Finite Group Databasebeta

← #14307333

Subgroups — #14307333

Order 1920.

504 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 130 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×#870C211yesmaximal, characteristic
2C4×D5⋊(C3⋊C8)C211yesmaximal, characteristic
3C3×#65689C211yesmaximal, characteristic
4#11746528C214yesmaximal
5#10604590—31nomaximal, Hall
6C2×D5⋊(C3⋊C8)C2212yes—
7C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
8#91759C411yescharacteristic, complemented
9C5×#870C411yescharacteristic, complemented
10C3×C42×D5C2211yescharacteristic
11D5×C4⋊Dic3C2212yes—
12D5×Dic3⋊C4—22no—
13#91388C412yescomplemented
14#91378—22no—
15C4×C3⋊#170—22no—
16C3×(C2×AGL(1,𝔽5))⋊C4—22no—
17#69554—51nomaximal, Hall
18D5×#125—31no—
19#65689D311yescharacteristic
20C4×D5⋊C8—31no—
21#64874—34no—
22C22×C3×AGL(1,𝔽5)—22no—
23C2×C3×C4×D5D412yes—
24C2×C3×C4×D5C2311yescharacteristic
25C2×D5×Dic3—22no—
26C2×C3⋊#170—22no—
27D5⋊(C3⋊C8)—22no—
28D5⋊(C3⋊C8)Q814yes—
29C3×C4⋊AGL(1,𝔽5)—24no—
30C3×C42×C5C2×C411yescharacteristic
31C4⋊Dic15C2×C412yes—
32#6712—22no—
33C5×C4⋊Dic3C2×C412yes—
34C5×Dic3⋊C4—22no—
35C3×C4×Dic5C2×C411yescharacteristic
36C3×C4×Dic5D412yes—
37Dic3⋊Dic5—22no—
38#6669—22no—
39#6668—22no—
40C2×#870—51no—
41C3×#382—51no—
42C2×C4×C3⋊C8—51no—
43#4529—54no—
44C2×C4⋊AGL(1,𝔽5)C2×D312yes—
45C2×D5⋊C8—32no—
46C5×#125—31no—
47D5×C4⋊C4—32no—
48D5×C4⋊C4—62no—
49#4036—32no—
50#4035—62no—
51C42×D5C2×D311yescharacteristic
52#4016—31no—
53(C2×AGL(1,𝔽5))⋊C4—22no—
54C4×#170—62no—
55#1991—151noSylow
56C22×C3×D5C2×D411yescharacteristic
57C2×C3×AGL(1,𝔽5)—42no—
58C2×C3×AGL(1,𝔽5)—44no—
59C2×C3×C4×C5C22⋊C412yes—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×Dic15—22no—
62C2×C5×Dic3—22no—
63C2×C3×Dic5C22⋊C412yes—
64C2×C3×Dic5C2×D411yescharacteristic
65C3×C4×D5—24no—
66C3×C4×D5C2×Q812yes—
67C3×C4×D5#4112yes—
68D5×Dic3—44no—
69C3⋊#170—24no—
70C2×C3×C4⋊C4—52no—
71C2×C3×C42—51no—
72C2×C4⋊Dic3—52no—
73C2×Dic3⋊C4—102no—
74C22×C3⋊C8—52no—
75#870—51no—
76#870—52no—
77#870—102no—
78#870AGL(1,𝔽5)11yescharacteristic, complemented
79C3×#95—102no—
80C4×C3⋊C8—102no—
81C22×AGL(1,𝔽5)—22no—
82C2×C4×D5—62no—
83C2×C4×D5#6712yes—
84C2×C4×D5C22×D311yescharacteristic
85C2×#170—62no—
86C4⋊AGL(1,𝔽5)—24no—
87D5⋊C8—34no—
88D5⋊C8—62no—
89C5×C4⋊C4—32no—
90C5×C4⋊C4—62no—
91C42×C5C4×D311yescharacteristic
92C4⋊Dic5—32no—
93C4⋊Dic5—62no—
94#683—62no—
95#683—62no—
96#683—62no—
97C4×Dic5C4×D311yescharacteristic
98C4×Dic5D1212yes—
99C2×#125—151no—
100C2×C4×C8—151no—
101#382—51no—
102#340—154no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C2×C3×D5#12411yescharacteristic
105C2×C3×D5C4⋊Q811yescharacteristic
106C2×C3×D5#13514yes—
107C3×AGL(1,𝔽5)—82no—
108C3×C4×C5—22no—
109C3×C4×C5C4×Q812yes—
110Dic15—42no—
111C3×Dic5—22no—
112C3×Dic5C22⋊Q812yes—
113C5×Dic3—42no—
114C22×C3×C4—51no—
115C22×C3×C4—52no—
116C22×C3×C4—102no—
117C22×Dic3—102no—
118C3×C4⋊C4—104no—
119C3×C42—52no—
120C3×C42—51no—
121C3×C42C2×AGL(1,𝔽5)11yescharacteristic
122C4⋊Dic3—52no—
123C4⋊Dic3—102no—
124C4⋊Dic3C2×AGL(1,𝔽5)12yes—
125Dic3⋊C4—22no—
126Dic3⋊C4—102no—
127Dic3⋊C4—102no—
128Dic3⋊C4—102no—
129C2×C3⋊C8—54no—
130C2×C3⋊C8—102no—
