Finite Group Databasebeta

← #14289729

Subgroups — #14289729

Order 1920.

376 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752481C211yesmaximal, characteristic
2C5×#4850C211yesmaximal, characteristic
3#11746963C211yesmaximal, characteristic
4#11746923C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic
6C3×#64702C211yesmaximal, characteristic
7#11745842C211yesmaximal, characteristic
8#10601955—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91385—21no—
14#91381—21no—
15#91340—21no—
16#91339—22no—
17#91331—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×#818—21no—
21C5×#816—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90988—21no—
24#90975—21no—
25#90972—22no—
26#68458—51nomaximal, Hall
27#65901—31no—
28C5×#477—31no—
29#65380—31no—
30#65370—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64702D311yescharacteristic
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×Dic10—21no—
38C2×C3×C5×C8—21no—
39C3×C42×C5C2311yescharacteristic
40C4⋊Dic15D411yescharacteristic
41#6712—21no—
42C4×Dic15—21no—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D412yes—
51C2×C3×#168—21no—
52#6669—22no—
53#6669—22no—
54#6668—22no—
55Dic3×Dic5—22no—
56#5721—51no—
57#5093—51no—
58#4850—51no—
59#4850D511yescharacteristic
60C3×#332—51no—
61#4484—51no—
62#4484—51no—
63C5×C4⋊Q8—31no—
64C4×C5×Q8—31no—
65#4090—61no—
66#4035—62no—
67#4033—61no—
68#4016—61no—
69#4015C2×D311yescharacteristic
70C4×Dic10—31no—
71C4×Dic10—61no—
72C5×#107—61no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×#103—61no—
75#3967—62no—
76#3942—61no—
77#3939—61no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1636—151noSylow
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—21no—
85C2×Dic15—21no—
86Dic30—21no—
87Dic30Q1612yes—
88C2×C5×Dic3—21no—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—41no—
91C5×Dic6—21no—
92C5×Dic6—21no—
93C5×Dic6—42no—
94C2×C3×Dic5—22no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97C3×C5×C8—41no—
98C3⋊#168—41no—
99C3×#168—41no—
100C3×C4⋊Q8—51no—
101Q8×Dic3—101no—
102#944—101no—
103#890—101no—
104#889—102no—
105#887—101no—
106#869C2×D511yescharacteristic
107C4×Dic6—51no—
108C4×Dic6C2×D511yescharacteristic
109C3×C4⋊C8—51no—
110C3×C4⋊C8C2×D511yescharacteristic
111#818—21no—
112#818—101no—
113#816—21no—
114#816—101no—
115#810—102no—
116C4×C3⋊C8—51no—
117C2×C5×Q8—31no—
118C2×C5×Q8—61no—
119C2×Dic10—21no—
120C2×Dic10—31no—
121C2×C5×C8—21no—
122C5×C4⋊C4—31no—
123C5×C4⋊C4—61no—
124C5×C4⋊C4—61no—
125C5×C4⋊C4—61no—
126C42×C5—61no—
127C42×C5C22×D311yescharacteristic
128C4⋊Dic5—21no—
129C4⋊Dic5—31no—
130C4⋊Dic5D1212yes—
131#683—62no—
132#683—62no—
133#683—62no—
134#683—61no—
135C4×Dic5—62no—
136C4×Dic5—61no—
137C2×#168—21no—
138C2×#168—61no—
139#557—151no—
140#487—151no—
141#477—31no—
142#477—151no—
143#332—51no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5C2×Q1611yescharacteristic
149C3×C4×C5#13511yescharacteristic
150C3×C4×C5#13711yescharacteristic
151C3×C4×C5#13711yescharacteristic
152Dic15—22no—
153Dic15—41no—
154C3×Dic5—42no—
155C5×Dic3—41no—
156C5×Dic3—41no—
157C5×Dic3—81no—
158C2×C3×Q8—101no—
159C2×Dic6—21no—
160C2×Dic6—51no—
161C2×Dic6C22⋊D511yescharacteristic
162C2×C3×C8—21no—
163C2×C3×C8—101no—
164C3×C4⋊C4—52no—
165C3×C4⋊C4—101no—
166C3×C42C22×D511yescharacteristic
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—51no—
170C4⋊Dic3—102no—
171C4⋊Dic3C22⋊D511yescharacteristic
172Dic3⋊C4—21no—
