Finite Group Databasebeta

← #14307366

Subgroups — #14307366

Order 1920.

520 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 134 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
2#11752347C211yesmaximal, characteristic
3C3×#65676C211yesmaximal, characteristic
4#11746530C214yesmaximal
5#10604591—31nomaximal, Hall
6C2×C4⋊ΓL(1,𝔽16)—22no—
7C2×C4⋊ΓL(1,𝔽16)C2212yes—
8C2×C3×D5⋊C8C2212yes—
9#91759C411yescharacteristic, complemented
10C5×#870C411yescharacteristic, complemented
11C3×C42×D5C2211yescharacteristic
12D5×C4⋊Dic3C2212yes—
13D5×Dic3⋊C4—22no—
14#91388C412yescomplemented
15#91378—22no—
16C3×#4002—22no—
17#69827—51nomaximal, Hall
18D5×#125—31no—
19#65688—31no—
20#65676D311yescharacteristic
21#64874—34no—
22C22×ΓL(1,𝔽16)—22no—
23C2×C3×C4×D5D412yes—
24C2×C3×C4×D5C2311yescharacteristic
25C2×D5×Dic3—22no—
26C4⋊ΓL(1,𝔽16)—24no—
27C4⋊ΓL(1,𝔽16)—44no—
28C2×C3×#170—22no—
29C3×D5⋊C8—22no—
30C3×D5⋊C8Q814yes—
31C3×C42×C5C2×C411yescharacteristic
32C4⋊Dic15C2×C412yes—
33#6712—22no—
34C5×C4⋊Dic3C2×C412yes—
35C5×Dic3⋊C4—22no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38Dic3⋊Dic5—22no—
39#6669—22no—
40#6668—22no—
41C2×#870—51no—
42C2×C3×#97—51no—
43#4935—51no—
44#4551—54no—
45C2×C4⋊AGL(1,𝔽5)—32no—
46C2×C4⋊AGL(1,𝔽5)—62no—
47C2×D5⋊C8C2×D312yes—
48C5×#125—31no—
49D5×C4⋊C4—32no—
50D5×C4⋊C4—62no—
51#4036—32no—
52#4035—62no—
53C42×D5C2×D311yescharacteristic
54#4016—31no—
55#4002—22no—
56#1992—151noSylow
57C22×C3×D5C2×D411yescharacteristic
58C2×ΓL(1,𝔽16)—42no—
59C2×ΓL(1,𝔽16)—44no—
60C2×C3×C4×C5C22⋊C412yes—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×Dic15—22no—
63C2×C5×Dic3—22no—
64C2×C3×Dic5C22⋊C412yes—
65C2×C3×Dic5C2×D411yescharacteristic
66C3×C4×D5—22no—
67C3×C4×D5—22no—
68C3×C4×D5C2×Q812yes—
69C3×C4×D5#4112yes—
70D5×Dic3—42no—
71D5×Dic3—42no—
72C3×#170—24no—
73C22×C3×C8—52no—
74C2×C3×C42—51no—
75C2×C4⋊Dic3—52no—
76C2×C4⋊Dic3—52no—
77C2×C4⋊Dic3—102no—
78C2×Dic3⋊C4—102no—
79#870—51no—
80#870—52no—
81#870—102no—
82#870AGL(1,𝔽5)11yescharacteristic, complemented
83C3×#97—102no—
84C22×AGL(1,𝔽5)—62no—
85C2×C4×D5—62no—
86C2×C4×D5D1212yes—
87C2×C4×D5C22×D311yescharacteristic
88C2×#170—22no—
89C4⋊AGL(1,𝔽5)—64no—
90C4⋊AGL(1,𝔽5)—124no—
91D5⋊C8—22no—
92D5⋊C8Dic614yes—
93C5×C4⋊C4—32no—
94C5×C4⋊C4—62no—
95C42×C5C4×D311yescharacteristic
96C4⋊Dic5—32no—
97C4⋊Dic5—62no—
98#683—62no—
99#683—62no—
100#683—62no—
101C4×Dic5C4×D311yescharacteristic
102C4×Dic5#6712yes—
103C2×#125—151no—
104C2×#97—51no—
105#384—151no—
106#340—154no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×C3×D5#12411yescharacteristic
109C2×C3×D5C4⋊Q811yescharacteristic
110C2×C3×D5AGL(1,ℤ/8)12yes—
111C2×C3×D5#13712yes—
112ΓL(1,𝔽16)—82no—
113C3×C4×C5—22no—
114C3×C4×C5C4×Q812yes—
115Dic15—42no—
116C3×Dic5—22no—
117C3×Dic5C22⋊Q812yes—
118C5×Dic3—42no—
119C22×C3×C4—51no—
120C22×C3×C4—52no—
121C22×Dic3—102no—
122C22×Dic3—102no—
123C2×C3×C8—54no—
124C2×C3×C8—102no—
125C2×C3×C8—102no—
126C3×C42—52no—
127C3×C42—51no—
128C3×C42C2×AGL(1,𝔽5)11yescharacteristic
129C4⋊Dic3—52no—
130C4⋊Dic3—102no—
131C4⋊Dic3—104no—
132C4⋊Dic3—204no—
133C4⋊Dic3C2×AGL(1,𝔽5)12yes—
134Dic3⋊C4—22no—
135Dic3⋊C4—102no—
136Dic3⋊C4—102no—
137Dic3⋊C4—102no—
138C22×D5C2×D1211yescharacteristic
139C2×AGL(1,𝔽5)—122no—
140C2×AGL(1,𝔽5)—124no—
141C2×C4×C5—62no—
142C2×C4×C5(C2×D3)⋊C412yes—
