Finite Group Databasebeta

← #14289718

Subgroups — #14289718

Order 1920.

376 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#5567C211yesmaximal, characteristic
2#11751122C211yesmaximal, characteristic
3#11746961C211yesmaximal, characteristic
4#11746930C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic
6#11745857C211yesmaximal, characteristic
7#11745843C211yesmaximal, characteristic
8#10602729—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#944—21no—
12C5×#889—22no—
13C5×#887—21no—
14C5×#870—21no—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6—21no—
17C4×C5×Dic6C2211yescharacteristic
18#91119—21no—
19#91091—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23#90988—21no—
24#90975—22no—
25#90973—21no—
26#68268—51nomaximal, Hall
27C5×#557—31no—
28#65382—31no—
29#65310—31no—
30#65310—31no—
31#64767—31no—
32Q8⋊#168—31no—
33Q8⋊#168D311yescharacteristic
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6D411yescharacteristic
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C42×C5—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×C4⋊Dic3D412yes—
48C5×Dic3⋊C4—22no—
49C5×Dic3⋊C4—22no—
50C5×Dic3⋊C4—22no—
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—22no—
53C4×C5×Dic3—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#5567D511yescharacteristic
57#5021—51no—
58#4850—51no—
59#4681—51no—
60C3×Q8⋊C8—51no—
61#4486—51no—
62#4456—51no—
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8—61no—
65C5×#125—61no—
66C5×#125—62no—
67C4×C5×Q8—31no—
68C4×C5×Q8—61no—
69C4×C5×Q8—61no—
70C4×C5×Q8C2×D311yescharacteristic
71#4015—31no—
72#3967—61no—
73#3967—61no—
74#3942—62no—
75#3939—61no—
76#3939—61no—
77C4⋊#168—31no—
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—41no—
89Dic30—42no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—22no—
93C5×Dic6—21no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C5×Dic6Q1612yes—
97C3⋊#168—41no—
98C3×#168—41no—
99C3×#168—41no—
100C3×C4×Q8C2×D511yescharacteristic
101#944—21no—
102#889—22no—
103#887—21no—
104#870—21no—
105#869—51no—
106#869C2×D511yescharacteristic
107C4×Dic6—21no—
108C4×Dic6C2×D511yescharacteristic
109C3×C4⋊C8—51no—
110C3×C4×C8—51no—
111#835—101no—
112#818—101no—
113#816—101no—
114#816—102no—
115#807—101no—
116C4⋊(C3⋊C8)—51no—
117C2×C5×Q8—31no—
118C2×C5×Q8—61no—
119C2×C5×Q8D1211yescharacteristic
120C2×Dic10—61no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—31no—
123C5×C4⋊C4—32no—
124C5×C4⋊C4—62no—
125C5×C4⋊C4—62no—
126C5×C4⋊C4—62no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4D1211yescharacteristic
130C42×C5—21no—
131C42×C5—62no—
132C42×C5—61no—
133C42×C5C22×D311yescharacteristic
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136C2×#168—21no—
137C2×#168—21no—
138C2×#168—61no—
139#557—31no—
140#487—151no—
141#477—151no—
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—81no—
155C5×Dic3—22no—
156C5×Dic3—42no—
157C5×Dic3—41no—
158C2×C3×Q8C22⋊D511yescharacteristic
159C2×Dic6—21no—
160C2×Dic6—101no—
161C2×Dic6C22⋊D511yescharacteristic
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—101no—
170C4⋊Dic3—101no—
171C4⋊Dic3C22⋊D512yes—
172C4⋊Dic3C22⋊D511yescharacteristic
173Dic3⋊C4—22no—
174Dic3⋊C4—22no—
175Dic3⋊C4—22no—
176Dic3⋊C4—21no—
177C4×Dic3—22no—
178C4×Dic3—21no—
179C2×C3⋊C8—101no—
180C5×Q8—21no—
181C5×Q8—21no—
182C5×Q8—32no—
183C5×Q8—61no—
184C5×Q8—121no—
185C5×Q8—121no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—61no—
189C2×C4×C5—61no—
190C2×C4×C5—62no—
191C2×C4×C5C2×D1211yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×Dic5—121no—
195Dic10—122no—
196#168—41no—
197#168—41no—
198#168—121no—
199C4⋊Q8—31no—
200C4⋊Q8—61no—
201C4⋊Q8—151no—
202#125—61no—
203#125—62no—
204C4×Q8—31no—
205C4×Q8—61no—
206C4×Q8—61no—
207C4×Q8D3×D511yescharacteristic
208#107—301no—
209#107—301no—
210C4⋊C8—51no—
211C4⋊C8—151no—
212#103—302no—
213#103—301no—
214#103—301no—
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×C4C2×C22⋊D511yescharacteristic
224C2×C3×C4C2×C22⋊D511yescharacteristic
225C2×C3×C4C2×C22⋊D511yescharacteristic
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—22no—
229C2×Dic3—201no—
230Dic6—21no—
231Dic6—41no—
232Dic6—41no—
233Dic6—202no—
234Dic6#68912yes—
235C3×C8—201no—
236C3×C8—201no—
237C3⋊C8—201no—
238C22×C5#88211yescharacteristic
239C4×C5—21no—
240C4×C5—41no—
241C4×C5—41no—
242C4×C5—62no—
243C4×C5—122no—
244C4×C5—121no—
245C4×C5#90411yescharacteristic
246C4×C5#90911yescharacteristic
247C4×C5#91511yescharacteristic
248C4×C5D3×Q1611yescharacteristic
249Dic5—241no—
250C2×Q8—31no—
251C2×Q8—61no—
252C2×Q8—301no—
253C2×Q8#120311yescharacteristic
254C2×C8—101no—
255C2×C8—101no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—32no—
259C4⋊C4—31no—
260C4⋊C4—62no—
261C4⋊C4—62no—
262C4⋊C4—62no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#120311yescharacteristic
268C42—21no—
269C42—62no—
270C42—61no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#409911yescharacteristic
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4#408811yescharacteristic
278C3×C4C2×#68911yescharacteristic
279C3×C4#409611yescharacteristic
280C3×C4#409711yescharacteristic
281Dic3—22no—
282Dic3—42no—
283Dic3—41no—
284Dic3—401no—
285C2×C5#473311yescharacteristic
286C2×C5#480911yescharacteristic
287C2×C5#482711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—32no—
291Q8—61no—
292Q8—121no—
293Q8—121no—
294Q8—602no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—62no—
300C2×C4—601no—
301C2×C4C2×#120311yescharacteristic
302C2×C4D3×C22⋊D511yescharacteristic
303C2×C4D3×C22⋊D511yescharacteristic
304C8—201no—
305C8—201no—
306C8—601no—
307C2×C3#6551711yescharacteristic
308C2×C3#6552811yescharacteristic
309C2×C3#6553411yescharacteristic
310C5#6826811yescharacteristic, complemented, Sylow
311C22#9157011yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—62no—
316C4—122no—
317C4—121no—
318C4—1201no—
319C4#9130311yescharacteristic
320C4#9132211yescharacteristic
321C4D3×#68911yescharacteristic
322C4#9151811yescharacteristic
323C3#1060272911yescharacteristic, complemented, Sylow
324C2#1174836111yescharacteristic
325C2#1174930211yescharacteristic
326C2#1174945911yescharacteristic
subgroupG/H
centerC22#91570
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#10602729semidirect

Maximal subgroups

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

subgroupindex
C5×#55672
#117511222
#117469612
#117469302
C3×Q8⋊#1682
#117458572
#117458432
#106027293
#682685