Finite Group Databasebeta

← #14289352

Subgroups — #14289352

Order 1920.

628 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752737C211yesmaximal, characteristic
2#11751185C211yesmaximal, characteristic, complemented
3C5×#5085C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11745853C211yesmaximal, characteristic, complemented
6#11745838C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10602059—31nomaximal, Hall
9C2×#6777—21no—
10C2×D5×D12—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic, complemented
12C4×D60C2211yescharacteristic
13C2×C5×#215—22no—
14C5×#874C2211yescharacteristic
15C3×C4×D20C2211yescharacteristic
16#91475—22no—
17#91466—21no—
18#91449—21no—
19#91093—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic, complemented
22C4×C5×C3⋊C8C2211yescharacteristic, complemented
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic, complemented
26#71143—51nomaximal, Hall
27#66051—31no—
28C5×#492—31no—
29#65373—31no—
30#65373D311yescharacteristic, complemented
31#64764—31no—
32#64679—31no—
33#64679—31no—
34C22×D3×D5—22no—
35C2×C3×C5×Q8—21no—
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12D412yes—
41C2×C3×D20D411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×#1203—22no—
44C2×#1201—22no—
45#6777—42no—
46#6777—42no—
47D5×D12—42no—
48D5×D12—42no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52#6714—21no—
53C4⋊Dic15D411yescharacteristic
54C2×C3⋊#168—21no—
55C5×#215—44no—
56C2×C5×C3⋊C8—21no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C2×C3×#168—21no—
60(C2×D3)⋊Dic5—22no—
61D4×D12—51no—
62C3×#476—51no—
63#5085D511yescharacteristic, complemented
64#5084—51no—
65D4⋊(C3⋊C8)—51no—
66#4485—51no—
67#4483—51no—
68C2×D4×D5—61no—
69C2×D4×D5—61no—
70C2×C5×SD16—62no—
71C5×C4⋊Q8C2×D311yescharacteristic, complemented
72C5×#127—31no—
73#4084—61no—
74#4084—61no—
75#4083—62no—
76C4×D20—31no—
77C4×D20C2×D311yescharacteristic
78C4×C5×C8—31no—
79#3941—21no—
80#3941—61no—
81#3940—21no—
82#3940—61no—
83C4⋊#168—31no—
84C4⋊#168C2×D311yescharacteristic, complemented
85#1629—151noSylow
86C22×D15—21no—
87C22×C5×D3—22no—
88C22×C3×D5—21no—
89C2×D3×D5—44no—
90C2×D3×D5—44no—
91C2×D3×D5—82no—
92C3×C5×Q8—42no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98D60—21no—
99D60SD1612yescomplemented
100C4×D15—41no—
101C4×D15—41no—
102C5×D12—42no—
103C5×D12—41no—
104C5×D12—41no—
105C5×D12—41no—
106C5×D12—41no—
107C2×C3×Dic5—21no—
108C3×D20—21no—
109C3×D20SD1612yescomplemented
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112#1203—44no—
113#1201—44no—
114C3⋊#168—41no—
115C3×#168—41no—
116C5×C3⋊C8—22no—
117C2×D3×D4—101no—
118C22×D12—101no—
119C3×C4⋊Q8C2×D511yescharacteristic, complemented
120C3×C4×D4—51no—
121C2×#215—22no—
122#930—101no—
123#895—101no—
124#882—102no—
125#874C2×D511yescharacteristic
126C4×D12—51no—
127C3×#106—101no—
128C3×C4⋊C8—51no—
129C3×#102—101no—
130#809—101no—
131#808—101no—
132C4⋊(C3⋊C8)—51no—
133C4×C3⋊C8C2×D511yescharacteristic, complemented
134C23×D5—62no—
135C2×C5×Q8—21no—
136C2×C5×D4—32no—
137C2×C5×D4—61no—
138C2×C5×D4—61no—
139C2×C22⋊D5—62no—
140C2×C22⋊D5—62no—
141D4×D5—122no—
142D4×D5—122no—
143D4×D5—122no—
144D4×D5—122no—
145C2×D20—31no—
146C2×D20#6711yescharacteristic
