×Dic30C2×C412yes—
25C2×C5×Dic6C2×C412yes—
26C2×C3×C4×D5D412yes—
27C2×C3×C4×D5C2311yescharacteristic
28C2×#1204—22no—
29C2×D5×Dic3—22no—
30D5×Dic6—24no—
31D5×Dic6—24no—
32C2×C3⋊#170—22no—
33D5⋊(C3⋊C8)—22no—
34D5⋊(C3⋊C8)D414yes—
35C3×C4⋊AGL(1,𝔽5)—24no—
36C3×C4⋊AGL(1,𝔽5)—44no—
37C3×C42×C5C2×C411yescharacteristic
38C4⋊Dic15—22no—
39C5×C4⋊Dic3—22no—
40C3×C4×Dic5C2×C411yescharacteristic
41C3×C4×Dic5D412yes—
42#6668—24no—
43C2×#869—51no—
44C3×#384—51no—
45C2×#810—54no—
46C2×C4×C3⋊C8—51no—
47C2×Q8×D5—32no—
48C2×C4⋊AGL(1,𝔽5)—22no—
49C2×C4⋊AGL(1,𝔽5)C2×D312yes—
50C2×D5⋊C8—32no—
51C5×C4⋊Q8—31no—
52#4090—32no—
53D5×C4⋊C4—62no—
54#4034—62no—
55C42×D5C2×D311yescharacteristic
56#4015—31no—
57#4009—68no—
58C4×#170—62no—
59#1956—151noSylow
60C22×C3×D5C2×D411yescharacteristic
61C2×C3×AGL(1,𝔽5)—42no—
62C2×C3×AGL(1,𝔽5)—44no—
63C2×C3×C4×C5C22⋊C412yes—
64C2×C3×C4×C5C22×C411yescharacteristic
65C2×Dic15—22no—
66Dic30—24no—
67C2×C5×Dic3—22no—
68C5×Dic6—24no—
69C2×C3×Dic5C22⋊C412yes—
70C2×C3×Dic5C2×D411yescharacteristic
71C3×C4×D5SD1614yes—
72C3×C4×D5Q1614yes—
73C3×C4×D5C2×D412yes—
74C3×C4×D5#4112yes—
75#1204—44no—
76D5×Dic3—42no—
77D5×Dic3—42no—
78C3⋊#170—24no—
79C22×Dic6—52no—
80C2×C3×C4⋊C4—52no—
81C2×C3×C4⋊C4—102no—
82C2×C3×C42—51no—
83C2×C4⋊Dic3—102no—
84C22×C3⋊C8—52no—
85#869—52no—
86#869—51no—
87#869—102no—
88#869AGL(1,𝔽5)11yescharacteristic, complemented
89#810—108no—
90C4×C3⋊C8—102no—
91C22×AGL(1,𝔽5)—22no—
92C2×C5×Q8—32no—
93Q8×D5—64no—
94Q8×D5—64no—
95C2×C4×D5—62no—
96C2×C4×D5#6712yes—
97C2×C4×D5C22×D311yescharacteristic
98C2×Dic10—32no—
99C2×Dic10—62no—
100C2×#170—62no—
101C4⋊AGL(1,𝔽5)—24no—
102C4⋊AGL(1,𝔽5)—44no—
103D5⋊C8—34no—
104D5⋊C8—62no—
105C5×C4⋊C4—62no—
106C42×C5C4×D311yescharacteristic
107C4⋊Dic5—62no—
108#683—64no—
109C4×Dic5C4×D311yescharacteristic
110C4×Dic5D1212yes—
111C2×C4⋊Q8—151no—
112C2×#103—154no—
113C2×C4×C8—151no—
114#384—51no—
115C22×C3×C5C2×C22⋊C411yescharacteristic
116C2×C3×D5#12411yescharacteristic
117C2×C3×D5#12711yescharacteristic
118C2×C3×D5C2×SD1612yes—
119C2×C3×D5C2×Q1612yes—
120C3×AGL(1,𝔽5)—82no—
121C3×C4×C5#10314yescomplemented
122C3×C4×C5C4×D412yes—
123Dic15—42no—
124C3×Dic5#10314yescomplemented
125C3×Dic5#12112yes—
126C5×Dic3—42no—
127C22×C3×C4—52no—
128C22×C3×C4—51no—
129C22×C3×C4—102no—
130C22×Dic3—102no—
131C2×Dic6—52no—
132C2×Dic6—104no—
133C2×Dic6—104no—
134C2×Dic6—102no—
135C2×Dic6C2×AGL(1,𝔽5)12yes—
136C3×C4⋊C4—104no—
137C3×C4⋊C4—204no—
138C3×C42—52no—
139C3×C42—51no—
140C3×C42C2×AGL(1,𝔽5)11yescharacteristic
141C4⋊Dic3—22no—
142C4⋊Dic3—104no—
143C4⋊Dic3—102no—
144C2×C3⋊C8—54no—
145C2×C3⋊C8—102no—
146C2×C3⋊C8—102no—
147C22×D5C2×#6711yescharacteristic
148C2×AGL(1,𝔽5)—44no—
149C2×AGL(1,𝔽5)—42no—
150C5×Q8—64no—
151C2×C4×C5—62no—
152C2×C4×C5(C2×D3)⋊C412yes—
153C2×C4×C5C2×C4×D311yescharacteristic
154C2×Dic5—62no—
155C2×Dic5(C2×D3)⋊C412yes—
156C2×Dic5C2×D1211yescharacteristic
157C4×D5—122no—
158C4×D5—122no—
159C4×D5#21414yes—
160C4×D5#21614yes—
161C4×D5D3×D412yes—
162C4×D5#23912yes—
163Dic10—64no—
164Dic10—124no—
165#170—64no—
166C22×Q8—152no—
167C22×C8—152no—
168C4⋊Q8—31no—
169C4⋊Q8—152no—
170C4⋊Q8—151no—
171C4⋊Q8—302no—
172C2×C4⋊C4—52no—
173C2×C4⋊C4—102no—
174C2×C4⋊C4—302no—
