Finite Group Databasebeta

← #14289708

Subgroups — #14289708

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#11752490C211yesmaximal, characteristic
2#11751180C211yesmaximal, characteristic
3C5×#5091C211yesmaximal, characteristic
4C3×#65380C211yesmaximal, characteristic
5#11745860C211yesmaximal, characteristic
6#11745842C211yesmaximal, characteristic
7#11745840C211yesmaximal, characteristic
8#10601951—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91389—21no—
14#91388—21no—
15#91343—22no—
16#91340—21no—
17Dic5×Dic6—21no—
18#91119—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#810—21no—
21C5×#807—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71162—51nomaximal, Hall
27#65904—31no—
28C5×#477—31no—
29#65380D311yescharacteristic
30#65370—31no—
31Q8⋊#168—31no—
32#64706—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×Dic10D411yescharacteristic
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15D412yes—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3D411yescharacteristic
45C5×Dic3⋊C4—21no—
46C4×C5×Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—21no—
50C3×C4×Dic5—21no—
51C2×C3×#168—21no—
52Dic3⋊Dic5—22no—
53Dic3⋊Dic5—22no—
54#6669—22no—
55Dic3×Dic5—22no—
56#5567—51no—
57C3×#477—51no—
58#5091D511yescharacteristic
59#5079—51no—
60#4535—51no—
61#4484—51no—
62#4482—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C4×C5×Q8—31no—
65Q8×Dic5—61no—
66#4036—61no—
67#4036—62no—
68#4015—31no—
69#4015—61no—
70C4×Dic10—61no—
71C4×Dic10C2×D311yescharacteristic
72C5×#107—61no—
73C5×C4⋊C8—31no—
74C5×#103—61no—
75#3967—62no—
76#3942—21no—
77#3939—21no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1636—151noSylow
81C3×C5×Q8—42no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87Dic30—41no—
88Dic30—41no—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—21no—
91C5×Dic6—21no—
92C5×Dic6Q1612yes—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×Dic10—21no—
96C3×Dic10—21no—
97C3⋊#168—41no—
98C3×#168—41no—
99C5×C3⋊C8—41no—
100C3×C4⋊Q8C2×D511yescharacteristic
101C3×C4×Q8—51no—
102#944—101no—
103#889—102no—
104#887—101no—
105#870—101no—
106#869—51no—
107C4×Dic6—101no—
108C4×Dic6C2×D511yescharacteristic
109C3×#107—101no—
110C3×C4⋊C8—51no—
111C3×#103—101no—
112#835—102no—
113#810—21no—
114#807—21no—
115C4⋊(C3⋊C8)C2×D511yescharacteristic
116C4×C3⋊C8—51no—
117C2×C5×Q8—21no—
118C2×C5×Q8—31no—
119C2×Dic10—61no—
120C2×Dic10#6711yescharacteristic
121C2×C5×C8—61no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—61no—
126C42×C5—61no—
127C42×C5C22×D311yescharacteristic
128C4⋊Dic5—32no—
129C4⋊Dic5—62no—
130C4⋊Dic5—62no—
131C4⋊Dic5—61no—
132C4⋊Dic5#6711yescharacteristic
133#683—21no—
134#683—62no—
135C4×Dic5—21no—
136C4×Dic5—62no—
137C2×#168—21no—
138C2×#168—61no—
139#557—151no—
140#487—151no—
141#477—31no—
142#477—51no—
143#332—151no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—81no—
149C3×C4×C5C2×Q1611yescharacteristic
150C3×C4×C5#13511yescharacteristic
151C3×C4×C5#13711yescharacteristic
152C3×C4×C5#13711yescharacteristic
153Dic15—42no—
154C3×Dic5—41no—
155C3×Dic5—41no—
156C5×Dic3—22no—
157C5×Dic3—41no—
158C2×C3×Q8—21no—
159C2×C3×Q8—51no—
160C2×Dic6—101no—
161C2×Dic6C22⋊D511yescharacteristic
162C2×C3×C8—101no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—51no—
166C3×C4⋊C4—101no—
167C3×C42—101no—
168C3×C42C22×D511yescharacteristic
169C4⋊Dic3—52no—
170C4⋊Dic3—101no—
