Finite Group Databasebeta

← #14288870

Subgroups — #14288870

Order 1920.

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

normal subgroups only

This group has 480 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#11756344C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3#11747083C211yesmaximal, characteristic, complemented
4#11747035C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745854C211yesmaximal, characteristic, complemented
7#11745844C211yesmaximal, characteristic, complemented
8#10599051—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91836—21no—
11#91783—22no—
12#91782—21no—
13#91764—21no—
14#91763C2211yescharacteristic
15C4×D60—21no—
16C4×Dic30C2211yescharacteristic
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6657—21no—
20C2×#6653—22no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3941—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90965—21no—
26#71031—51nomaximal, Hall
27#65919—31no—
28#65316D311yescharacteristic, complemented
29#65137—31no—
30#64984—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C4×D15—22no—
39C2×Dic30D411yescharacteristic
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—22no—
49#6714—22no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×#688—42no—
56C2×C3×#168—21no—
57#6657—42no—
58#6653—44no—
59#5585—51no—
60C3×#460—51no—
61#5075—51no—
62#5073—51no—
63#4535D511yescharacteristic, complemented
64#4485—51no—
65#4484—51no—
66C4×C5×Q8C2×D311yescharacteristic
67#4093—61no—
68C2×#688—21no—
69C2×D40—62no—
70C2×#677—61no—
71#4040—62no—
72#4039—61no—
73#4021—61no—
74#4020—31no—
75#4020C2×D311yescharacteristic
76C4×D20—61no—
77C4×Dic10—31no—
78C5×C4⋊C8—31no—
79C4×C5×C8—31no—
80#3953—61no—
81#3941—21no—
82C4⋊#168C2×D311yescharacteristic
83#1620—151noSylow
84C22×D15—22no—
85C22×C3×D5—41no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95D60—42no—
96D60—41no—
97D60—41no—
98D60—41no—
99D60—41no—
100C4×D15—82no—
101Dic30—21no—
102Dic30—21no—
103C3×D20—42no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3×#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C2×C3×SD16—101no—
112C3×#127—51no—
113C3×C4×Q8C2×D511yescharacteristic
114#947—101no—
115C2×#214—101no—
116C2×#213—102no—
117#894—102no—
118#893—101no—
119#875—101no—
120#874—51no—
121C4×D12—101no—
122C4×Dic6—51no—
123C3×C4⋊C8—51no—
124C3×#102—101no—
125#832—101no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×Q8#6711yescharacteristic
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—21no—
132C2×D20—32no—
133C2×D20—61no—
134C2×D20—61no—
135C2×C4×D5—62no—
136C2×Dic10—31no—
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4#6711yescharacteristic
141C42×C5—21no—
142C42×C5C22×D311yescharacteristic
143#688—42no—
144#685—62no—
145#685—62no—
146#685—62no—
147C4⋊Dic5—31no—
148#683—61no—
149C4×Dic5—61no—
150C2×#168—21no—
151D40—124no—
152#677—122no—
153#559—151no—
154#493—151no—
155#460—51no—
156#460—151no—
157#331—151no—
158Q8⋊C8—31no—
159Q8⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—42no—
162C2×D15—42no—
163C2×D15—42no—
164C2×C3×D5—81no—
165C2×C3×D5—81no—
166C2×C3×D5—81no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174Dic15—41no—
175Dic15—41no—
176C2×C3×Q8D2011yescharacteristic
177C2×C3×D4—101no—
178C2×C3×D4—101no—
179C2×C3×D4—101no—
180C2×D12—52no—
181C2×D12—101no—
182C2×D12—101no—
183C2×C4×D3—102no—
184C2×Dic6—51no—
185C3×SD16—202no—
186C2×C3×C8—101no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4D2011yescharacteristic
189C3×C42—21no—
190C3×C42C22×D511yescharacteristic
191#214—202no—
192#213—204no—
193(C2×D3)⋊C4—102no—
194(C2×D3)⋊C4—102no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3—51no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C22×D5—41no—
202C22×D5—62no—
203C5×Q8—21no—
204C5×Q8—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—61no—
211C2×Dic5—61no—