175C2×C42—51no—
176#103—308no—
177C4×C8—302no—
178C2×C3×C5#39011yescharacteristic
179C2×C3×C5C2×#10312yes—
180C3×D5#48712yes—
181C3×D5#49211yescharacteristic
182C3×D5#49411yescharacteristic
183C23×C3—51no—
184C2×C3×C4—52no—
185C2×C3×C4—51no—
186C2×C3×C4—52no—
187C2×C3×C4—52no—
188C2×C3×C4—54no—
189C2×C3×C4—54no—
190C2×C3×C4—202no—
191C2×C3×C4—204no—
192C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
193C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
194C2×Dic3—22no—
195C2×Dic3—102no—
196C2×Dic3—202no—
197C2×Dic3—202no—
198Dic6—24no—
199Dic6—104no—
200Dic6—204no—
201C3⋊C8—104no—
202C22×C5C2×(C2×D3)⋊C411yescharacteristic
203C2×D5C2×#21412yes—
204C2×D5#94011yescharacteristic
205C2×D5C2×#21612yes—
206C2×D5#94711yescharacteristic
207AGL(1,𝔽5)—82no—
208C4×C5—122no—
209C4×C5#81014yescomplemented
210C4×C5#89312yes—
211Dic5—122no—
212Dic5#81014yescomplemented
213Dic5#89512yes—
214C2×Q8—32no—
215C2×Q8—152no—
216C2×Q8—302no—
217C2×Q8—304no—
218C2×Q8—304no—
219C22×C4—52no—
220C22×C4—51no—
221C22×C4—102no—
222C22×C4—302no—
223C2×C8—154no—
224C2×C8—302no—
225C2×C8—302no—
226C4⋊C4—62no—
227C4⋊C4—104no—
228C4⋊C4—204no—
229C4⋊C4—304no—
230C4⋊C4—302no—
231C42—52no—
232C42—51no—
233C42D3×AGL(1,𝔽5)11yescharacteristic
234C3×C5#195611yescharacteristic, complemented, Hall
235C22×C3—51no—
236C22×C3—51no—
237C22×C3—52no—
238C22×C3—52no—
239C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
240C3×C4—52no—
241C3×C4—54no—
242C3×C4—402no—
243C3×C4#400914yescomplemented
244C3×C4D4×AGL(1,𝔽5)12yes—
245Dic3—42no—
246Dic3—202no—
247C2×C5C2×#81012yes—
248C2×C5#498811yescharacteristic
249D5#507611yescharacteristic
250D5#509211yescharacteristic
251D5#509312yes—
252C23—51no—
253Q8—64no—
254Q8—304no—
255Q8—604no—
256C2×C4—52no—
257C2×C4—51no—
258C2×C4—54no—
259C2×C4—54no—
260C2×C4—52no—
261C2×C4—52no—
262C2×C4—62no—
263C2×C4—202no—
264C2×C4—204no—
265C2×C4—302no—
266C2×C4—602no—
267C2×C4—602no—
268C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
269C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
270C8—304no—
271C2×C3—51no—
272C2×C3—52no—
273C2×C3—51no—
274C2×C3#6578011yescharacteristic
275C2×C3C2×#400912yes—
276C5#6957911yescharacteristic, complemented, Sylow
277C22—52no—
278C22—52no—
279C22—51no—
280C22—51no—
281C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
282C4—54no—
283C4—52no—
284C4—122no—
285C4—402no—
286C4—602no—
287C4#9115314yescomplemented
288C4#9192112yes—
289C3#1060467211yescharacteristic, complemented, Sylow
290C2—51no—
291C2—51no—
292C2—52no—
293C2C2×#9115312yes—
294C2#1175185711yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1956
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
10. #91758C4semidirect
11. C5×#869C4semidirect
15. #91376C4semidirect
88. #869AGL(1,𝔽5)semidirect
121. C3×C4×C5#103semidirect
124. C3×Dic5#103semidirect
209. C4×C5#810semidirect
212. Dic5#810semidirect
234. C3×C5#1956semidirect
243. C3×C4#4009semidirect
276. C5#69579semidirect
287. C4#91153semidirect
289. C3#10604672semidirect

Maximal subgroups

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

subgroupindex
D5×#8692
C4×D5⋊(C3⋊C8)2
C3×#656882
C2×#911532
#106046723
#695795