Finite Group Databasebeta

← #14284112

Subgroups — #14284112

Order 1920.

424 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#91388C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic
3C3×#65759C211yesmaximal, characteristic
4#11746507C214yesmaximal, complemented
5#10604266—31nomaximal, Hall
6C2×#6762—21no—
7C2×C4⋊Dic15C411yescharacteristic
8C2×C5×C4⋊Dic3C411yescharacteristic
9C2×C3×C4×Dic5C2211yescharacteristic
10C2×Dic3⋊Dic5—21no—
11C2×#6669—21no—
12#91388—21no—
13#91388—21no—
14#91388C412yes—
15#91388C2212yes—
16#91231C2212yes—
17C4×C3⋊#170—21no—
18C3×C22⋊#170—21no—
19C3×#4002C2212yes—
20C3×C4⋊#170—21no—
21#70812—51nomaximal, Hall
22C2×#4036—31no—
23#65759D311yescharacteristic
24C4×#704—31no—
25#64870—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15—21no—
28C22×C5×Dic3—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31#6762—24no—
32C2×C3⋊#170—22no—
33C2×C3×#170—22no—
34C4⋊Dic15—21no—
35C4⋊Dic15C2×C412yes—
36C5×C4⋊Dic3—21no—
37C5×C4⋊Dic3C2×C412yes—
38C3×C4×Dic5C2×C411yescharacteristic
39C3×C4×Dic5D411yescharacteristic
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5C2311yescharacteristic
42Dic3⋊Dic5—22no—
43Dic3⋊Dic5—22no—
44#6669—22no—
45#6669—22no—
46C2×#870—51no—
47C3×#432—51no—
48C4×#208—51no—
49#4465—54no—
50C2×#704—61no—
51C2×C5×C4⋊C4—31no—
52C2×C4⋊Dic5—31no—
53C2×C4⋊Dic5—61no—
54C2×#683—61no—
55C2×C4×Dic5C2×D311yescharacteristic
56#4036—32no—
57#4036—32no—
58#4036—61no—
59#4036—61no—
60C22⋊#170—21no—
61#4002—32no—
62#4002C2×D312yes—
63C4⋊#170—21no—
64C4×#170—61no—
65#1528—151noSylow
66C23×C3×C5C22⋊C411yescharacteristic
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22×C411yescharacteristic
70C2×Dic15—22no—
71C2×Dic15—42no—
72C2×C5×Dic3—22no—
73C2×C5×Dic3—42no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—41no—
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80C3⋊#170—24no—
81C3×#170—42no—
82C2×C3×C42—51no—
83C2×C4⋊Dic3—51no—
84C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
85C2×Dic3⋊C4—101no—
86C2×Dic3⋊C4—101no—
87C2×#208—101no—
88#870—52no—
89#870—52no—
90#870—101no—
91#870—101no—
92C3×C4⋊C8—101no—
93C3×C22⋊C8—101no—
94C3×#97—52no—
95#803—52no—
96C4×C3⋊C8—101no—
97C22×C4×C5—61no—
98C22×C4×C5C4×D311yescharacteristic
99C22×Dic5—61no—
100C22×Dic5D1211yescharacteristic
101C22×Dic5#6711yescharacteristic
102#704—64no—
103C2×#170—22no—
104C2×#170—62no—
105C5×C4⋊C4—32no—
106C5×C4⋊C4—61no—
107C4⋊Dic5—32no—
108C4⋊Dic5—61no—
109C4⋊Dic5—62no—
110C4⋊Dic5—62no—
111#683—62no—
112#683—62no—
113C4×Dic5C4×D311yescharacteristic
114C4×Dic5D1211yescharacteristic
115C4×Dic5#6711yescharacteristic
116C4×Dic5C22×D311yescharacteristic
117C2×#125—151no—
118#432—51no—
119C4×M16—151no—
120#330—154no—
121C22×C3×C5—21no—
122C22×C3×C5—21no—
123C22×C3×C5#10412yes—
124C22×C3×C5C2×C22⋊C411yescharacteristic
125C3×C4×C5—21no—
126C3×C4×C5#10112yes—
127Dic15—42no—
128C3×Dic5—21no—
129C3×Dic5—21no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C5×Dic3—42no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
136C22×Dic3—21no—
137C22×Dic3—101no—
138C2×C3×C8—102no—
139C3×C42—51no—
140C3×C42—51no—
141C3×C42—51no—
142C3×C42—51no—
143C4⋊Dic3—21no—
144C4⋊Dic3—52no—
145C4⋊Dic3—101no—
146C4⋊Dic3C2×AGL(1,𝔽5)12yes—
147Dic3⋊C4—102no—
148Dic3⋊C4—102no—
149Dic3⋊C4—102no—
150Dic3⋊C4—102no—
151#208—104no—
152C2×C3⋊C8—102no—
153C23×C5(C2×D3)⋊C411yescharacteristic
154C2×C4×C5—22no—