212D20—42no—
213D20—41no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—242no—
223Dic10—61no—
224Dic10—61no—
225C5×C8—62no—
226C5×C8—121no—
227#168—41no—
228C2×SD16—101no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—51no—
232#127—151no—
233#124—301no—
234#124—301no—
235#123—302no—
236C4×Q8—151no—
237C4×Q8D3×D511yescharacteristic
238C4×D4—301no—
239C4×D4—301no—
240C4⋊C8—31no—
241C4⋊C8—51no—
242#102—101no—
243#102—301no—
244C4×C8—31no—
245C2×C3×C5#44911yescharacteristic
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—82no—
249C3×D5—161no—
250C23×C3—201no—
251C22×D3—102no—
252C3×Q8—21no—
253C3×Q8—21no—
254C3×D4—202no—
255C3×D4—201no—
256C3×D4—201no—
257C3×D4—201no—
258C3×D4—201no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4C2×D2011yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×Dic3—101no—
265C2×Dic3—101no—
266D12—202no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—402no—
272Dic6—101no—
273Dic6—101no—
274C3×C8—201no—
275C3⋊C8—22no—
276C3⋊C8—41no—
277C22×C5#93711yescharacteristic
278C2×D5—81no—
279C2×D5—81no—
280C2×D5—81no—
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5#91411yescharacteristic
288C4×C5#91611yescharacteristic
289C4×C5#93211yescharacteristic
290C4×C5#95011yescharacteristic
291Dic5—121no—
292Dic5—121no—
293C2×Q8—151no—
294C2×Q8#120211yescharacteristic
295C2×D4—101no—
296C2×D4—101no—
297C2×D4—101no—
298C2×D4—152no—
299C2×D4—301no—
300C2×D4—301no—
301C22×C4—302no—
302SD16—202no—
303SD16—602no—
304D8—604no—
305C2×C8—61no—
306C2×C8—61no—
307C2×C8—101no—
308C4⋊C4—21no—
309C4⋊C4—151no—
310C4⋊C4—301no—
311C4⋊C4#120211yescharacteristic
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C42—21no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—401no—
320C22×C3—401no—
321C22×C3—401no—
322C22×C3#402811yescharacteristic
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4#405011yescharacteristic
330C3×C4#405411yescharacteristic
331C3×C4#406011yescharacteristic
332C3×C4#406511yescharacteristic
333Dic3—201no—
334Dic3—201no—
335C2×C5#503711yescharacteristic
336C2×C5#517211yescharacteristic
337C2×C5#519811yescharacteristic
338D5—161no—
339D5—242no—
340C23—201no—
341C23—302no—
342Q8—21no—
343Q8—21no—
344Q8—301no—
345Q8—301no—
346D4—202no—
347D4—201no—
348D4—201no—
349D4—201no—
350D4—201no—
351D4—602no—
352D4—601no—
353D4—601no—
354D4—601no—
355D4—601no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—1202no—
361C2×C4C2×#120211yescharacteristic
362C2×C4#679011yescharacteristic
363C2×C4#679011yescharacteristic
364C8—62no—
365C8—121no—
366C8—201no—
367C2×C3—801no—
368C2×C3#6502311yescharacteristic
369C2×C3#6510011yescharacteristic
370C2×C3#6511111yescharacteristic
371D3—402no—
372C5#7103111yescharacteristic, complemented, Sylow
373C22—401no—
374C22—401no—
375C22—401no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9157211yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—601no—
384C4—601no—
385C4#9131111yescharacteristic
386C4#9131211yescharacteristic
387C4#9150611yescharacteristic
388C4#9152111yescharacteristic
389C3#1059905111yescharacteristic, complemented, Sylow
390C2—801no—
391C2—1202no—
392C2#1174855011yescharacteristic
393C2#1174928811yescharacteristic
394C2#1174942111yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747035C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1620
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
1. #11756344C2semidirect
2. C3×#65316C2semidirect
3. #11747083C2semidirect
5. C5×#4535C2semidirect
6. #11745854C2semidirect
7. #11745844C2semidirect
28. #65316D3semidirect
63. #4535D5semidirect
318. C3×C5#1620semidirect
372. C5#71031semidirect
389. C3#10599051semidirect

Maximal subgroups

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

subgroupindex
#117563442
C3×#653162
#117470832
#117470352
C5×#45352
#117458542
#117458442
#105990513
#710315