Finite Group Databasebeta

← #14289719

Subgroups — #14289719

Order 1920.

376 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#11756326C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic
3#11746920C211yesmaximal, characteristic
4#11746917C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic
6#11745860C211yesmaximal, characteristic
7#11745844C211yesmaximal, characteristic
8#10599061—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91833—21no—
11#91778—22no—
12#91776—21no—
13#91759—21no—
14#91758C2211yescharacteristic
15C4×Dic30—21no—
16C4×Dic30C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×#3967—21no—
21C3×#3939—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90990—21no—
24#90974—21no—
25#90971—22no—
26#71162—51nomaximal, Hall
27#65901—31no—
28#65310D311yescharacteristic
29#65139—31no—
30#64970—31no—
31C5×Q8⋊C8—31no—
32#64706—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×Dic30D411yescharacteristic
37C2×C3×Dic10—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C42×C5—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15D412yes—
44C4⋊Dic15D411yescharacteristic
45#6712—22no—
46#6712—22no—
47#6712—22no—
48#6712—21no—
49C4×Dic15—22no—
50C4×Dic15—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#5567—51no—
57C3×#477—51no—
58#5091—51no—
59#5079—51no—
60#4535D511yescharacteristic
61#4484—51no—
62#4482—51no—
63C4×C5×Q8C2×D311yescharacteristic
64#4090—61no—
65#4035—62no—
66#4033—61no—
67#4016—61no—
68#4015—31no—
69#4015C2×D311yescharacteristic
70C4×Dic10—31no—
71C4×Dic10—61no—
72C5×C4⋊C8—31no—
73C4×C5×C8—31no—
74#3967—21no—
75#3950—61no—
76#3948—61no—
77#3948—62no—
78#3939—21no—
79C4⋊#168C2×D311yescharacteristic
80#1636—151noSylow
81C3×C5×Q8—21no—
82C3×C5×Q8—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—22no—
91Dic30—21no—
92Dic30—41no—
93Dic30—41no—
94Dic30Q1612yes—
95C2×C3×Dic5—41no—
96C3×Dic10—42no—
97C3×#168—41no—
98C5×C3⋊C8—41no—
99C5×C3⋊C8—41no—
100C3×C4⋊Q8—51no—
101C3×C4×Q8C2×D511yescharacteristic
102#944—101no—
103#889—102no—
104#887—101no—
105#870—101no—
106#869—51no—
107C4×Dic6—51no—
108C4×Dic6—101no—
109C3×#107—101no—
110C3×C4⋊C8—51no—
111C3×#103—101no—
112#835—102no—
113#810—101no—
114#807—101no—
115C4⋊(C3⋊C8)C2×D511yescharacteristic
116C4×C3⋊C8C2×D511yescharacteristic
117C2×C5×Q8#6711yescharacteristic
118C2×Dic10—21no—
119C2×Dic10—31no—
120C2×Dic10—61no—
121C2×C5×C8—61no—
122C2×C5×C8—61no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4#6711yescharacteristic
125C42×C5—21no—
126C42×C5C22×D311yescharacteristic
127C4⋊Dic5—21no—
128C4⋊Dic5—21no—
129C4⋊Dic5—32no—
130C4⋊Dic5—31no—
131C4⋊Dic5—61no—
132#683—62no—
133#683—62no—
134#683—62no—
135#683—61no—
136C4×Dic5—62no—
137C4×Dic5—61no—
138C2×#168—21no—
139#557—151no—
140#487—151no—
141#477—51no—
142#477—151no—
143#332—151no—
144Q8⋊C8—31no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×C4×C5—41no—
150C3×C4×C5C2×Q1611yescharacteristic
151C3×C4×C5#13511yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×C4×C5#13711yescharacteristic
154Dic15—22no—
155Dic15—42no—
156Dic15—41no—
157C3×Dic5—81no—
158C2×C3×Q8—101no—
159C2×C3×Q8D2011yescharacteristic
160C2×Dic6—51no—
161C2×Dic6—101no—
162C2×C3×C8—101no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—101no—
165C3×C4⋊C4—101no—
166C3×C4⋊C4D2011yescharacteristic
167C3×C42—21no—
168C3×C42C22×D511yescharacteristic
169C4⋊Dic3—51no—
170C4⋊Dic3—52no—
171C4⋊Dic3—101no—
172Dic3⋊C4—102no—
173Dic3⋊C4—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—101no—
