Finite Group Databasebeta

← #14281169

Subgroups — #14281169

Order 1920.

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

normal subgroups only

This group has 472 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×#91333C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic
3C3×#65757C211yesmaximal, characteristic
4#11746569C214yesmaximal
5#10604295—31nomaximal, Hall
6C22×Dic30C411yescharacteristic
7C2×C5×C4⋊Dic3C411yescharacteristic
8C2×C3×C4×Dic5C2211yescharacteristic
9C2×#6669C2212yes—
10C2×Dic3×Dic5C412yes—
11#91333—21no—
12#91333—21no—
13#91333—21no—
14#91333—21no—
15#91241C2212yes—
16#91233—21no—
17#91231—21no—
18C3×C22⋊#170C2212yes—
19C3×#4004—21no—
20C3×#4002—21no—
21#70830—51nomaximal, Hall
22C2×#4033—31no—
23#65757—31no—
24#65757D311yescharacteristic
25#64914—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15C2×C412yes—
28C2×Dic30—21no—
29C2×Dic30—21no—
30C2×Dic30—24no—
31C22×C5×Dic3C2×C412yes—
32C22×C3×Dic5C2×C411yescharacteristic
33C22×C3×Dic5C2311yescharacteristic
34C2×C3⋊#170—22no—
35C2×C3×#170—22no—
36C5×C4⋊Dic3—21no—
37C5×C4⋊Dic3—21no—
38C3×C4×Dic5D411yescharacteristic
39C3×C4×Dic5D411yescharacteristic
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5D411yescharacteristic
42#6669—22no—
43#6669—22no—
44Dic3×Dic5—22no—
45Dic3×Dic5—22no—
46C2×C4×Dic6—51no—
47C3×#432—51no—
48#4926—51no—
49#4469—54no—
50C22×Dic10—31no—
51C2×C5×C4⋊C4—31no—
52C2×#683—32no—
53C2×C4×Dic5—32no—
54C2×C4×Dic5C2×D311yescharacteristic
55#4033—61no—
56#4033—61no—
57#4033—61no—
58#4033—61no—
59C22⋊#170—32no—
60C22⋊#170C2×D312yes—
61#4004—21no—
62#4004—61no—
63#4002—21no—
64#4002—61no—
65#1467—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—22no—
72C2×Dic15M1614yes—
73Dic30—24no—
74Dic30—24no—
75C2×C5×Dic3—22no—
76C2×C5×Dic3—42no—
77C2×C3×Dic5—22no—
78C2×C3×Dic5—41no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C22⋊C411yescharacteristic
81C2×C3×Dic5C2×D411yescharacteristic
82C2×C3×Dic5C2×D411yescharacteristic
83C3⋊#170—42no—
84C3×#170—42no—
85C22×Dic6—51no—
86C2×C3×C42—51no—
87C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
88C2×Dic3⋊C4—52no—
89C2×C4×Dic3—52no—
90C4×Dic6—101no—
91C4×Dic6—101no—
92C4×Dic6—101no—
93C4×Dic6—101no—
94C3×C4⋊C8—101no—
95C3×C22⋊C8—52no—
96C3×#97—101no—
97#830—52no—
98C4⋊(C3⋊C8)—101no—
99#803—101no—
100C22×C4×C5—32no—
101C22×C4×C5C4×D311yescharacteristic
102C22×Dic5—32no—
103C22×Dic5C4×D311yescharacteristic
104C22×Dic5C22×D311yescharacteristic
105C2×Dic10—64no—
106C2×Dic10—61no—
107C2×Dic10—61no—
108C2×#170—22no—
109C2×#170—62no—
110C5×C4⋊C4—61no—
111C5×C4⋊C4—61no—
112#683—62no—
113#683—62no—
114C4×Dic5—62no—
115C4×Dic5—62no—
116C4×Dic5D1211yescharacteristic
117C4×Dic5D1211yescharacteristic
118C4×Dic5#6711yescharacteristic
119C4×Dic5#6711yescharacteristic
120C2×C4×Q8—151no—
121#432—51no—
122#432—151no—
123#324—154no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5C2×C22⋊C411yescharacteristic
127C22×C3×C5C2×M1612yes—
128C3×C4×C5—21no—
129C3×C4×C5—21no—
130Dic15—24no—
131C3×Dic5—21no—
132C3×Dic5—21no—
133C3×Dic5—21no—
134C3×Dic5#10112yes—
135C5×Dic3—42no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
139C22×Dic3—52no—
140C22×Dic3C2×AGL(1,𝔽5)12yes—
141C2×Dic6—104no—
142C2×Dic6—101no—
143C2×Dic6—101no—
144C2×C3×C8—102no—
145C3×C42—51no—
146C3×C42—51no—
147C3×C42—51no—
148C3×C42—51no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151Dic3⋊C4—102no—
152Dic3⋊C4—102no—
153C4×Dic3—102no—
154C4×Dic3—102no—
155C2×C3⋊C8—102no—