171C4⋊Dic3C22⋊D511yescharacteristic
172Dic3⋊C4—21no—
173Dic3⋊C4—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—102no—
176C4×Dic3—21no—
177C4×Dic3—102no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—101no—
180C5×Q8—32no—
181C5×Q8—42no—
182C5×Q8—61no—
183C2×C4×C5—41no—
184C2×C4×C5—61no—
185C2×C4×C5—61no—
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5C2×#6711yescharacteristic
189C2×Dic5—21no—
190C2×Dic5—21no—
191C2×Dic5—62no—
192Dic10—21no—
193Dic10—21no—
194Dic10—121no—
195Dic10—121no—
196C5×C8—121no—
197#168—41no—
198#168—121no—
199C4⋊Q8—151no—
200C4⋊Q8—301no—
201C4⋊Q8D3×D511yescharacteristic
202#125—301no—
203#125—302no—
204C4×Q8—31no—
205C4×Q8—51no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—61no—
209#107—101no—
210C4⋊C8—31no—
211C4⋊C8—51no—
212#103—61no—
213#103—101no—
214#103—302no—
215C4×C8—151no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—42no—
220C3×Q8—101no—
221C3×Q8—101no—
222C2×C3×C4—41no—
223C2×C3×C4—101no—
224C2×C3×C4—101no—
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4D4×D511yescharacteristic
227C2×C3×C4C2×C22⋊D511yescharacteristic
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—102no—
231Dic6—21no—
232Dic6—201no—
233Dic6—201no—
234Dic6#68912yes—
235C3×C8—201no—
236C3⋊C8—41no—
237C3⋊C8—201no—
238C22×C5#93711yescharacteristic
239C4×C5—21no—
240C4×C5—62no—
241C4×C5—81no—
242C4×C5—121no—
243C4×C5D3×Q1611yescharacteristic
244C4×C5#91811yescharacteristic
245C4×C5#94211yescharacteristic
246C4×C5#95011yescharacteristic
247Dic5—41no—
248Dic5—41no—
249Dic5—122no—
250C2×Q8—21no—
251C2×Q8—31no—
252C2×Q8—51no—
253C2×Q8—301no—
254C2×C8—61no—
255C2×C8—101no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—31no—
260C4⋊C4—51no—
261C4⋊C4—61no—
262C4⋊C4—101no—
263C4⋊C4—152no—
264C4⋊C4—302no—
265C4⋊C4—302no—
266C4⋊C4—302no—
267C4⋊C4—301no—
268C42—61no—
269C42—101no—
270C42—302no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—81no—
276C3×C4—201no—
277C3×C4—201no—
278C3×C4#406411yescharacteristic
279C3×C4#406511yescharacteristic
280C3×C4C2×#68911yescharacteristic
281C3×C4#409711yescharacteristic
282Dic3—22no—
283Dic3—41no—
284Dic3—202no—
285C2×C5#504711yescharacteristic
286C2×C5#518611yescharacteristic
287C2×C5#520111yescharacteristic
288Q8—32no—
289Q8—42no—
290Q8—61no—
291Q8—101no—
292Q8—101no—
293Q8—601no—
294Q8—601no—
295C2×C4—41no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—302no—
301C2×C4D5×#6711yescharacteristic
302C2×C4D3×C22⋊D511yescharacteristic
303C2×C4#679011yescharacteristic
304C8—121no—
305C8—201no—
306C8—601no—
307C2×C3#6533911yescharacteristic
308C2×C3#6547611yescharacteristic
309C2×C3#6549011yescharacteristic
310C5#7116211yescharacteristic, complemented, Sylow
311C22#9157711yescharacteristic
312C4—21no—
313C4—62no—
314C4—81no—
315C4—121no—
316C4—201no—
317C4—201no—
318C4—602no—
319C4D3×#68911yescharacteristic
320C4#9151011yescharacteristic
321C4#9151511yescharacteristic
322C4#9151611yescharacteristic
323C3#1060195111yescharacteristic, complemented, Sylow
324C2#1174916611yescharacteristic
325C2#1174940111yescharacteristic
326C2#1174940611yescharacteristic
subgroupG/H
centerC22#91577
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#71162semidirect
323. C3#10601951semidirect

Maximal subgroups

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

subgroupindex
#117524902
#117511802
C5×#50912
C3×#653802
#117458602
#117458422
#117458402
#106019513
#711625