Finite Group Databasebeta

← #14289369

Subgroups — #14289369

Order 1920.

628 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D12×D20C211yesmaximal, characteristic
2#11750794C211yesmaximal, characteristic, complemented
3#11746883C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic, complemented
5C5×#4459C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10598988—31nomaximal, Hall
9C2×D3×D20—21no—
10C2×D5×D12—21no—
11C2×#6706—22no—
12#91763C2211yescharacteristic
13#91758C2211yescharacteristic, complemented
14C4×C5×D12C2211yescharacteristic
15C3×C4×D20C2211yescharacteristic
16#91476—22no—
17#91460—21no—
18#91450—21no—
19C3×C4×C5×C8C2211yescharacteristic, complemented
20C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
21C3×C4⋊#168C2211yescharacteristic, complemented
22#90987—21no—
23#90985—21no—
24#90967—21no—
25#90965—21no—
26#68195—51nomaximal, Hall
27D4×D20—31no—
28#65297—31no—
29#65131—31no—
30#64982—31no—
31C5×D4⋊C8—31no—
32#64705—31no—
33#64679D311yescharacteristic, complemented
34C22×D3×D5—22no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×Dic30—21no—
39C2×C5×D12D411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C3×D20D411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×#1203—22no—
44C2×#1202—22no—
45D3×D20—42no—
46D3×D20—42no—
47D5×D12—42no—
48D5×D12—42no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53#6706—44no—
54C5×(C2×D3)⋊C4—21no—
55C5×C4⋊Dic3D411yescharacteristic
56C2×C5×C3⋊C8—21no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C2×C3×#168—21no—
60#6667—22no—
61D4×D12—51no—
62#5008—51no—
63#4842—51no—
64#4693—51no—
65C3×D4⋊C8—51no—
66#4485—51no—
67#4459D511yescharacteristic, complemented
68C2×D4×D5—61no—
69C22×D20—61no—
70C4×C5×D4—31no—
71#4076—61no—
72C2×#677—62no—
73#4041—61no—
74#4028—62no—
75#4020—31no—
76C4×D20C2×D311yescharacteristic
77#4015—31no—
78C5×C4⋊C8—31no—
79C4×C5×C8C2×D311yescharacteristic, complemented
80#3964—61no—
81#3953—61no—
82#3949—61no—
83#3940—61no—
84C4⋊#168C2×D311yescharacteristic, complemented
85#1629—151noSylow
86C22×D15—22no—
87C22×C5×D3—21no—
88C22×C3×D5—21no—
89C2×D3×D5—44no—
90C2×D3×D5—44no—
91C2×D3×D5—82no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—41no—
96D60—42no—
97D60—41no—
98D60—41no—
99D60—41no—
100D60—41no—
101Dic30—42no—
102C2×C5×Dic3—21no—
103C5×D12—21no—
104C5×D12SD1612yescomplemented
105C4×C5×D3—41no—
106C4×C5×D3—41no—
107C2×C3×Dic5—21no—
108C3×D20—21no—
109C3×D20SD1612yescomplemented
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112#1203—44no—
113#1202—44no—
114C3×C5×C8—22no—
115C3×#168—41no—
116C5×C3⋊C8—41no—
117C2×D3×D4—101no—
118C22×D12—101no—
119C3×C4×D4—51no—
120#930—101no—
121C2×#204—102no—
122#895—101no—
123#882—102no—
124#874—51no—
125C4×D12C2×D511yescharacteristic
126#869—51no—
127C3×C4⋊C8—51no—
128C3×C4×C8C2×D511yescharacteristic, complemented
129#832—101no—
130#821—101no—
131#817—101no—
132#808—101no—
133C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
134C23×D5—62no—
135C2×C5×D4—31no—
136C22×C4×C5—61no—
137C2×C22⋊D5—62no—
138D4×D5—122no—
139D4×D5—122no—
140C2×D20—32no—
141C2×D20—62no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—122no—
145C2×D20—122no—
146C2×D20D1211yescharacteristic
147C2×C4×D5—21no—
148C2×Dic10—61no—
