Finite Group Databasebeta

← #14291000

Subgroups — #14291000

Order 1920.

456 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 75 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#11756442C211yesmaximal, characteristic
2C3×C5×#489C211yesmaximal, characteristic, complemented
3#11751190C211yesmaximal, characteristic, complemented
4#11751187C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#11746285C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic, complemented
8#10602037—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic, complemented
10C3×C5×#124C2211yescharacteristic
11#91836—21no—
12C2×#6718—21no—
13C2×#6717—21no—
14#91826—21no—
15#91774—21no—
16#91774—21no—
17#91771—21no—
18#91771—21no—
19#91764C2211yescharacteristic
20#91764C2211yescharacteristic
21C3×C5×#103—21no—
22C3×C5×#102—21no—
23C3×C5×#97C2211yescharacteristic, complemented
24#91094—21no—
25#91093—21no—
26#91087C2211yescharacteristic, complemented
27#91087C2211yescharacteristic, complemented
28#71244—51nomaximal, Hall
29#66017—31no—
30C5×#489D311yescharacteristic, complemented
31#65378—31no—
32#65375—31no—
33#64760—31no—
34#64684—31no—
35#64684—31no—
36C23×D15—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C2×D60—21no—
43C2×D60D411yescharacteristic
44C2×D60D411yescharacteristic
45C2×Dic30D411yescharacteristic
46C2×Dic30D411yescharacteristic
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C22⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53#6719—21no—
54#6718—42no—
55#6717—42no—
56#6714—21no—
57#6714—21no—
58#6714—21no—
59#6714—21no—
60#6714—21no—
61#6714—21no—
62C4×Dic15—21no—
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65#5683—51no—
66C3×#489D511yescharacteristic, complemented
67#5089—51no—
68#5086—51no—
69#4540—51no—
70#4464—51no—
71#4464—51no—
72C5×C4⋊Q8C2×D311yescharacteristic, complemented
73C5×#124C2×D311yescharacteristic
74#4093—61no—
75C2×#689—61no—
76C2×#688—61no—
77#4083—61no—
78#4031—61no—
79#4031—61no—
80#4028—61no—
81#4028—61no—
82#4021—31no—
83#4021—31no—
84C5×#103—21no—
85C5×#102—21no—
86C5×#97C2×D311yescharacteristic, complemented
87#3942—61no—
88#3941—61no—
89#3935—31no—
90#3935—31no—
91#1659—151noSylow
92C23×C3×C5—21no—
93C22×D15—21no—
94C22×D15—21no—
95C22×D15—81no—
96C22×D15—81no—
97C22×D15—81no—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C3×C5×Q8—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107#1220—81no—
108#1220—81no—
109C2×Dic15—21no—
110C2×Dic15—21no—
111D60—41no—
112D60—41no—
113D60—81no—
114Dic30—41no—
115Dic30—41no—
116C3×C5×C8—41no—
117C3⋊#168—22no—
118C3⋊#168—41no—
119C3×C4⋊Q8C2×D511yescharacteristic, complemented
120C3×#124C2×D511yescharacteristic
121#947—101no—
122C2×#216—101no—
123C2×#215—101no—
124#937—101no—
125#885—101no—
126#885—101no—
127#882—101no—
128#882—101no—
129#875—51no—
130#875—51no—
131C3×#103—21no—
132C3×#102—21no—
133C3×#97C2×D511yescharacteristic, complemented
134#810—101no—
135#809—101no—
136#803—51no—
137#803—51no—
138C23×D5—61no—
139C2×C5×Q8—21no—
140C2×C5×Q8#6711yescharacteristic
141C2×C5×D4#6711yescharacteristic
142C2×C22⋊D5—61no—
143C2×C22⋊D5—61no—
144C2×D20—31no—
145C2×D20—31no—
146C2×D20—61no—
147C2×Dic10—31no—
148C2×Dic10—31no—
149C2×C5×C8—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C22⋊C4—21no—
153C5×C22⋊C4—21no—
154C42×C5C22×D311yescharacteristic
155C22⋊Dic5—61no—
156#689—122no—
157#688—122no—
158#685—61no—
159#685—61no—
160#685—61no—
161#685—61no—
162#685—61no—
163#685—61no—
164C4×Dic5—61no—
165C2×#168—61no—
166C2×#168—61no—
167H(3,𝔽4)—151no—
168#497—151no—
169#489—151no—
170#489D1511yescharacteristic, complemented
171#329—151no—