143C2×C4×C5C2×C4×D311yescharacteristic
144C2×Dic5—62no—
145C2×Dic5(C2×D3)⋊C412yes—
146C2×Dic5C2×#6711yescharacteristic
147C4×D5—22no—
148C4×D5—22no—
149C4×D5—122no—
150C4×D5—122no—
151C4×D5C2×Dic612yes—
152C4×D5#23512yes—
153#170—24no—
154C22×C8—52no—
155#125—31no—
156#125—152no—
157#125—151no—
158#125—302no—
159C2×C4⋊C4—152no—
160C2×C4⋊C4—152no—
161C2×C4⋊C4—302no—
162C2×C4⋊C4—302no—
163C2×C42—51no—
164#97—102no—
165C2×C3×C5#39111yescharacteristic
166C2×C3×C5#41712yes—
167C3×D5#49011yescharacteristic
168C3×D5#49111yescharacteristic
169C3×D5#50112yes—
170C23×C3—51no—
171C2×C3×C4—51no—
172C2×C3×C4—52no—
173C2×C3×C4—52no—
174C2×C3×C4—52no—
175C2×C3×C4—102no—
176C2×C3×C4—102no—
177C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
178C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
179C2×Dic3—22no—
180C2×Dic3—102no—
181C2×Dic3—202no—
182C2×Dic3—202no—
183C2×Dic3—202no—
184C2×Dic3—204no—
185C3×C8—104no—
186C22×C5C2×(C2×D3)⋊C411yescharacteristic
187C2×D5#86911yescharacteristic
188C2×D5#87511yescharacteristic
189C2×D5#90812yes—
190C2×D5#90912yes—
191AGL(1,𝔽5)—242no—
192C4×C5—22no—
193C4×C5—122no—
194C4×C5C4×Dic612yes—
195Dic5—22no—
196Dic5—122no—
197Dic5#92412yes—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—302no—
201C22×C4—302no—
202C2×C8—54no—
203C2×C8—102no—
204C2×C8—102no—
205C4⋊C4—32no—
206C4⋊C4—62no—
207C4⋊C4—152no—
208C4⋊C4—302no—
209C4⋊C4—302no—
210C4⋊C4—302no—
211C4⋊C4—304no—
212C4⋊C4—302no—
213C4⋊C4—604no—
214C42—52no—
215C42—51no—
216C42D3×AGL(1,𝔽5)11yescharacteristic
217C3×C5#199211yescharacteristic, complemented, Hall
218C22×C3—52no—
219C22×C3—52no—
220C22×C3—51no—
221C22×C3—51no—
222C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
223C3×C4—22no—
224C3×C4—52no—
225C3×C4—102no—
226C3×C4Q8×AGL(1,𝔽5)12yes—
227Dic3—42no—
228Dic3—202no—
229Dic3—402no—
230C2×C5#492911yescharacteristic
231C2×C5#513312yes—
232D5#470212yes—
233D5#470311yescharacteristic
234D5#471311yescharacteristic
235C23—51no—
236C2×C4—51no—
237C2×C4—52no—
238C2×C4—52no—
239C2×C4—52no—
240C2×C4—62no—
241C2×C4—102no—
242C2×C4—102no—
243C2×C4—302no—
244C2×C4—602no—
245C2×C4—602no—
246C2×C4—602no—
247C2×C4—604no—
248C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
249C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
250C8—104no—
251C2×C3—51no—
252C2×C3—51no—
253C2×C3—52no—
254C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
255C2×C3#6579312yes—
256C5#6982711yescharacteristic, complemented, Sylow
257C22—52no—
258C22—52no—
259C22—51no—
260C22—51no—
261C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
262C4—22no—
263C4—52no—
264C4—102no—
265C4—122no—
266C4—602no—
267C4—1202no—
268C4AGL(1,𝔽5)×Dic612yes—
269C3#1060459111yescharacteristic, complemented, Sylow
270C2—51no—
271C2—52no—
272C2—51no—
273C2#1175170812yes—
274C2#1175174911yescharacteristic
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#1992
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
9. #91759C4semidirect
10. C5×#870C4semidirect
14. #91388C4semidirect
82. #870AGL(1,𝔽5)semidirect
217. C3×C5#1992semidirect
256. C5#69827semidirect
269. C3#10604591semidirect

Maximal subgroups

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

subgroupindex
D5×#8702
#117523472
C3×#656762
#117465302
#106045913
#698275