149C2×C5×C8—21no—
150C2×C5×C8—61no—
151C5×C4⋊C4—31no—
152C5×C22⋊C4—61no—
153C42×C5C22×D311yescharacteristic
154#685—21no—
155#685—62no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158C4⋊Dic5D1211yescharacteristic
159C2×#168—21no—
160#677—124no—
161D42—151no—
162#492—151no—
163#476—151no—
164#476—151no—
165#331—151no—
166D4⋊C8—31no—
167D4⋊C8—51no—
168C22×C3×C5#12011yescharacteristic
169C2×D15—42no—
170C2×D15—42no—
171C2×D15—42no—
172C2×C5×D3—22no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C3×D5—22no—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178D3×D5—88no—
179C3×C4×C5—21no—
180C3×C4×C5C2×SD1611yescharacteristic
181C3×C4×C5C2×SD1611yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184Dic15—81no—
185C3×Dic5—41no—
186C5×Dic3—41no—
187C23×D3—102no—
188C2×C3×D4—51no—
189C22×C3×C4—101no—
190C2×#67—102no—
191D3×D4—202no—
192D3×D4—202no—
193C2×D12—52no—
194C2×D12—102no—
195C2×D12—101no—
196C2×D12—101no—
197C2×D12—202no—
198C2×D12—202no—
199C2×D12D2011yescharacteristic
200C2×C4×D3—21no—
201C2×Dic6—101no—
202C2×C3×C8—21no—
203C2×C3×C8—101no—
204C3×C4⋊C4—51no—
205C3×C22⋊C4—101no—
206C3×C42C22×D511yescharacteristic
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—102no—
209C4⋊Dic3—101no—
210C4⋊Dic3—101no—
211C4⋊Dic3D2011yescharacteristic
212C2×C3⋊C8—21no—
213#204—204no—
214C23×C5—61no—
215C22×D5—21no—
216C22×D5—62no—
217C22×D5—124no—
218C22×D5—124no—
219C22×D5—242no—
220C5×D4—32no—
221C5×D4—61no—
222C2×C4×C5—61no—
223C2×C4×C5—121no—
224C2×C4×C5—121no—
225C2×C4×C5C2×D1211yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C22⋊D5—124no—
229C2×Dic5—21no—
230C2×Dic5—121no—
231D20—21no—
232D20—122no—
233D20—124no—
234D20—121no—
235D20—121no—
236D20—121no—
237D20—121no—
238D20#20412yescomplemented
239C4×D5—41no—
240C4×D5—41no—
241Dic10—122no—
242C5×C8—22no—
243C5×C8—121no—
244#168—41no—
245C22×D4—301no—
246C22×D4—301no—
247C2×SD16—302no—
248C4⋊Q8—151no—
249#127—151no—
250#121—301no—
251#121—301no—
252#120—302no—
253C4×D4—31no—
254C4×D4—51no—
255#106—301no—
256#106—301no—
257C4⋊C8—31no—
258C4⋊C8—51no—
259#102—301no—
260#102—301no—
261C4×C8D3×D511yescharacteristic, complemented
262C2×C3×C5#45011yescharacteristic
263C2×C3×C5#45011yescharacteristic
264C2×C3×C5#45311yescharacteristic
265D15—82no—
266C3×D5—42no—
267C5×D3—42no—
268C23×C3—101no—
269C22×D3—21no—
270C22×D3—102no—
271C22×D3—204no—
272C22×D3—204no—
273C22×D3—402no—
274C3×D4—52no—
275C3×D4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—201no—
278C2×C3×C4—201no—
279C2×C3×C4C2×D2011yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282#67—204no—
283C2×Dic3—21no—
284C2×Dic3—201no—
285D12—21no—
286D12—202no—
287D12—204no—
288D12—201no—
289D12—201no—
290D12—201no—
291D12—201no—
292D12#67712yescomplemented
293C4×D3—41no—
294C4×D3—41no—
295Dic6—202no—
296C3×C8—22no—
297C3×C8—201no—
298C3⋊C8—41no—
299C22×C5—62no—
300C22×C5—121no—
301C22×C5—121no—
302C22×C5#88211yescharacteristic
303C2×D5—22no—
304C2×D5—41no—
305C2×D5—41no—
306C2×D5—122no—
307C2×D5—122no—
308C2×D5—122no—
309C2×D5—248no—
310C4×C5—21no—
311C4×C5—121no—
312C4×C5C2×#20411yescharacteristic
313C4×C5#90811yescharacteristic
314C4×C5#91111yescharacteristic
315C4×C5D3×SD1611yescharacteristic
316Dic5—41no—
317Dic5—241no—
318C24—302no—
319C2×Q8—301no—