147C2×C4×D5—21no—
148C2×C4×D5—61no—
149C5×SD16—124no—
150C2×C5×C8—61no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C42×C5C22×D311yescharacteristic
154C22⋊Dic5—62no—
155#685—21no—
156#685—61no—
157C4⋊Dic5—31no—
158C4⋊Dic5#6711yescharacteristic
159C2×#168—21no—
160C2×#168—61no—
161D42—151no—
162#492—31no—
163#476—51no—
164#476—151no—
165#331—151no—
166D4⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5#12011yescharacteristic
169C2×D15—22no—
170C2×D15—41no—
171C2×D15—41no—
172C2×C5×D3—42no—
173C2×C5×D3—42no—
174C2×C5×D3—42no—
175C2×C3×D5—22no—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178D3×D5—88no—
179C3×C4×C5—21no—
180C3×C4×C5—81no—
181C3×C4×C5C2×SD1611yescharacteristic
182C3×C4×C5C2×SD1611yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185Dic15—41no—
186C3×Dic5—41no—
187C23×D3—102no—
188C2×C3×Q8—21no—
189C2×C3×D4—51no—
190C22×C3×C4—101no—
191C2×#67—102no—
192D3×D4—202no—
193D3×D4—202no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—51no—
197C2×D12—102no—
198C2×D12—202no—
199C2×D12—202no—
200C2×D12C22⋊D512yes—
201C2×C4×D3—101no—
202C2×C3×C8—101no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—51no—
206C3×C22⋊C4—101no—
207C3×C42C22×D511yescharacteristic
208#215—44no—
209(C2×D3)⋊C4—102no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—101no—
214C23×C5—62no—
215C22×D5—21no—
216C22×D5—61no—
217C22×D5—124no—
218C22×D5—124no—
219C22×D5—242no—
220C5×Q8—42no—
221C5×D4—122no—
222C5×D4—121no—
223C5×D4—121no—
224C5×D4—121no—
225C5×D4—121no—
226C2×C4×C5—41no—
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C22⋊D5—124no—
231C22⋊D5—124no—
232C2×Dic5—21no—
233C2×Dic5—61no—
234D20—21no—
235D20—32no—
236D20—61no—
237D20#21512yescomplemented
238C4×D5—41no—
239C4×D5—41no—
240C4×D5—121no—
241C4×D5—121no—
242C5×C8—62no—
243#168—41no—
244#168—121no—
245C22×D4—301no—
246C22×D4—301no—
247C2×SD16—62no—
248C4⋊Q8D3×D511yescharacteristic, complemented
249#127—31no—
250#121—301no—
251#121—301no—
252#120—302no—
253C4×D4—51no—
254C4×D4—151no—
255#106—101no—
256#106—301no—
257C4⋊C8—51no—
258C4⋊C8—151no—
259#102—101no—
260#102—301no—
261C4×C8—31no—
262C2×C3×C5#45011yescharacteristic
263C2×C3×C5#45011yescharacteristic
264C2×C3×C5#45311yescharacteristic
265D15—42no—
266C3×D5—42no—
267C5×D3—82no—
268C23×C3—101no—
269C22×D3—22no—
270C22×D3—101no—
271C22×D3—204no—
272C22×D3—204no—
273C22×D3—402no—
274C3×Q8—42no—
275C3×D4—52no—
276C3×D4—101no—
277C2×C3×C4—41no—
278C2×C3×C4—101no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4D4×D511yescharacteristic
283C2×C3×C4C2×C22⋊D511yescharacteristic
284#67—204no—
285C2×Dic3—101no—
286D12—42no—
287D12—41no—
288D12—41no—
289D12—41no—
290D12—41no—
291D12—52no—
292D12—101no—
293D12—204no—
294C4×D3—201no—
295C4×D3—201no—
296C3×C8—201no—
297C3⋊C8—22no—
298C3⋊C8—201no—
299C22×C5—122no—
300C22×C5—122no—
301C22×C5—122no—
302C22×C5#93711yescharacteristic
303C2×D5—22no—
304C2×D5—41no—
305C2×D5—41no—
306C2×D5—62no—
307C2×D5—121no—
308C2×D5—121no—
309C2×D5—248no—
310C4×C5—21no—
311C4×C5—81no—
312C4×C5D3×SD1611yescharacteristic
313C4×C5#91411yescharacteristic
314C4×C5C2×#21511yescharacteristic
315C4×C5#94911yescharacteristic
316Dic5—41no—
317Dic5—121no—
318C24—302no—
319C2×Q8—21no—
320C2×D4—32no—
