Finite Group Databasebeta

← #14289873

Subgroups — #14289873

Order 1920.

616 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 95 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#11756476C211yesmaximal, characteristic
2C3×C5×#486C211yesmaximal, characteristic, complemented
3#11751188C211yesmaximal, characteristic, complemented
4#11751184C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10601991—31nomaximal, Hall
9C2×D4×D15—21no—
10C2×D4×D15—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic, complemented
12C3×C5×#127C2211yescharacteristic
13C2×#6717—21no—
14#91827—21no—
15#91827—21no—
16#91826—22no—
17C4×D60C2211yescharacteristic
18C4×D60C2211yescharacteristic
19C3×C5×#102—22no—
20C3×C4×C5×C8C2211yescharacteristic, complemented
21#91119—21no—
22#91093—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic, complemented
25C4⋊(C3⋊#168)C2211yescharacteristic, complemented
26#71198—51nomaximal, Hall
27#66051—31no—
28C5×#486D311yescharacteristic, complemented
29#65376—31no—
30#65372—31no—
31#64764—31no—
32#64679—31no—
33#64679—31no—
34C23×D15—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D412yes—
39C2×#1220—22no—
40C2×#1220—22no—
41D4×D15—42no—
42D4×D15—42no—
43D4×D15—42no—
44D4×D15—42no—
45C2×D60D411yescharacteristic
46C2×D60D411yescharacteristic
47C2×C4×D15—21no—
48C2×C4×D15—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53#6719—22no—
54#6717—42no—
55#6714—21no—
56#6714—21no—
57C4⋊Dic15D411yescharacteristic
58C4⋊Dic15D411yescharacteristic
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61#5717—51no—
62C3×#486D511yescharacteristic, complemented
63#5087—51no—
64#5083—51no—
65#4544—51no—
66#4459—51no—
67#4459—51no—
68C2×D4×D5—61no—
69C2×D4×D5—61no—
70C5×C4⋊Q8C2×D311yescharacteristic, complemented
71C5×#127C2×D311yescharacteristic
72C2×#688—61no—
73#4084—61no—
74#4084—61no—
75#4083—62no—
76C4×D20—31no—
77C4×D20—31no—
78C5×#102—22no—
79C4×C5×C8C2×D311yescharacteristic, complemented
80#3967—61no—
81#3941—61no—
82#3939—61no—
83C4⋊#168—31no—
84C4⋊#168—31no—
85#1639—151noSylow
86C23×C3×C5—22no—
87C22×D15—21no—
88C22×D15—21no—
89C22×D15—44no—
90C22×D15—44no—
91C22×D15—82no—
92C3×C5×Q8—41no—
93C3×C5×Q8—41no—
94C3×C5×D4—42no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103#1220—44no—
104#1220—44no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107D60—21no—
108D60—21no—
109D60D812yes—
110D60SD1612yescomplemented
111C4×D15—41no—
112C4×D15—41no—
113C4×D15—41no—
114C4×D15—41no—
115C3×C5×C8—41no—
116C3⋊#168—41no—
117C3⋊#168—41no—
118C2×D3×D4—101no—
119C2×D3×D4—101no—
120C3×C4⋊Q8C2×D511yescharacteristic, complemented
121C3×#127C2×D511yescharacteristic
122C2×#215—101no—
123#938—101no—
124#938—101no—
125#937—102no—
126C4×D12—51no—
127C4×D12—51no—
128C3×#102—22no—
129C3×C4×C8C2×D511yescharacteristic, complemented
130#835—101no—
131#809—101no—
132#807—101no—
133C4⋊(C3⋊C8)—51no—
134C4⋊(C3⋊C8)—51no—
135C23×D5—62no—
136C2×C5×Q8—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4#6712yes—
140C2×C22⋊D5—62no—
141C2×C22⋊D5—62no—
142D4×D5—122no—
143D4×D5—122no—
144D4×D5—122no—
145D4×D5—122no—
146C2×D20—31no—
147C2×D20—31no—
148C2×C4×D5—61no—
149C2×C4×D5—61no—
