Finite Group Databasebeta

← #14289408

Subgroups — #14289408

Order 1920.

436 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752662C211yesmaximal, characteristic
2#11750794C211yesmaximal, characteristic
3#11746961C211yesmaximal, characteristic, complemented
4#11746916C211yesmaximal, characteristic, complemented
5C5×#4456C211yesmaximal, characteristic, complemented
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic
8#10599053—31nomaximal, Hall
9C2×#6706—22no—
10#91763C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91433—22no—
15#91428—21no—
16#91418—21no—
17#91375—21no—
18#91374—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90990—21no—
23#90988—21no—
24#90973—21no—
25#90971—21no—
26#68260—51nomaximal, Hall
27#65919—31no—
28#65310—31no—
29#65139—31no—
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60D412yes—
37C2×Dic30—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×#1200—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45#6706—44no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54#6667—22no—
55#6667—22no—
56#6667—22no—
57#5585—51no—
58#5021—51no—
59#4850—51no—
60#4693—51no—
61C3×Q8⋊C8—51no—
62#4485—51no—
63#4456D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4093—61no—
66C2×#677—62no—
67#4040—62no—
68#4039—61no—
69#4021—61no—
70#4020—31no—
71C4×D20—61no—
72#4015—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3950—61no—
78#3948—61no—
79#3939—61no—
80C4⋊#168C2×D311yescharacteristic
81#1630—151noSylow
82C22×D15—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—41no—
87D60—42no—
88D60—41no—
89D60—41no—
90D60—41no—
91D60—41no—
92Dic30—42no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×Dic6—21no—
96C5×Dic6—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101#1200—82no—
102C3×C5×C8—22no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C3×C4×Q8—51no—
106#947—101no—
107C2×#204—102no—
108#894—102no—
109#893—101no—
110#875—101no—
111#874—51no—
112C4×D12—101no—
113#869—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4×C8C2×D511yescharacteristic
117#835—101no—
118#818—101no—
119#816—101no—
120#807—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C2×C5×Q8—31no—
123C2×D20—32no—
124C2×D20—61no—
125C2×D20—61no—
126C2×C4×D5—62no—
127C2×Dic10—61no—
128C2×Dic10D1211yescharacteristic
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#685—62no—
136#685—62no—
137#685—62no—
138C4⋊Dic5—61no—
139C4⋊Dic5—61no—
140C4⋊Dic5D1211yescharacteristic
141#683—21no—
142C4×Dic5—21no—
143C2×#168—21no—
144#677—124no—
145#559—151no—
146#492—151no—
147#477—151no—
148#477—151no—
149#331—151no—
150Q8⋊C8—31no—
151Q8⋊C8—51no—
152C22×C3×C5#12011yescharacteristic
153C2×D15—42no—
154C2×D15—42no—
155C2×D15—42no—
156C3×C4×C5—21no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—81no—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C2×C3×Q8—51no—
167C2×D12—52no—
168C2×D12—101no—
169C2×D12—101no—
170C2×C4×D3—102no—
171C2×Dic6—101no—
172C2×Dic6D2011yescharacteristic
173C2×C3×C8—21no—
174C2×C3×C8—101no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—101no—
177C3×C42—101no—
178C3×C42C22×D511yescharacteristic
179(C2×D3)⋊C4—102no—
180(C2×D3)⋊C4—102no—
181(C2×D3)⋊C4—102no—
182C4⋊Dic3—101no—
183C4⋊Dic3—101no—
184C4⋊Dic3D2011yescharacteristic
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C2×C3⋊C8—21no—
188#204—204no—
189C22×D5—62no—
190C5×Q8—61no—
191C5×Q8—61no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—121no—
200D20—122no—
