Finite Group Databasebeta

← #14289354

Subgroups — #14289354

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#11751186C211yesmaximal, characteristic, complemented
3C5×#5084C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11745854C211yesmaximal, characteristic, complemented
6#11745836C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601936—31nomaximal, Hall
9C2×D3×D20—21no—
10C2×D5×D12—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic, complemented
12C2×#6717—22no—
13#91763C2211yescharacteristic
14C4×C5×D12C2211yescharacteristic
15C3×C4×D20C2211yescharacteristic
16#91476—22no—
17#91460—21no—
18#91450—21no—
19C4×C3⋊#168C2211yescharacteristic, complemented
20C5×#809—21no—
21C5×#808—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic, complemented
26#71143—51nomaximal, Hall
27D4×D20—31no—
28C5×#476—31no—
29#65374—31no—
30#65373D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64705—31no—
33#64703—31no—
34C22×D3×D5—22no—
35C2×C3×C5×Q8—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D412yes—
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—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52#6717—44no—
53C2×C3⋊#168—21no—
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—
62C3×#476—51no—
63#5085—51no—
64#5084D511yescharacteristic, complemented
65D4⋊(C3⋊C8)—51no—
66#4485—51no—
67#4483—51no—
68C2×D4×D5—61no—
69C22×D20—61no—
70C5×C4⋊Q8C2×D311yescharacteristic, complemented
71C4×C5×D4—31no—
72C2×#688—62no—
73#4076—61no—
74#4041—61no—
75#4028—62no—
76#4020—31no—
77C4×D20C2×D311yescharacteristic
78C5×#106—61no—
79C5×C4⋊C8—31no—
80C5×#102—61no—
81#3941—21no—
82#3940—21no—
83C4⋊#168C2×D311yescharacteristic, complemented
84C4×#168—31no—
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—
92C3×C5×Q8—42no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97D60—42no—
98D60—41no—
99D60—41no—
100D60—41no—
101D60—41no—
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⋊#168—22no—
115C3×#168—41no—
116C5×C3⋊C8—41no—
117C2×D3×D4—101no—
118C22×D12—101no—
119C3×C4⋊Q8C2×D511yescharacteristic, complemented
120C3×C4×D4—51no—
121C2×#215—102no—
122#930—101no—
123#895—101no—
124#882—102no—
125#874—51no—
126C4×D12C2×D511yescharacteristic
127C3×#106—101no—
128C3×C4⋊C8—51no—
129C3×#102—101no—
130#809—21no—
131#808—21no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
133C4×C3⋊C8—51no—
134C23×D5—62no—
135C2×C5×Q8—21no—
136C2×C5×D4—31no—
137C22×C4×C5—61no—
138C2×C22⋊D5—62no—
139D4×D5—122no—
140D4×D5—122no—
141C2×D20—32no—
142C2×D20—62no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—122no—
146C2×D20—122no—
147C2×D20#6711yescharacteristic
148C2×C4×D5—21no—
149C2×C5×C8—61no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—31no—
153C5×C22⋊C4—61no—
154C42×C5C22×D311yescharacteristic
155#688—124no—
156#685—21no—
157#685—62no—
158C4⋊Dic5#6711yescharacteristic
159C2×#168—21no—
160C2×#168—61no—
161D42—151no—
162#492—151no—
163#476—31no—
164#476—51no—
165#331—151no—
166D4⋊C8—151no—
167D4⋊C8—151no—
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×C5—81no—
181C3×C4×C5C2×SD1611yescharacteristic
182C3×C4×C5C2×SD1611yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×Dic5—41no—
186C5×Dic3—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—52no—
195C2×D12—102no—
196C2×D12—101no—
197C2×D12—101no—
198C2×D12—202no—
199C2×D12—202no—
200C2×D12C22⋊D511yescharacteristic
201C2×C4×D3—21no—
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—204no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—102no—
211C4⋊Dic3C22⋊D511yescharacteristic
212C2×C3⋊C8—21no—
213C2×C3⋊C8—101no—
214C23×C5—61no—
215C22×D5—21no—
216C22×D5—62no—
217C22×D5—124no—
218C22×D5—124no—
219C22×D5—242no—
220C5×Q8—42no—
221C5×D4—32no—
222C5×D4—61no—
223C2×C4×C5—41no—
224C2×C4×C5—61no—
225C2×C4×C5—121no—
226C2×C4×C5—121no—
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C22⋊D5—124no—
231C2×Dic5—21no—