131C2×C3⋊C8—102no—
132C22×D5C2×#6711yescharacteristic
133C2×AGL(1,𝔽5)—42no—
134C2×AGL(1,𝔽5)—44no—
135C2×C4×C5—62no—
136C2×C4×C5(C2×D3)⋊C412yes—
137C2×C4×C5C2×C4×D311yescharacteristic
138C2×Dic5—62no—
139C2×Dic5(C2×D3)⋊C412yes—
140C2×Dic5C2×D1211yescharacteristic
141C4×D5—24no—
142C4×D5—124no—
143C4×D5#23712yes—
144C4×D5D3×Q812yes—
145#170—64no—
146C22×C8—152no—
147#125—31no—
148#125—152no—
149#125—151no—
150#125—302no—
151C2×C4⋊C4—52no—
152C2×C4⋊C4—152no—
153C2×C4⋊C4—302no—
154C2×C42—51no—
155C4×C8—302no—
156#95—102no—
157C2×C3×C5#39111yescharacteristic
158C2×C3×C5#41612yes—
159C3×D5#48812yes—
160C3×D5#49912yes—
161C23×C3—51no—
162C2×C3×C4—51no—
163C2×C3×C4—52no—
164C2×C3×C4—52no—
165C2×C3×C4—52no—
166C2×C3×C4—104no—
167C2×C3×C4—202no—
168C2×C3×C4—204no—
169C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
170C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
171C2×Dic3—22no—
172C2×Dic3—102no—
173C2×Dic3—204no—
174C3⋊C8—104no—
175C22×C5C2×(C2×D3)⋊C411yescharacteristic
176C2×D5#93611yescharacteristic
177C2×D5#94411yescharacteristic
178C2×D5#95014yes—
179AGL(1,𝔽5)—82no—
180C4×C5—22no—
181C4×C5—122no—
182C4×C5#88712yes—
183Dic5—22no—
184Dic5—122no—
185Dic5#89712yes—
186C22×C4—51no—
187C22×C4—52no—
188C22×C4—102no—
189C22×C4—302no—
190C2×C8—154no—
191C2×C8—302no—
192C2×C8—302no—
193C4⋊C4—32no—
194C4⋊C4—62no—
195C4⋊C4—104no—
196C4⋊C4—152no—
197C4⋊C4—302no—
198C4⋊C4—302no—
199C4⋊C4—302no—
200C4⋊C4—302no—
201C42—52no—
202C42—51no—
203C42D3×AGL(1,𝔽5)11yescharacteristic
204C3×C5#199111yescharacteristic, complemented, Hall
205C22×C3—54no—
206C22×C3—51no—
207C22×C3—51no—
208C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
209C3×C4—22no—
210C3×C4—52no—
211C3×C4—102no—
212C3×C4—402no—
213C3×C4Q8×AGL(1,𝔽5)12yes—
214Dic3—42no—
215Dic3—202no—
216C2×C5#497311yescharacteristic
217C2×C5#500212yes—
218D5#505612yes—
219D5#506512yes—
220C23—51no—
221C2×C4—51no—
222C2×C4—52no—
223C2×C4—52no—
224C2×C4—52no—
225C2×C4—62no—
226C2×C4—104no—
227C2×C4—202no—
228C2×C4—204no—
229C2×C4—302no—
230C2×C4—604no—
231C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
232C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
233C8—304no—
234C2×C3—52no—
235C2×C3—52no—
236C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
237C2×C3#6579412yes—
238C5#6955411yescharacteristic, complemented, Sylow
239C22—54no—
240C22—51no—
241C22—51no—
242C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
243C4—22no—
244C4—52no—
245C4—102no—
246C4—122no—
247C4—402no—
248C4—602no—
249C4ΓL(1,𝔽16)⋊Q812yes—
250C3#1060459011yescharacteristic, complemented, Sylow
251C2—52no—
252C2—52no—
253C2#1175170312yes—
254C2#1175175211yescharacteristic
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#1991
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
8. #91759C4semidirect
9. C5×#870C4semidirect
13. #91388C4semidirect
78. #870AGL(1,𝔽5)semidirect
204. C3×C5#1991semidirect
238. C5#69554semidirect
250. C3#10604590semidirect

Maximal subgroups

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

subgroupindex
D5×#8702
C4×D5⋊(C3⋊C8)2
C3×#656892
#117465282
#106045903
#695545