156C23×C5C2×C4×D311yescharacteristic
157C2×C4×C5—22no—
158C2×C4×C5—62no—
159C2×C4×C5—122no—
160C2×C4×C5(C2×D3)⋊C411yescharacteristic
161C2×C4×C5(C2×D3)⋊C411yescharacteristic
162C2×Dic5—22no—
163C2×Dic5—34no—
164C2×Dic5—41no—
165C2×Dic5—62no—
166C2×Dic5—62no—
167C2×Dic5(C2×D3)⋊C411yescharacteristic
168C2×Dic5(C2×D3)⋊C411yescharacteristic
169C2×Dic5C2×D1211yescharacteristic
170C2×Dic5C2×#6711yescharacteristic
171Dic10—64no—
172Dic10—64no—
173#170—42no—
174#170—122no—
175C22×Q8—151no—
176C4×Q8—301no—
177C4×Q8—301no—
178C4×Q8—301no—
179C4×Q8—301no—
180C2×C4⋊C4—31no—
181C2×C4⋊C4—152no—
182C2×C42—51no—
183C2×C42—152no—
184C4⋊C8—101no—
185C4⋊C8—301no—
186C22⋊C8—52no—
187C22⋊C8—152no—
188#97—101no—
189#97—301no—
190C2×C3×C5—22no—
191C2×C3×C5#40711yescharacteristic
192C2×C3×C5#41011yescharacteristic
193C2×C3×C5C2×#10111yescharacteristic
194C23×C3C22×AGL(1,𝔽5)11yescharacteristic
195C2×C3×C4—22no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—102no—
201C2×C3×C4—201no—
202C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
203C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
204C2×Dic3—22no—
205C2×Dic3—42no—
206C2×Dic3—54no—
207C2×Dic3—102no—
208C2×Dic3—102no—
209Dic6—104no—
210Dic6—104no—
211C3×C8—202no—
212C3⋊C8—202no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5D3×M1612yes—
216C22×C5C2×(C2×D3)⋊C411yescharacteristic
217C4×C5—21no—
218C4×C5—21no—
219C4×C5—122no—
220Dic5—21no—
221Dic5—21no—
222Dic5—21no—
223Dic5—64no—
224Dic5#82412yes—
225C2×Q8—304no—
226C2×Q8—301no—
227C2×Q8—301no—
228C22×C4—32no—
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—152no—
232C22×C4D3×AGL(1,𝔽5)11yescharacteristic
233C2×C8—102no—
234C2×C8—302no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—302no—
238C4⋊C4—302no—
239C42—51no—
240C42—51no—
241C42—51no—
242C42—51no—
243C42—302no—
244C42—302no—
245C3×C5#146711yescharacteristic, complemented, Hall
246C22×C3—21no—
247C22×C3—21no—
248C22×C3D5⋊M1612yes—
249C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—52no—
253C3×C4—101no—
254C3×C4—101no—
255C3×C4—101no—
256Dic3—42no—
257Dic3—104no—
258C2×C5—22no—
259C2×C5#500611yescharacteristic
260C2×C5#512611yescharacteristic
261C2×C5C2×#82411yescharacteristic
262C23C2×D3×AGL(1,𝔽5)11yescharacteristic
263Q8—304no—
264Q8—304no—
265C2×C4—22no—
266C2×C4—51no—
267C2×C4—51no—
268C2×C4—51no—
269C2×C4—51no—
270C2×C4—62no—
271C2×C4—102no—
272C2×C4—122no—
273C2×C4—154no—
274C2×C4—201no—
275C2×C4—302no—
276C2×C4—302no—
277C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
278C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
279C8—202no—
280C8—602no—
281C2×C3—22no—
282C2×C3#6575511yescharacteristic
283C2×C3#6577111yescharacteristic
284C2×C3D5⋊#10111yescharacteristic
285C5#7083011yescharacteristic, complemented, Sylow
286C22—21no—
287C22—21no—
288C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
289C22#9193112yes—
290C4—21no—
291C4—21no—
292C4—52no—
293C4—101no—
294C4—101no—
295C4—101no—
296C4—122no—
297C4—304no—
298C3#1060429511yescharacteristic, complemented, Sylow
299C2—22no—
300C2#1175181611yescharacteristic
301C2D5⋊#82411yescharacteristic
302C2#1175200311yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1467
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
245. C3×C5#1467semidirect
285. C5#70830semidirect
298. C3#10604295semidirect

Maximal subgroups

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

subgroupindex
C2×#913332
#117524162
C3×#657572
#117465692
#106042953
#708305