176C4×Dic3—102no—
177C4×Dic3—101no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C5×Q8—21no—
181C5×Q8—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5D3×D411yescharacteristic
185C2×C4×C5D3×D411yescharacteristic
186C2×C4×C5C2×#6711yescharacteristic
187C2×Dic5—41no—
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5—62no—
191Dic10—32no—
192Dic10—42no—
193Dic10—61no—
194Dic10—121no—
195Dic10—121no—
196C5×C8—121no—
197C5×C8—121no—
198#168—41no—
199C4⋊Q8—51no—
200C4⋊Q8—151no—
201C4⋊Q8—301no—
202#125—301no—
203#125—302no—
204C4×Q8—151no—
205C4×Q8—301no—
206C4×Q8—301no—
207C4×Q8D3×D511yescharacteristic
208#107—101no—
209#107—301no—
210C4⋊C8—31no—
211C4⋊C8—51no—
212#103—101no—
213#103—301no—
214#103—302no—
215C4×C8—31no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—202no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—201no—
225C2×C3×C4C2×D2011yescharacteristic
226C2×C3×C4D4×D511yescharacteristic
227C2×C3×C4D4×D511yescharacteristic
228C2×Dic3—101no—
229C2×Dic3—101no—
230C2×Dic3—102no—
231Dic6—52no—
232Dic6—101no—
233Dic6—201no—
234Dic6—201no—
235C3×C8—201no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C22×C5#93711yescharacteristic
239C4×C5—21no—
240C4×C5—41no—
241C4×C5—41no—
242C4×C5D3×Q1611yescharacteristic
243C4×C5#91811yescharacteristic
244C4×C5#94211yescharacteristic
245C4×C5#95011yescharacteristic
246Dic5—62no—
247Dic5—81no—
248Dic5—121no—
249Dic5—122no—
250C2×Q8—101no—
251C2×Q8—151no—
252C2×Q8—301no—
253C2×Q8#120211yescharacteristic
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—101no—
257C4⋊C4—21no—
258C4⋊C4—101no—
259C4⋊C4—101no—
260C4⋊C4—152no—
261C4⋊C4—151no—
262C4⋊C4—302no—
263C4⋊C4—302no—
264C4⋊C4—302no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#120211yescharacteristic
268C42—21no—
269C42—302no—
270C42—301no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#402811yescharacteristic
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—401no—
278C3×C4#405011yescharacteristic
279C3×C4#405511yescharacteristic
280C3×C4#406111yescharacteristic
281C3×C4D5×Q1611yescharacteristic
282Dic3—102no—
283Dic3—201no—
284Dic3—202no—
285C2×C5#504711yescharacteristic
286C2×C5#518611yescharacteristic
287C2×C5#520111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—152no—
291Q8—202no—
292Q8—301no—
293Q8—601no—
294Q8—601no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—201no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—302no—
301C2×C4C2×#120211yescharacteristic
302C2×C4#679011yescharacteristic
303C2×C4#679011yescharacteristic
304C8—121no—
305C8—121no—
306C8—201no—
307C2×C3#6502211yescharacteristic
308C2×C3#6509711yescharacteristic
309C2×C3#6511611yescharacteristic
310C5#7116211yescharacteristic, complemented, Sylow
311C22#9157211yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—302no—
316C4—401no—
317C4—601no—
318C4—602no—
319C4#9131111yescharacteristic
320C4#9131511yescharacteristic
321C4#9151111yescharacteristic
322C4#9152411yescharacteristic
323C3#1059906111yescharacteristic, complemented, Sylow
324C2#1174855211yescharacteristic
325C2#1174931011yescharacteristic
326C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1636
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
272. C3×C5#1636semidirect
310. C5#71162semidirect
323. C3#10599061semidirect

Maximal subgroups

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

subgroupindex
#117563262
C3×#653102
#117469202
#117469172
C5×#45352
#117458602
#117458442
#105990613
#711625