Finite Group Databasebeta

← #14289342

Subgroups — #14289342

Order 1920.

628 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 101 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
1D4×D60C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic, complemented
3#11751186C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10601936—31nomaximal, Hall
9C2×D4×D15—21no—
10C22×D60—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic, complemented
12C3×C4×C5×D4C2211yescharacteristic
13C2×#6717—22no—
14#91819—21no—
15#91784—21no—
16#91771—22no—
17#91763C2211yescharacteristic
18C4×D60C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic, complemented
21C3×C5×#102—21no—
22#91093—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic, complemented
25C4×C3⋊#168C2211yescharacteristic, complemented
26#71143—51nomaximal, Hall
27D4×D20—31no—
28C5×#476D311yescharacteristic, complemented
29#65374—31no—
30#65373—31no—
31D4⋊#168—31no—
32#64705—31no—
33#64703—31no—
34C23×D15—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×#1220—22no—
39D4×D15—42no—
40D4×D15—42no—
41C2×D60—22no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—42no—
45C2×D60—42no—
46C2×D60D411yescharacteristic
47C2×D60D412yes—
48C2×C4×D15—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C42×C5C2311yescharacteristic
55#6717—44no—
56#6714—22no—
57#6714—21no—
58C4⋊Dic15D411yescharacteristic
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61D4×D12—51no—
62C3×#476D511yescharacteristic, complemented
63#5085—51no—
64#5084—51no—
65D4⋊(C3⋊C8)—51no—
66#4485—51no—
67#4483—51no—
68C2×D4×D5—61no—
69C22×D20—61no—
70C5×C4⋊Q8C2×D311yescharacteristic, complemented
71C4×C5×D4C2×D311yescharacteristic
72C2×#688—62no—
73#4076—61no—
74#4041—61no—
75#4028—62no—
76#4020—31no—
77C4×D20—31no—
78C5×#106—21no—
79C5×C4⋊C8C2×D311yescharacteristic, complemented
80C5×#102—21no—
81#3941—61no—
82#3940—61no—
83C4⋊#168—31no—
84C4×#168—31no—
85#1629—151noSylow
86C23×C3×C5—21no—
87C22×D15—21no—
88C22×D15—22no—
89C22×D15—44no—
90C22×D15—44no—
91C22×D15—82no—
92C3×C5×Q8—42no—
93C3×C5×D4—21no—
94C3×C5×D4SD1612yescomplemented
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—44no—
103C2×Dic15—21no—
104D60—21no—
105D60—42no—
106D60—44no—
107D60—41no—
108D60—41no—
109D60—41no—
110D60—41no—
111D60SD1612yescomplemented
112C4×D15—41no—
113C4×D15—41no—
114C3×C5×C8—41no—
115C3⋊#168—22no—
116C3⋊#168—41no—
117C2×D3×D4—101no—
118C22×D12—101no—
119C3×C4⋊Q8C2×D511yescharacteristic, complemented
120C3×C4×D4C2×D511yescharacteristic
121C2×#215—102no—
122#930—101no—
123#895—101no—
124#882—102no—
125#874—51no—
126C4×D12—51no—
127C3×#106—21no—
128C3×C4⋊C8C2×D511yescharacteristic, complemented
129C3×#102—21no—
130#809—101no—
131#808—101no—
132C4⋊(C3⋊C8)—51no—
133C4×C3⋊C8—51no—
134C23×D5—62no—
135C2×C5×Q8—21no—
136C2×C5×D4#6711yescharacteristic
137C22×C4×C5—21no—
138C2×C22⋊D5—62no—
139D4×D5—122no—
140D4×D5—122no—
141C2×D20—31no—
142C2×D20—32no—
143C2×D20—62no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—122no—
147C2×D20—122no—
148C2×C4×D5—61no—
149C2×C5×C8—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4#6711yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5C22×D311yescharacteristic