320C2×D4—31no—
321C2×D4—51no—
322C2×D4—152no—
323C2×D4—302no—
324C2×D4—302no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4—602no—
328C2×D4—602no—
329C2×D4—602no—
330C2×D4—602no—
331C22×C4—61no—
332C22×C4—101no—
333SD16—604no—
334C2×C8—21no—
335C2×C8—61no—
336C2×C8—101no—
337C4⋊C4—31no—
338C4⋊C4—51no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C22⋊C4—61no—
342C22⋊C4—101no—
343C22⋊C4—302no—
344C42C2×D3×D511yescharacteristic
345C3×C5#162911yescharacteristic, complemented, Hall
346C22×C3—102no—
347C22×C3—201no—
348C22×C3—201no—
349C22×C3#402811yescharacteristic
350C2×D3—22no—
351C2×D3—41no—
352C2×D3—41no—
353C2×D3—202no—
354C2×D3—202no—
355C2×D3—202no—
356C2×D3—408no—
357C3×C4—21no—
358C3×C4—201no—
359C3×C4C2×#67711yescharacteristic
360C3×C4#405411yescharacteristic
361C3×C4#405711yescharacteristic
362C3×C4D5×SD1611yescharacteristic
363Dic3—41no—
364Dic3—401no—
365C2×C5—122no—
366C2×C5#473111yescharacteristic
367C2×C5#477611yescharacteristic
368C2×C5#482211yescharacteristic
369D5—42no—
370D5—242no—
371C23—61no—
372C23—101no—
373C23—302no—
374C23—604no—
375C23—604no—
376C23—1202no—
377Q8—602no—
378D4—32no—
379D4—52no—
380D4—61no—
381D4—101no—
382D4—602no—
383D4—604no—
384D4—604no—
385D4—601no—
386D4—601no—
387D4—601no—
388D4—601no—
389C2×C4—61no—
390C2×C4—101no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4—201no—
394C2×C4—201no—
395C2×C4—601no—
396C2×C4D5×D1211yescharacteristic
397C2×C4D3×D2011yescharacteristic
398C2×C4#679011yescharacteristic
399C8—22no—
400C8—121no—
401C8—201no—
402C2×C3—202no—
403C2×C3#6502011yescharacteristic
404C2×C3#6506511yescharacteristic
405C2×C3#6511111yescharacteristic
406D3—42no—
407D3—402no—
408C5#6819511yescharacteristic, complemented, Sylow
409C22—62no—
410C22—102no—
411C22—121no—
412C22—121no—
413C22—201no—
414C22—201no—
415C22—602no—
416C22—602no—
417C22—602no—
418C22—1208no—
419C22#9147611yescharacteristic
420C4—21no—
421C4—121no—
422C4—201no—
423C4—1201no—
424C4D5×#20411yescharacteristic
425C4#9125011yescharacteristic
426C4D3×#67711yescharacteristic
427C4#9125411yescharacteristic
428C3#1059898811yescharacteristic, complemented, Sylow
429C2—122no—
430C2—202no—
431C2—1202no—
432C2#1174711811yescharacteristic
433C2#1174811511yescharacteristic
434C2#1174812011yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalD12×D20C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1629
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
2. #11750794C2semidirect
3. #11746883C2semidirect
4. #11746881C2semidirect
5. C5×#4459C2semidirect
6. C3×#64679C2semidirect
7. #11745854C2semidirect
13. #91758C22semidirect
19. C3×C4×C5×C8C22semidirect
20. C5×C4⋊(C3⋊C8)C22semidirect
21. C3×C4⋊#168C22semidirect
33. #64679D3semidirect
67. #4459D5semidirect
79. C4×C5×C8C2×D3semidirect
84. C4⋊#168C2×D3semidirect
104. C5×D12SD16semidirect
109. C3×D20SD16semidirect
128. C3×C4×C8C2×D5semidirect
133. C4⋊(C3⋊C8)C2×D5semidirect
238. D20#204semidirect
261. C4×C8D3×D5semidirect
292. D12#677semidirect
345. C3×C5#1629semidirect
408. C5#68195semidirect
428. C3#10598988semidirect

Maximal subgroups

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

subgroupindex
D12×D202
#117507942
#117468832
#117468812
C5×#44592
C3×#646792
#117458542
#105989883
#681955