201D20—121no—
202D20—121no—
203D20—121no—
204D20—121no—
205C4×D5—242no—
206Dic10—21no—
207Dic10—21no—
208Dic10—122no—
209C5×C8—22no—
210C5×C8—121no—
211#168—41no—
212C2×SD16—302no—
213C4⋊Q8—151no—
214#127—151no—
215#124—301no—
216#124—301no—
217#123—302no—
218C4×Q8—31no—
219C4×Q8—51no—
220C4×D4—301no—
221C4×D4—301no—
222#107—301no—
223#107—301no—
224C4⋊C8—31no—
225C4⋊C8—51no—
226#103—301no—
227#103—301no—
228C4×C8D3×D511yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232D15—82no—
233C22×D3—102no—
234C3×Q8—101no—
235C3×Q8—101no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4C2×D2011yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—201no—
244D12—202no—
245D12—201no—
246D12—201no—
247D12—201no—
248D12—201no—
249C4×D3—402no—
250Dic6—21no—
251Dic6—21no—
252Dic6—202no—
253C3×C8—22no—
254C3×C8—201no—
255C3⋊C8—41no—
256C22×C5#88211yescharacteristic
257C2×D5—122no—
258C2×D5—122no—
259C2×D5—122no—
260C4×C5—21no—
261C4×C5—121no—
262C4×C5—121no—
263C4×C5#90411yescharacteristic
264C4×C5#90911yescharacteristic
265C4×C5#91611yescharacteristic
266C4×C5#91811yescharacteristic
267Dic5—41no—
268Dic5—41no—
269Dic5—241no—
270C2×Q8—31no—
271C2×Q8—51no—
272C2×Q8—301no—
273C2×D4—152no—
274C2×D4—301no—
275C2×D4—301no—
276C22×C4—302no—
277SD16—604no—
278C2×C8—21no—
279C2×C8—61no—
280C2×C8—101no—
281C4⋊C4—31no—
282C4⋊C4—51no—
283C4⋊C4—61no—
284C4⋊C4—101no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C22⋊C4—302no—
288C22⋊C4—302no—
289C22⋊C4—302no—
290C42—61no—
291C42—101no—
292C42C2×D3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3#402811yescharacteristic
295C2×D3—202no—
296C2×D3—202no—
297C2×D3—202no—
298C3×C4—21no—
299C3×C4—201no—
300C3×C4—201no—
301C3×C4#405011yescharacteristic
302C3×C4#405511yescharacteristic
303C3×C4#406211yescharacteristic
304C3×C4#406411yescharacteristic
305Dic3—41no—
306Dic3—41no—
307Dic3—401no—
308C2×C5#473311yescharacteristic
309C2×C5#480811yescharacteristic
310C2×C5#482211yescharacteristic
311D5—242no—
312C23—302no—
313Q8—61no—
314Q8—61no—
315Q8—101no—
316Q8—101no—
317Q8—602no—
318D4—602no—
319D4—601no—
320D4—601no—
321D4—601no—
322D4—601no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—601no—
328C2×C4—1202no—
329C2×C4D5×D1211yescharacteristic
330C2×C4D3×D2011yescharacteristic
331C2×C4#679011yescharacteristic
332C8—22no—
333C8—121no—
334C8—201no—
335C2×C3#6502211yescharacteristic
336C2×C3#6509911yescharacteristic
337C2×C3#6511111yescharacteristic
338D3—402no—
339C5#6826011yescharacteristic, complemented, Sylow
340C22—602no—
341C22—602no—
342C22—602no—
343C22#9147611yescharacteristic
344C4—21no—
345C4—121no—
346C4—121no—
347C4—201no—
348C4—201no—
349C4—1201no—
350C4#9126111yescharacteristic
351C4#9126311yescharacteristic
352C4#9126911yescharacteristic
353C4#9127211yescharacteristic
354C3#1059905311yescharacteristic, complemented, Sylow
355C2—1202no—
356C2#1174711811yescharacteristic
357C2#1174816511yescharacteristic
358C2#1174816611yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1630
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
3. #11746961C2semidirect
4. #11746916C2semidirect
5. C5×#4456C2semidirect
6. C3×#64676C2semidirect
33. #64676D3semidirect
63. #4456D5semidirect
293. C3×C5#1630semidirect
339. C5#68260semidirect
354. C3#10599053semidirect

Maximal subgroups

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

subgroupindex
#117526622
#117507942
#117469612
#117469162
C5×#44562
C3×#646762
#117458542
#105990533
#682605