155#688—124no—
156#685—62no—
157#685—61no—
158C4⋊Dic5—31no—
159C2×#168—61no—
160C2×#168—61no—
161D42—151no—
162#492—151no—
163#476—151no—
164#476D1511yescharacteristic, complemented
165#331—151no—
166D4⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—22no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5#12011yescharacteristic
172C2×D15—22no—
173C2×D15—41no—
174C2×D15—41no—
175C2×D15—42no—
176C2×D15—42no—
177C2×D15—42no—
178C2×D15—88no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—81no—
182C3×C4×C5C2×SD1611yescharacteristic
183C3×C4×C5C2×SD1611yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
186Dic15—41no—
187C23×D3—102no—
188C2×C3×Q8—21no—
189C2×C3×D4C22⋊D511yescharacteristic
190C22×C3×C4—21no—
191C2×#67—102no—
192D3×D4—202no—
193D3×D4—202no—
194C2×D12—51no—
195C2×D12—52no—
196C2×D12—102no—
197C2×D12—101no—
198C2×D12—101no—
199C2×D12—202no—
200C2×D12—202no—
201C2×C4×D3—101no—
202C2×C3×C8—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4C22⋊D511yescharacteristic
206C3×C22⋊C4—21no—
207C3×C42C22×D511yescharacteristic
208#215—204no—
209(C2×D3)⋊C4—102no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214C23×C5—21no—
215C22×D5—61no—
216C22×D5—62no—
217C22×D5—124no—
218C22×D5—124no—
219C22×D5—242no—
220C5×Q8—42no—
221C5×D4—21no—
222C5×D4#21512yescomplemented
223C2×C4×C5—21no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C22⋊D5—124no—
231C2×Dic5—61no—
232D20—32no—
233D20—61no—
234D20—122no—
235D20—124no—
236D20—121no—
237D20—121no—
238D20—121no—
239D20—121no—
240C4×D5—121no—
241C4×D5—121no—
242C5×C8—41no—
243#168—62no—
244#168—121no—
245C22×D4—301no—
246C22×D4—301no—
247C2×SD16—302no—
248C4⋊Q8C2×D1511yescharacteristic, complemented
249#127—151no—
250#121—301no—
251#121—301no—
252#120—302no—
253C4×D4—151no—
254C4×D4C2×D1511yescharacteristic
255#106—21no—
256#106—301no—
257C4⋊C8—151no—
258C4⋊C8C2×D1511yescharacteristic, complemented
259#102—21no—
260#102—301no—
261C4×C8—151no—
262C2×C3×C5—42no—
263C2×C3×C5#45011yescharacteristic
264C2×C3×C5#45011yescharacteristic
265C2×C3×C5#45311yescharacteristic
266D15—42no—
267D15—82no—
268C23×C3—21no—
269C22×D3—101no—
270C22×D3—102no—
271C22×D3—204no—
272C22×D3—204no—
273C22×D3—402no—
274C3×Q8—42no—
275C3×D4—21no—
276C3×D4#68812yescomplemented
277C2×C3×C4—21no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4D4×D511yescharacteristic
283C2×C3×C4C2×C22⋊D511yescharacteristic
284#67—204no—
285C2×Dic3—101no—
286D12—52no—
287D12—101no—
288D12—202no—
289D12—204no—
290D12—201no—
291D12—201no—
292D12—201no—
293D12—201no—
294C4×D3—201no—
295C4×D3—201no—
296C3×C8—41no—
297C3⋊C8—102no—
298C3⋊C8—201no—
299C22×C5—22no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5#93711yescharacteristic
303C2×D5—62no—
304C2×D5—121no—
305C2×D5—121no—
306C2×D5—122no—
307C2×D5—122no—
308C2×D5—122no—
309C2×D5—248no—
310C4×C5—21no—
311C4×C5—41no—
312C4×C5—81no—
313C4×C5D3×SD1611yescharacteristic
314C4×C5#91411yescharacteristic
315C4×C5C2×#21511yescharacteristic
316C4×C5#94911yescharacteristic
317Dic5—121no—
318C24—302no—
319C2×Q8—21no—
320C2×D4—151no—
321C2×D4—152no—
322C2×D4—302no—
323C2×D4—302no—
324C2×D4—301no—
325C2×D4—301no—