150C2×C5×C8—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C42×C5C22×D311yescharacteristic
154C22⋊Dic5—62no—
155#688—122no—
156#685—61no—
157#685—61no—
158C4⋊Dic5—31no—
159C4⋊Dic5—31no—
160C2×#168—61no—
161C2×#168—61no—
162D42—151no—
163#486D1511yescharacteristic, complemented
164#474—151no—
165#461—151no—
166#331—151no—
167D4⋊C8—151no—
168D4⋊C8—151no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5—42no—
172C22×C3×C5#12011yescharacteristic
173C2×D15—22no—
174C2×D15—22no—
175C2×D15—41no—
176C2×D15—41no—
177C2×D15—41no—
178C2×D15—41no—
179C2×D15—88no—
180C3×C4×C5—21no—
181C3×C4×C5—81no—
182C3×C4×C5C2×D811yescharacteristic
183C3×C4×C5C2×SD1611yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
186Dic15—41no—
187Dic15—41no—
188C23×D3—102no—
189C2×C3×Q8—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4C22⋊D512yes—
193C2×#67—102no—
194C2×#67—102no—
195D3×D4—202no—
196D3×D4—202no—
197D3×D4—202no—
198D3×D4—202no—
199C2×D12—51no—
200C2×D12—51no—
201C2×C4×D3—101no—
202C2×C4×D3—101no—
203C2×C3×C8—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C42C22×D511yescharacteristic
207#217—102no—
208#215—202no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3—51no—
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C23×C5—22no—
216C22×D5—61no—
217C22×D5—61no—
218C22×D5—124no—
219C22×D5—124no—
220C22×D5—242no—
221C5×Q8—41no—
222C5×Q8—41no—
223C5×D4—42no—
224C5×D4—41no—
225C5×D4—41no—
226C5×D4—41no—
227C5×D4—41no—
228C2×C4×C5—41no—
229C2×C4×C5D3×D411yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C2×C4×C5C2×#6711yescharacteristic
232C22⋊D5—124no—
233C22⋊D5—124no—
234C2×Dic5—61no—
235C2×Dic5—61no—
236D20—32no—
237D20—32no—
238D20—61no—
239D20—61no—
240C4×D5—121no—
241C4×D5—121no—
242C4×D5—121no—
243C4×D5—121no—
244C5×C8—41no—
245#168—121no—
246#168—121no—
247C22×D4—301no—
248C22×D4—301no—
249C2×SD16—301no—
250C4⋊Q8C2×D1511yescharacteristic, complemented
251#127C2×D1511yescharacteristic
252#121—301no—
253#121—301no—
254#120—302no—
255C4×D4—151no—
256C4×D4—151no—
257#107—301no—
258C4⋊C8—151no—
259C4⋊C8—151no—
260#103—301no—
261#102—22no—
262#102—301no—
263C4×C8C2×D1511yescharacteristic, complemented
264C2×C3×C5—82no—
265C2×C3×C5#44711yescharacteristic
266C2×C3×C5#45011yescharacteristic
267C2×C3×C5#45511yescharacteristic
268D15—42no—
269D15—42no—
270C23×C3—22no—
271C22×D3—101no—
272C22×D3—101no—
273C22×D3—204no—
274C22×D3—204no—
275C22×D3—402no—
276C3×Q8—41no—
277C3×Q8—41no—
278C3×D4—42no—
279C3×D4—41no—
280C3×D4—41no—
281C3×D4—41no—
282C3×D4—41no—
283C2×C3×C4—41no—
284C2×C3×C4D4×D511yescharacteristic
285C2×C3×C4D4×D511yescharacteristic
286C2×C3×C4C2×C22⋊D511yescharacteristic
287#67—204no—
288#67—204no—
289C2×Dic3—101no—
290C2×Dic3—101no—
291D12—52no—
292D12—52no—
293D12—101no—
294D12—101no—
295C4×D3—201no—
296C4×D3—201no—
297C4×D3—201no—
298C4×D3—201no—
299C3×C8—41no—
300C3⋊C8—201no—
301C3⋊C8—201no—
302C22×C5—42no—
303C22×C5—42no—
304C22×C5—42no—
305C22×C5#93711yescharacteristic
306C2×D5—62no—
307C2×D5—62no—
308C2×D5—121no—
309C2×D5—121no—
310C2×D5—121no—
311C2×D5—121no—
312C2×D5—248no—
313C4×C5—21no—
314C4×C5—81no—
315C4×C5D3×D811yescharacteristic
316C4×C5#91111yescharacteristic
317C4×C5D3×SD1611yescharacteristic
318C4×C5#91411yescharacteristic
