Finite Group Databasebeta

← #14289710

Subgroups — #14289710

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#11756480C211yesmaximal, characteristic
2C5×#5093C211yesmaximal, characteristic
3#11746963C211yesmaximal, characteristic
4#11746963C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic
6#11745844C211yesmaximal, characteristic
7#11745844C211yesmaximal, characteristic
8#10602029—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10Q8×Dic15—21no—
11#91833—21no—
12#91779—21no—
13#91778—22no—
14#91776—21no—
15C4×Dic30C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C5×#810—22no—
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90988—21no—
24#90975—21no—
25#90975—21no—
26#68458—51nomaximal, Hall
27#66055—31no—
28C5×#487—31no—
29#65380—31no—
30#65380—31no—
31#64767D311yescharacteristic
32#64676—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×Dic30D411yescharacteristic
37C2×C5×Dic6—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D412yes—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—22no—
42C4⋊Dic15D411yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—22no—
45#6712—22no—
46#6712—21no—
47#6712—21no—
48C4×Dic15—22no—
49C4×Dic15—21no—
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#5721—51no—
57#5093D511yescharacteristic
58#4850—51no—
59#4850—51no—
60C3×#332—51no—
61#4484—51no—
62#4484—51no—
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8C2×D311yescharacteristic
65Q8×Dic5—61no—
66#4090—61no—
67#4036—61no—
68#4035—62no—
69#4033—61no—
70C4×Dic10—31no—
71C4×Dic10—31no—
72C5×#103—62no—
73C4×C5×C8—31no—
74#3942—61no—
75#3942—61no—
76#3939—61no—
77#3939—61no—
78C4⋊#168C2×D311yescharacteristic
79C4⋊#168C2×D311yescharacteristic
80#1636—151noSylow
81C3×C5×Q8—41no—
82C3×C5×Q8—41no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30—21no—
93Dic30—21no—
94Dic30Q1612yes—
95C2×C5×Dic3—41no—
96C5×Dic6—42no—
97C3×#168—41no—
98C3×#168—41no—
99C5×C3⋊C8—41no—
100C3×C4⋊Q8C2×D511yescharacteristic
101Q8×Dic3—101no—
102#944—101no—
103#890—101no—
104#889—102no—
105#887—101no—
106#869C2×D511yescharacteristic
107C4×Dic6—51no—
108C4×Dic6—51no—
109C3×C4⋊C8—51no—
110C3×C4⋊C8—51no—
111#818—101no—
112#818—101no—
113#816—101no—
114#816—101no—
115#810—22no—
116C4×C3⋊C8C2×D511yescharacteristic
117C2×C5×Q8—21no—
118C2×C5×Q8—61no—
119C2×Dic10—31no—
120C2×Dic10—31no—
121C2×C5×C8—61no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—61no—
124C5×C4⋊C4—61no—
125C5×C4⋊C4D1212yes—
126C42×C5C22×D311yescharacteristic
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
129C4⋊Dic5—62no—
130#683—62no—
131#683—62no—
132#683—61no—
133#683—61no—
134C4×Dic5—62no—
135C4×Dic5—61no—
136C4×Dic5—61no—
137C2×#168—21no—
138C2×#168—21no—
139#557—151no—
140#487—31no—
141#477—151no—
142#477—151no—
143#332—51no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—42no—
149C3×C4×C5C2×Q1611yescharacteristic
150C3×C4×C5#13511yescharacteristic
151C3×C4×C5#13711yescharacteristic
152C3×C4×C5#13711yescharacteristic
153Dic15—22no—
154Dic15—41no—
155Dic15—41no—
156Dic15—41no—
157C5×Dic3—81no—
158C2×C3×Q8—21no—
159C2×Dic6—21no—
160C2×Dic6—51no—
161C2×Dic6—51no—
162C2×C3×C8—101no—
163C2×C3×C8—101no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4C22⋊D512yes—
166C3×C42C22×D511yescharacteristic
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—51no—
170C4⋊Dic3—51no—