326C2×D4—602no—
327C2×D4—602no—
328C2×D4—602no—
329C2×D4—602no—
330C2×D4#122011yescharacteristic
331C22×C4—21no—
332C22×C4—301no—
333SD16—604no—
334C2×C8—21no—
335C2×C8—301no—
336C2×C8—301no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—151no—
340C4⋊C4#122011yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—302no—
343C22⋊C4—301no—
344C42C22×D1511yescharacteristic
345C3×C5#162911yescharacteristic, complemented, Hall
346C22×C3—22no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3#408311yescharacteristic
350C2×D3—102no—
351C2×D3—201no—
352C2×D3—201no—
353C2×D3—202no—
354C2×D3—202no—
355C2×D3—202no—
356C2×D3—408no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—81no—
360C3×C4D5×SD1611yescharacteristic
361C3×C4#406011yescharacteristic
362C3×C4C2×#68811yescharacteristic
363C3×C4#409511yescharacteristic
364Dic3—201no—
365C2×C5—42no—
366C2×C5#504611yescharacteristic
367C2×C5#516911yescharacteristic
368C2×C5#519811yescharacteristic
369D5—122no—
370D5—242no—
371C23—21no—
372C23—301no—
373C23—302no—
374C23—604no—
375C23—604no—
376C23—1202no—
377Q8—42no—
378D4—21no—
379D4—152no—
380D4—301no—
381D4—602no—
382D4—604no—
383D4—604no—
384D4—601no—
385D4—601no—
386D4—601no—
387D4—601no—
388D4#671712yescomplemented
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—301no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4D4×D1511yescharacteristic
397C2×C4D4×D1511yescharacteristic
398C2×C4C2×#122011yescharacteristic
399C8—41no—
400C8—302no—
401C8—601no—
402C2×C3—42no—
403C2×C3#6533511yescharacteristic
404C2×C3#6545811yescharacteristic
405C2×C3#6548711yescharacteristic
406D3—202no—
407D3—402no—
408C5#7114311yescharacteristic, complemented, Sylow
409C22—22no—
410C22—41no—
411C22—41no—
412C22—302no—
413C22—601no—
414C22—601no—
415C22—602no—
416C22—602no—
417C22—602no—
418C22—1208no—
419C22#9182611yescharacteristic
420C4—21no—
421C4—41no—
422C4—81no—
423C4—601no—
424C4SD16×D1511yescharacteristic
425C4#9180311yescharacteristic
426C4C2×#671711yescharacteristic
427C4#9183811yescharacteristic
428C3#1060193611yescharacteristic, complemented, Sylow
429C2—42no—
430C2—602no—
431C2—1202no—
432C2#1175114711yescharacteristic
433C2#1175127011yescharacteristic
434C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalD4×D60C2
hypercenter#476D15
hypocenterC3×C5#1629
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×C5×#476C2semidirect
3. #11751186C2semidirect
4. #11751185C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746306C2semidirect
7. #11746304C2semidirect
11. C3×C5×C4⋊Q8C22semidirect
20. C3×C5×C4⋊C8C22semidirect
24. C4⋊(C3⋊#168)C22semidirect
25. C4×C3⋊#168C22semidirect
28. C5×#476D3semidirect
62. C3×#476D5semidirect
70. C5×C4⋊Q8C2×D3semidirect
79. C5×C4⋊C8C2×D3semidirect
94. C3×C5×D4SD16semidirect
111. D60SD16semidirect
119. C3×C4⋊Q8C2×D5semidirect
128. C3×C4⋊C8C2×D5semidirect
164. #476D15semidirect
222. C5×D4#215semidirect
248. C4⋊Q8C2×D15semidirect
258. C4⋊C8C2×D15semidirect
276. C3×D4#688semidirect
345. C3×C5#1629semidirect
388. D4#6717semidirect
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
D4×D602
C3×C5×#4762
#117511862
#117511852
D4⋊(C3⋊#168)2
#117463062
#117463042
#106019363
#711435