173Dic3⋊C4—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—101no—
176C4×Dic3—21no—
177C4×Dic3—102no—
178C4×Dic3—101no—
179C2×C3⋊C8—101no—
180C5×Q8—61no—
181C5×Q8—61no—
182C5×Q8—122no—
183C2×C4×C5—61no—
184C2×C4×C5—61no—
185C2×C4×C5—121no—
186C2×C4×C5C2×D1211yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×Dic5—22no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192Dic10—32no—
193Dic10—41no—
194Dic10—41no—
195Dic10—61no—
196C5×C8—41no—
197#168—41no—
198#168—121no—
199C4⋊Q8—31no—
200C4⋊Q8—51no—
201C4⋊Q8—301no—
202#125—301no—
203#125—302no—
204C4×Q8—31no—
205C4×Q8—151no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—61no—
209#107—301no—
210C4⋊C8—51no—
211C4⋊C8D3×D511yescharacteristic
212#103—61no—
213#103—302no—
214#103—301no—
215C4×C8—151no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—201no—
220C3×Q8—201no—
221C2×C3×C4—102no—
222C2×C3×C4D4×D511yescharacteristic
223C2×C3×C4D4×D511yescharacteristic
224C2×C3×C4C2×C22⋊D511yescharacteristic
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—41no—
228C2×Dic3—101no—
229C2×Dic3—101no—
230Dic6—21no—
231Dic6—21no—
232Dic6—42no—
233Dic6—52no—
234Dic6—101no—
235C3×C8—41no—
236C3×C8—201no—
237C3⋊C8—201no—
238C22×C5#88211yescharacteristic
239C4×C5—21no—
240C4×C5—121no—
241C4×C5—121no—
242C4×C5—241no—
243C4×C5#91211yescharacteristic
244C4×C5#91511yescharacteristic
245C4×C5#91511yescharacteristic
246C4×C5D3×Q1611yescharacteristic
247Dic5—42no—
248Dic5—62no—
249Dic5—121no—
250C2×Q8—31no—
251C2×Q8—61no—
252C2×Q8—101no—
253C2×Q8—151no—
254C2×C8—21no—
255C2×C8—101no—
256C2×C8—301no—
257C4⋊C4—31no—
258C4⋊C4—52no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4—101no—
263C4⋊C4—151no—
264C4⋊C4—302no—
265C4⋊C4—302no—
266C4⋊C4—302no—
267C4⋊C4—301no—
268C42—61no—
269C42—302no—
270C42—301no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—202no—
276C3×C4D5×Q1611yescharacteristic
277C3×C4#406411yescharacteristic
278C3×C4#408811yescharacteristic
279C3×C4#409611yescharacteristic
280Dic3—41no—
281Dic3—41no—
282Dic3—81no—
283Dic3—102no—
284Dic3—201no—
285C2×C5#475311yescharacteristic
286C2×C5#478311yescharacteristic
287C2×C5#480911yescharacteristic
288Q8—61no—
289Q8—61no—
290Q8—122no—
291Q8—152no—
292Q8—201no—
293Q8—201no—
294Q8—301no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—102no—
298C2×C4—121no—
299C2×C4—301no—
300C2×C4—301no—
301C2×C4D5×D1211yescharacteristic
302C2×C4#677711yescharacteristic
303C2×C4D3×C22⋊D511yescharacteristic
304C8—41no—
305C8—201no—
306C8—601no—
307C2×C3#6533611yescharacteristic
308C2×C3#6547511yescharacteristic
309C2×C3#6549011yescharacteristic
310C5#6845811yescharacteristic, complemented, Sylow
311C22#9147511yescharacteristic
312C4—21no—
313C4—121no—
314C4—121no—
315C4—202no—
316C4—241no—
317C4—302no—
318C4—601no—
319C4#9126411yescharacteristic
320C4#9127811yescharacteristic
321C4#9149311yescharacteristic
322C4#9151811yescharacteristic
323C3#1060195511yescharacteristic, complemented, Sylow
324C2#1174751411yescharacteristic
325C2#1174813111yescharacteristic
326C2#1174825911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1636
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
272. C3×C5#1636semidirect
310. C5#68458semidirect
323. C3#10601955semidirect

Maximal subgroups

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

subgroupindex
#117524812
C5×#48502
#117469632
#117469232
#117463052
C3×#647022
#117458422
#106019553
#684585