321C2×D4—51no—
322C2×D4—61no—
323C2×D4—61no—
324C2×D4—151no—
325C2×D4—302no—
326C2×D4—302no—
327C2×D4—602no—
328C2×D4—602no—
329C2×D4—602no—
330C2×D4—602no—
331C22×C4—101no—
332C22×C4—301no—
333SD16—124no—
334C2×C8—61no—
335C2×C8—101no—
336C2×C8—301no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—51no—
340C4⋊C4—151no—
341C22⋊C4—101no—
342C22⋊C4—302no—
343C22⋊C4—301no—
344C42C2×D3×D511yescharacteristic
345C3×C5#162911yescharacteristic, complemented, Hall
346C22×C3—102no—
347C22×C3—201no—
348C22×C3—201no—
349C22×C3#408311yescharacteristic
350C2×D3—42no—
351C2×D3—42no—
352C2×D3—42no—
353C2×D3—102no—
354C2×D3—201no—
355C2×D3—201no—
356C2×D3—408no—
357C3×C4—21no—
358C3×C4—81no—
359C3×C4—201no—
360C3×C4D5×SD1611yescharacteristic
361C3×C4D5×SD1611yescharacteristic
362C3×C4#406011yescharacteristic
363C3×C4#406011yescharacteristic
364Dic3—201no—
365C2×C5—242no—
366C2×C5#504611yescharacteristic
367C2×C5#516911yescharacteristic
368C2×C5#519811yescharacteristic
369D5—42no—
370D5—122no—
371C23—62no—
372C23—101no—
373C23—301no—
374C23—604no—
375C23—604no—
376C23—1202no—
377Q8—42no—
378D4—52no—
379D4—101no—
380D4—122no—
381D4—121no—
382D4—121no—
383D4—121no—
384D4—121no—
385D4—152no—
386D4—301no—
387D4—604no—
388D4—604no—
389C2×C4—41no—
390C2×C4—101no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4—301no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4D5×#6711yescharacteristic
397C2×C4D3×C22⋊D511yescharacteristic
398C2×C4#679011yescharacteristic
399C8—62no—
400C8—201no—
401C8—601no—
402C2×C3—202no—
403C2×C3#6536611yescharacteristic
404C2×C3#6545811yescharacteristic
405C2×C3#6545811yescharacteristic
406D3—82no—
407D3—202no—
408C5#7114311yescharacteristic, complemented, Sylow
409C22—102no—
410C22—122no—
411C22—122no—
412C22—122no—
413C22—201no—
414C22—201no—
415C22—302no—
416C22—601no—
417C22—601no—
418C22—1208no—
419C22#9157711yescharacteristic
420C4—21no—
421C4—81no—
422C4—201no—
423C4—601no—
424C4D5×#21511yescharacteristic
425C4#9150211yescharacteristic
426C4#9150511yescharacteristic
427C4#9150611yescharacteristic
428C3#1060205911yescharacteristic, complemented, Sylow
429C2—202no—
430C2—242no—
431C2—602no—
432C2#1174916511yescharacteristic
433C2#1174939711yescharacteristic
434C2#1174939911yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752737C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1629
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
2. #11751185C2semidirect
3. C5×#5085C2semidirect
4. C3×#65373C2semidirect
5. #11745853C2semidirect
6. #11745838C2semidirect
7. #11745835C2semidirect
11. C3×C5×C4⋊Q8C22semidirect
21. C4⋊(C3⋊#168)C22semidirect
22. C4×C5×C3⋊C8C22semidirect
25. C3×C4⋊#168C22semidirect
30. #65373D3semidirect
63. #5085D5semidirect
71. C5×C4⋊Q8C2×D3semidirect
84. C4⋊#168C2×D3semidirect
99. D60SD16semidirect
109. C3×D20SD16semidirect
119. C3×C4⋊Q8C2×D5semidirect
133. C4×C3⋊C8C2×D5semidirect
237. D20#215semidirect
248. C4⋊Q8D3×D5semidirect
345. C3×C5#1629semidirect
408. C5#71143semidirect
428. C3#10602059semidirect

Maximal subgroups

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

subgroupindex
#117527372
#117511852
C5×#50852
C3×#653732
#117458532
#117458382
#117458352
#106020593
#711435