Finite Group Databasebeta

← #14289716

Subgroups — #14289716

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
2C5×#5021C211yesmaximal, characteristic
3#11746963C211yesmaximal, characteristic
4#11746929C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic
6#11745859C211yesmaximal, characteristic
7#11745845C211yesmaximal, characteristic
8#10601955—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
17C5×#869C2211yescharacteristic
18C5×#835—21no—
19C5×#807—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23#90988—21no—
24#90975—21no—
25#90973—22no—
26#68268—51nomaximal, Hall
27#65901—31no—
28C5×#477—31no—
29#65380—31no—
30#65370—31no—
31Q8⋊#168D311yescharacteristic
32#64704—31no—
33#64702—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×Dic30D411yescharacteristic
37C2×C5×Dic6—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—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#5567—51no—
57#5021D511yescharacteristic
58#4850—51no—
59#4681—51no—
60C3×Q8⋊C8—51no—
61#4486—51no—
62#4456—51no—
63C5×C4⋊Q8—31no—
64C4×C5×Q8C2×D311yescharacteristic
65#4090—61no—
66#4035—62no—
67#4033—61no—
68#4016—61no—
69#4015—31no—
70C4×Dic10—31no—
71C4×Dic10—61no—
72C5×#107—61no—
73C5×C4⋊C8—31no—
74C5×#103—61no—
75#3967—62no—
76#3942—61no—
77#3939—61no—
78C4⋊#168C2×D311yescharacteristic
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×C5×Dic3—41no—
96C5×Dic6—42no—
97C3×#168—41no—
98C3×#168—41no—
99C5×C3⋊C8—41no—
100C3×C4×Q8C2×D511yescharacteristic
101#944—101no—
102#889—102no—
103#887—101no—
104#870—101no—
105#869—51no—
106#869C2×D511yescharacteristic
107C4×Dic6—51no—
108C4×Dic6—101no—
109C3×C4⋊C8—51no—
110C3×C4×C8—51no—
111#835—21no—
112#818—101no—
113#816—101no—
114#816—102no—
115#807—21no—
116C4⋊(C3⋊C8)C2×D511yescharacteristic
117C2×C5×Q8—61no—
118C2×C5×Q8D1211yescharacteristic
119C2×Dic10—31no—
120C2×Dic10—61no—
121C2×C5×C8—61no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—61no—
124C5×C4⋊C4—61no—
125C5×C4⋊C4D1211yescharacteristic
126C42×C5—21no—
127C42×C5C22×D311yescharacteristic
128C4⋊Dic5—31no—
129C4⋊Dic5—32no—
130C4⋊Dic5—61no—
131#683—62no—
132#683—62no—
133#683—62no—
134#683—61no—
135C4×Dic5—62no—
136C4×Dic5—61no—
137C2×#168—21no—
138C2×#168—21no—
139#557—151no—
140#487—151no—
141#477—31no—
142#477—151no—
143#332—151no—
144Q8⋊C8—51no—
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—
157C5×Dic3—81no—
158C2×C3×Q8C22⋊D511yescharacteristic
159C2×Dic6—21no—
160C2×Dic6—51no—
161C2×Dic6—101no—
162C2×C3×C8—101no—
163C2×C3×C8—101no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4C22⋊D511yescharacteristic
166C3×C42—21no—
167C3×C42C22×D511yescharacteristic
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3—52no—
171C4⋊Dic3—51no—
172C4⋊Dic3—101no—
173Dic3⋊C4—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—102no—
176Dic3⋊C4—101no—
177C4×Dic3—102no—
178C4×Dic3—101no—
179C2×C3⋊C8—21no—
180C5×Q8—21no—
181C5×Q8—21no—
182C5×Q8—122no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—121no—
186C2×C4×C5C2×D1211yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×Dic5—61no—
190C2×Dic5—61no—
191C2×Dic5—62no—
192Dic10—32no—
193Dic10—61no—
194Dic10—121no—
195Dic10—121no—
196C5×C8—121no—
197#168—41no—
198#168—41no—
199C4⋊Q8—31no—
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—61no—
209#107—301no—
210C4⋊C8—31no—
211C4⋊C8—51no—
212#103—61no—
213#103—301no—
214#103—302no—
215C4×C8—51no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—21no—
220C3×Q8—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4D4×D511yescharacteristic
224C2×C3×C4D4×D511yescharacteristic
225C2×C3×C4C2×C22⋊D511yescharacteristic
226C2×Dic3—41no—
227C2×Dic3—101no—
228C2×Dic3—101no—
229C2×Dic3—102no—
230Dic6—42no—
231Dic6—52no—
232Dic6—101no—
233Dic6—201no—
234Dic6—201no—
235C3×C8—201no—
236C3×C8—201no—
237C3⋊C8—41no—
238C22×C5#88211yescharacteristic
239C4×C5—21no—
240C4×C5—41no—
241C4×C5—41no—
242C4×C5—241no—
243C4×C5#90411yescharacteristic
244C4×C5#90911yescharacteristic
245C4×C5#91511yescharacteristic
246C4×C5D3×Q1611yescharacteristic
247Dic5—62no—
248Dic5—122no—
249Dic5—121no—
250C2×Q8—61no—
251C2×Q8—151no—
252C2×Q8—301no—
253C2×Q8#120311yescharacteristic
254C2×C8—61no—
255C2×C8—101no—
256C2×C8—101no—
257C4⋊C4—21no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—152no—
261C4⋊C4—151no—
262C4⋊C4—302no—
263C4⋊C4—302no—
264C4⋊C4—302no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#120311yescharacteristic
268C42—21no—
269C42—302no—
270C42—301no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4D5×Q1611yescharacteristic
278C3×C4#406411yescharacteristic
279C3×C4#408811yescharacteristic
280C3×C4#409611yescharacteristic
281Dic3—81no—
282Dic3—102no—
283Dic3—202no—
284Dic3—201no—
285C2×C5#473311yescharacteristic
286C2×C5#480911yescharacteristic
287C2×C5#482711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—122no—
291Q8—152no—
292Q8—301no—
293Q8—601no—
294Q8—601no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—121no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—302no—
301C2×C4C2×#120311yescharacteristic
302C2×C4#679011yescharacteristic
303C2×C4#679011yescharacteristic
304C8—121no—
305C8—201no—
306C8—201no—
307C2×C3#6533611yescharacteristic
308C2×C3#6547511yescharacteristic
309C2×C3#6549011yescharacteristic
310C5#6826811yescharacteristic, complemented, Sylow
311C22#9157311yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—241no—
316C4—302no—
317C4—601no—
318C4—602no—
319C4#9130311yescharacteristic
320C4#9132111yescharacteristic
321C4#9151111yescharacteristic
322C4#9152211yescharacteristic
323C3#1060195511yescharacteristic, complemented, Sylow
324C2#1174856611yescharacteristic
325C2#1174930811yescharacteristic
326C2#1174946111yescharacteristic
subgroupG/H
centerC22#91573
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#68268semidirect
323. C3#10601955semidirect

Maximal subgroups

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

subgroupindex
#117563262
C5×#50212
#117469632
#117469292
C3×Q8⋊#1682
#117458592
#117458452
#106019553
#682685