171C4⋊Dic3—102no—
172Dic3⋊C4—102no—
173Dic3⋊C4—102no—
174Dic3⋊C4—101no—
175Dic3⋊C4—101no—
176C4×Dic3—102no—
177C4×Dic3—101no—
178C4×Dic3—101no—
179C2×C3⋊C8—21no—
180C5×Q8—41no—
181C5×Q8—41no—
182C5×Q8—122no—
183C2×C4×C5—22no—
184C2×C4×C5—121no—
185C2×C4×C5C2×D1211yescharacteristic
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192Dic10—32no—
193Dic10—61no—
194Dic10—61no—
195Dic10—61no—
196C5×C8—121no—
197#168—41no—
198#168—41no—
199C4⋊Q8—31no—
200C4⋊Q8—301no—
201C4⋊Q8D3×D511yescharacteristic
202#125—301no—
203#125—302no—
204C4×Q8—151no—
205C4×Q8—151no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—301no—
209#107—301no—
210C4⋊C8—51no—
211C4⋊C8—51no—
212#103—62no—
213#103—301no—
214#103—301no—
215C4×C8—31no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—41no—
220C3×Q8—41no—
221C2×C3×C4—22no—
222C2×C3×C4D4×D511yescharacteristic
223C2×C3×C4D4×D511yescharacteristic
224C2×C3×C4C2×C22⋊D511yescharacteristic
225C2×Dic3—41no—
226C2×Dic3—101no—
227C2×Dic3—101no—
228C2×Dic3—101no—
229C2×Dic3—101no—
230Dic6—42no—
231Dic6—52no—
232Dic6—101no—
233Dic6—101no—
234Dic6—101no—
235C3×C8—201no—
236C3×C8—201no—
237C3⋊C8—41no—
238C22×C5#88211yescharacteristic
239C4×C5—21no—
240C4×C5—42no—
241C4×C5—241no—
242C4×C5#91211yescharacteristic
243C4×C5#91511yescharacteristic
244C4×C5#91511yescharacteristic
245C4×C5D3×Q1611yescharacteristic
246Dic5—62no—
247Dic5—121no—
248Dic5—121no—
249Dic5—121no—
250C2×Q8—21no—
251C2×Q8—61no—
252C2×Q8—151no—
253C2×Q8—151no—
254C2×C8—61no—
255C2×C8—101no—
256C2×C8—101no—
257C4⋊C4—21no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—151no—
261C4⋊C4—151no—
262C4⋊C4—302no—
263C4⋊C4—302no—
264C4⋊C4—302no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#120312yes—
268C42—302no—
269C42—301no—
270C42—301no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—42no—
276C3×C4#406111yescharacteristic
277C3×C4#406211yescharacteristic
278C3×C4D5×Q1611yescharacteristic
279C3×C4#406411yescharacteristic
280Dic3—81no—
281Dic3—102no—
282Dic3—201no—
283Dic3—201no—
284Dic3—201no—
285C2×C5#475311yescharacteristic
286C2×C5#478311yescharacteristic
287C2×C5#480911yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—122no—
291Q8—152no—
292Q8—301no—
293Q8—301no—
294Q8—301no—
295C2×C4—22no—
296C2×C4—121no—
297C2×C4—301no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—301no—
301C2×C4C2×#120311yescharacteristic
302C2×C4#679011yescharacteristic
303C2×C4#679011yescharacteristic
304C8—121no—
305C8—201no—
306C8—201no—
307C2×C3#6535111yescharacteristic
308C2×C3#6546211yescharacteristic
309C2×C3#6547511yescharacteristic
310C5#6845811yescharacteristic, complemented, Sylow
311C22#9157311yescharacteristic
312C4—21no—
313C4—42no—
314C4—241no—
315C4—302no—
316C4—601no—
317C4—601no—
318C4—601no—
319C4#9148811yescharacteristic
320C4#9149711yescharacteristic
321C4#9151111yescharacteristic
322C4#9152211yescharacteristic
323C3#1060202911yescharacteristic, complemented, Sylow
324C2#1174906111yescharacteristic
325C2#1174930811yescharacteristic
326C2#1174938911yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊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#68458semidirect
323. C3#10602029semidirect

Maximal subgroups

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

subgroupindex
#117564802
C5×#50932
#117469632
C3×#647672
#117458442
#106020293
#684585