155C2×C4×C5—62no—
156C2×C4×C5—122no—
157C2×C4×C5(C2×D3)⋊C411yescharacteristic
158C2×C4×C5C2×C4×D311yescharacteristic
159C2×Dic5—22no—
160C2×Dic5—41no—
161C2×Dic5—62no—
162C2×Dic5—122no—
163C2×Dic5(C2×D3)⋊C411yescharacteristic
164C2×Dic5(C2×D3)⋊C411yescharacteristic
165C2×Dic5C2×D1211yescharacteristic
166C2×Dic5C2×#6711yescharacteristic
167#170—42no—
168#170—64no—
169C2×M16—301no—
170#125—152no—
171#125—152no—
172#125—301no—
173#125—301no—
174C2×C4⋊C4—31no—
175C2×C4⋊C4—151no—
176C2×C4⋊C4—301no—
177C2×C4⋊C4—301no—
178C2×C42—51no—
179C4⋊C8—101no—
180C22⋊C8—101no—
181#97—52no—
182#97—152no—
183C4×C8—301no—
184C2×C3×C5—22no—
185C2×C3×C5C2×#10111yescharacteristic
186C2×C3×C5C2×#10411yescharacteristic
187C2×C3×C5#42111yescharacteristic
188C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
189C2×C3×C4—22no—
190C2×C3×C4—51no—
191C2×C3×C4—51no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—102no—
195C2×C3×C4—201no—
196C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
197C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
198C2×Dic3—22no—
199C2×Dic3—42no—
200C2×Dic3—102no—
201C2×Dic3—202no—
202C3×C8—202no—
203C3⋊C8—104no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5#82512yes—
207C22×C5C2×(C2×D3)⋊C411yescharacteristic
208C4×C5—21no—
209C4×C5—122no—
210C4×C5#82412yes—
211Dic5—21no—
212Dic5—21no—
213Dic5—21no—
214Dic5—21no—
215Dic5—122no—
216C22×C4—51no—
217C22×C4—51no—
218C22×C4—61no—
219C22×C4—301no—
220C22×C4D3×AGL(1,𝔽5)11yescharacteristic
221M16—304no—
222C2×C8—102no—
223C2×C8—302no—
224C4⋊C4—32no—
225C4⋊C4—61no—
226C4⋊C4—152no—
227C4⋊C4—302no—
228C4⋊C4—302no—
229C4⋊C4—302no—
230C4⋊C4—302no—
231C4⋊C4—301no—
232C42—51no—
233C42—51no—
234C42—51no—
235C42—51no—
236C3×C5#152811yescharacteristic, complemented, Hall
237C22×C3—21no—
238C22×C3—21no—
239C22×C3#401012yes—
240C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
241C3×C4—21no—
242C3×C4—101no—
243C3×C4—101no—
244C3×C4—101no—
245C3×C4—101no—
246C3×C4#400512yes—
247Dic3—42no—
248Dic3—202no—
249C2×C5—22no—
250C2×C5#500511yescharacteristic
251C2×C5C2×#82411yescharacteristic
252C2×C5C2×#82511yescharacteristic
253C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
254C2×C4—22no—
255C2×C4—51no—
256C2×C4—51no—
257C2×C4—51no—
258C2×C4—51no—
259C2×C4—62no—
260C2×C4—102no—
261C2×C4—122no—
262C2×C4—201no—
263C2×C4—302no—
264C2×C4—602no—
265C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
266C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
267C8—202no—
268C8—304no—
269C2×C3—22no—
270C2×C3C2×#400511yescharacteristic
271C2×C3#6576911yescharacteristic
272C2×C3C2×#401011yescharacteristic
273C5#7081211yescharacteristic, complemented, Sylow
274C22—21no—
275C22—21no—
276C22#9115712yes—
277C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
278C4—21no—
279C4—101no—
280C4—101no—
281C4—101no—
282C4—101no—
283C4—122no—
284C4—602no—
285C4#9117512yes—
286C3#1060426611yescharacteristic, complemented, Sylow
287C2—22no—
288C2#1175171911yescharacteristic
289C2C2×#9115711yescharacteristic
290C2C2×#9117511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1528
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746507C2semidirect
236. C3×C5#1528semidirect
273. C5#70812semidirect
286. C3#10604266semidirect

Maximal subgroups

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

subgroupindex
C2×#913882
C4×#67622
C3×#657592
#117465072
#106042663
#708125