319Dic5—121no—
320Dic5—121no—
321C24—302no—
322C2×Q8—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4—302no—
328C2×D4—302no—
329C2×D4—602no—
330C2×D4—602no—
331C2×D4—602no—
332C2×D4—602no—
333C2×D4#122012yes—
334C22×C4—301no—
335C22×C4—301no—
336SD16—602no—
337C2×C8—21no—
338C2×C8—301no—
339C2×C8—301no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—151no—
343C4⋊C4—151no—
344C22⋊C4—302no—
345C22⋊C4—301no—
346C22⋊C4—301no—
347C42C22×D1511yescharacteristic
348C3×C5#163911yescharacteristic, complemented, Hall
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3#408311yescharacteristic
353C2×D3—102no—
354C2×D3—102no—
355C2×D3—201no—
356C2×D3—201no—
357C2×D3—201no—
358C2×D3—201no—
359C2×D3—408no—
360C3×C4—21no—
361C3×C4—81no—
362C3×C4D5×D811yescharacteristic
363C3×C4#405711yescharacteristic
364C3×C4D5×SD1611yescharacteristic
365C3×C4#406011yescharacteristic
366Dic3—201no—
367Dic3—201no—
368C2×C5—82no—
369C2×C5#506111yescharacteristic
370C2×C5#515611yescharacteristic
371C2×C5#516911yescharacteristic
372D5—122no—
373D5—122no—
374C23—22no—
375C23—301no—
376C23—301no—
377C23—604no—
378C23—604no—
379C23—1202no—
380Q8—41no—
381Q8—41no—
382D4—42no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—152no—
388D4—152no—
389D4—301no—
390D4—301no—
391D4—604no—
392D4—604no—
393C2×C4—41no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4—601no—
400C2×C4D4×D1511yescharacteristic
401C2×C4D4×D1511yescharacteristic
402C2×C4C2×#122011yescharacteristic
403C8—41no—
404C8—601no—
405C8—601no—
406C2×C3—82no—
407C2×C3#6535011yescharacteristic
408C2×C3#6544511yescharacteristic
409C2×C3#6545811yescharacteristic
410D3—202no—
411D3—202no—
412C5#7119811yescharacteristic, complemented, Sylow
413C22—42no—
414C22—42no—
415C22—42no—
416C22—302no—
417C22—302no—
418C22—601no—
419C22—601no—
420C22—601no—
421C22—601no—
422C22—1208no—
423C22#9182611yescharacteristic
424C4—21no—
425C4—81no—
426C4—601no—
427C4—601no—
428C4D8×D1511yescharacteristic
429C4#9180011yescharacteristic
430C4SD16×D1511yescharacteristic
431C4#9180311yescharacteristic
432C3#1060199111yescharacteristic, complemented, Sylow
433C2—82no—
434C2—602no—
435C2—602no—
436C2#1175116211yescharacteristic
437C2#1175125711yescharacteristic
438C2#1175127011yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radical#11756476C2
hypercenter#486D15
hypocenterC3×C5#1639
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C3×C5×#486C2semidirect
3. #11751188C2semidirect
4. #11751184C2semidirect
5. #11746365C2semidirect
6. #11746280C2semidirect
7. #11746280C2semidirect
11. C3×C5×C4⋊Q8C22semidirect
20. C3×C4×C5×C8C22semidirect
24. C4⋊(C3⋊#168)C22semidirect
25. C4⋊(C3⋊#168)C22semidirect
28. C5×#486D3semidirect
62. C3×#486D5semidirect
70. C5×C4⋊Q8C2×D3semidirect
79. C4×C5×C8C2×D3semidirect
110. D60SD16semidirect
120. C3×C4⋊Q8C2×D5semidirect
129. C3×C4×C8C2×D5semidirect
163. #486D15semidirect
250. C4⋊Q8C2×D15semidirect
263. C4×C8C2×D15semidirect
348. C3×C5#1639semidirect
412. C5#71198semidirect
432. C3#10601991semidirect

Maximal subgroups

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

subgroupindex
#117564762
C3×C5×#4862
#117511882
#117511842
#117463652
#117462802
#106019913
#711985