232D20—21no—
233D20—122no—
234D20—124no—
235D20—121no—
236D20—121no—
237D20—121no—
238D20—121no—
239D20#21512yescomplemented
240C4×D5—41no—
241C4×D5—41no—
242C5×C8—121no—
243#168—41no—
244#168—62no—
245C22×D4—301no—
246C22×D4—301no—
247C2×SD16—302no—
248C4⋊Q8D3×D511yescharacteristic, complemented
249#127—151no—
250#121—301no—
251#121—301no—
252#120—302no—
253C4×D4—31no—
254C4×D4—51no—
255#106—61no—
256#106—101no—
257C4⋊C8—31no—
258C4⋊C8—51no—
259#102—61no—
260#102—101no—
261C4×C8—151no—
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×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—21no—
286D12—21no—
287D12—202no—
288D12—204no—
289D12—201no—
290D12—201no—
291D12—201no—
292D12—201no—
293D12#68812yescomplemented
294C4×D3—41no—
295C4×D3—41no—
296C3×C8—201no—
297C3⋊C8—41no—
298C3⋊C8—102no—
299C22×C5—62no—
300C22×C5—121no—
301C22×C5—121no—
302C22×C5#93711yescharacteristic
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—81no—
312C4×C5—121no—
313C4×C5D3×SD1611yescharacteristic
314C4×C5#91411yescharacteristic
315C4×C5C2×#21511yescharacteristic
316C4×C5#94911yescharacteristic
317Dic5—41no—
318C24—302no—
319C2×Q8—21no—
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—61no—
335C2×C8—101no—
336C2×C8—301no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—31no—
340C4⋊C4—51no—
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#408311yescharacteristic
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—81no—
359C3×C4—201no—
360C3×C4D5×SD1611yescharacteristic
361C3×C4#406011yescharacteristic
362C3×C4C2×#68811yescharacteristic
363C3×C4#409511yescharacteristic
364Dic3—41no—
365C2×C5—122no—
366C2×C5#504611yescharacteristic
367C2×C5#516911yescharacteristic
368C2×C5#519811yescharacteristic
369D5—42no—
370D5—242no—
371C23—61no—
372C23—101no—
373C23—302no—
374C23—604no—
375C23—604no—
376C23—1202no—
377Q8—42no—
378D4—32no—
379D4—52no—
380D4—61no—
381D4—101no—
382D4—602no—
383D4—604no—
384D4—604no—
385D4—601no—
386D4—601no—
387D4—601no—
388D4—601no—
389C2×C4—41no—
390C2×C4—61no—
391C2×C4—101no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4D5×#6711yescharacteristic
397C2×C4D3×C22⋊D511yescharacteristic
398C2×C4#679011yescharacteristic
399C8—121no—
400C8—201no—
401C8—302no—
402C2×C3—202no—
403C2×C3#6533511yescharacteristic
404C2×C3#6545811yescharacteristic
405C2×C3#6548711yescharacteristic
406D3—42no—
407D3—402no—
408C5#7114311yescharacteristic, complemented, Sylow
409C22—62no—
410C22—102no—
411C22—121no—
412C22—121no—
413C22—201no—
414C22—201no—
415C22—602no—
416C22—602no—
417C22—602no—
418C22—1208no—
419C22#9157711yescharacteristic
420C4—21no—
421C4—81no—
422C4—121no—
423C4—201no—
424C4D5×#21511yescharacteristic
425C4#9150211yescharacteristic
426C4D3×#68811yescharacteristic
427C4#9150411yescharacteristic
428C3#1060193611yescharacteristic, complemented, Sylow
429C2—122no—
430C2—202no—
431C2—1202no—
432C2#1174916411yescharacteristic
433C2#1174939711yescharacteristic
434C2#1174939811yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalD12×D20C2
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. #11751186C2semidirect
3. C5×#5084C2semidirect
4. C3×#65373C2semidirect
5. #11745854C2semidirect
6. #11745836C2semidirect
7. #11745834C2semidirect
11. C3×C5×C4⋊Q8C22semidirect
19. C4×C3⋊#168C22semidirect
22. C5×C4⋊(C3⋊C8)C22semidirect
25. C3×C4⋊#168C22semidirect
30. #65373D3semidirect
64. #5084D5semidirect
70. C5×C4⋊Q8C2×D3semidirect
83. C4⋊#168C2×D3semidirect
104. C5×D12SD16semidirect
109. C3×D20SD16semidirect
119. C3×C4⋊Q8C2×D5semidirect
132. C4⋊(C3⋊C8)C2×D5semidirect
239. D20#215semidirect
248. C4⋊Q8D3×D5semidirect
293. D12#688semidirect
345. C3×C5#1629semidirect
408. C5#71143semidirect
428. C3#10601936semidirect

Maximal subgroups

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

subgroupindex
D12×D202
#117511862
C5×#50842
C3×#653732
#117458542
#117458362
#117458342
#106019363
#711435