172#329—151no—
173#329—151no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5#12011yescharacteristic
178C2×D15—41no—
179C2×D15—41no—
180C2×D15—41no—
181C2×D15—41no—
182C2×D15—41no—
183C2×D15—41no—
184C2×D15—84no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—41no—
189C3×C4×C5—81no—
190Dic15—41no—
191Dic15—41no—
192C23×D3—101no—
193C2×C3×Q8—21no—
194C2×C3×Q8C22⋊D511yescharacteristic
195C2×C3×D4C22⋊D511yescharacteristic
196C2×#67—101no—
197C2×#67—101no—
198C2×D12—51no—
199C2×D12—51no—
200C2×D12—101no—
201C2×Dic6—51no—
202C2×Dic6—51no—
203C2×C3×C8—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C42C22×D511yescharacteristic
209#217—101no—
210#216—202no—
211#215—202no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—101no—
214(C2×D3)⋊C4—101no—
215(C2×D3)⋊C4—101no—
216(C2×D3)⋊C4—101no—
217(C2×D3)⋊C4—101no—
218C4×Dic3—101no—
219C2×C3⋊C8—101no—
220C2×C3⋊C8—101no—
221C23×C5—21no—
222C22×D5—61no—
223C22×D5—61no—
224C22×D5—241no—
225C22×D5—241no—
226C22×D5—241no—
227C5×Q8—41no—
228C5×Q8—41no—
229C5×Q8—41no—
230C5×D4—41no—
231C2×C4×C5—21no—
232C2×C4×C5—41no—
233C2×C4×C5D3×D411yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×C4×C5C2×#6711yescharacteristic
236C22⋊D5—241no—
237C22⋊D5—241no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240D20—121no—
241D20—121no—
242D20—241no—
243Dic10—121no—
244Dic10—121no—
245C5×C8—41no—
246#168—62no—
247#168—121no—
248C2×Q16—301no—
249C2×SD16—301no—
250C4⋊Q8C2×D1511yescharacteristic, complemented
251#124—151no—
252#124—151no—
253#124—301no—
254#124—301no—
255#124—301no—
256#124C2×D1511yescharacteristic
257#120—301no—
258#120—301no—
259#120—301no—
260#103—21no—
261#103—301no—
262#102—21no—
263#102—301no—
264#97—151no—
265#97—151no—
266#97C2×D1511yescharacteristic, complemented
267C2×C3×C5—81no—
268C2×C3×C5#45311yescharacteristic
269C2×C3×C5#45511yescharacteristic
270C2×C3×C5#45511yescharacteristic
271D15—81no—
272D15—81no—
273C23×C3—21no—
274C22×D3—101no—
275C22×D3—101no—
276C22×D3—401no—
277C22×D3—401no—
278C22×D3—401no—
279C3×Q8—41no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×D4—41no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4D4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288#67—401no—
289#67—401no—
290C2×Dic3—101no—
291C2×Dic3—101no—
292D12—201no—
293D12—201no—
294D12—401no—
295Dic6—201no—
296Dic6—201no—
297C3×C8—41no—
298C3⋊C8—102no—
299C3⋊C8—201no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5#93711yescharacteristic
304C2×D5—121no—
305C2×D5—121no—
306C2×D5—121no—
307C2×D5—121no—
308C2×D5—121no—
309C2×D5—121no—
310C2×D5—244no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—41no—
315C4×C5—81no—
316Dic5—121no—
317Dic5—121no—
318C24—301no—
319C2×Q8—21no—
320C2×Q8—151no—
321C2×Q8—151no—
322C2×Q8#122011yescharacteristic
323C2×D4—151no—
324C2×D4—151no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4—301no—
328C2×D4#122011yescharacteristic
329Q16—602no—
330SD16—602no—
331C2×C8—21no—
332C2×C8—301no—
333C2×C8—301no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C22⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C42—301no—
346C42C22×D1511yescharacteristic
347C3×C5#165911yescharacteristic, complemented, Hall
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3#408311yescharacteristic
352C2×D3—201no—
353C2×D3—201no—
354C2×D3—201no—
355C2×D3—201no—
356C2×D3—201no—
357C2×D3—201no—
358C2×D3—404no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—41no—
363C3×C4—81no—
364Dic3—201no—
365Dic3—201no—
366C2×C5—81no—
367C2×C5#506111yescharacteristic
368C2×C5#519811yescharacteristic
369C2×C5#520211yescharacteristic
370D5—241no—
371D5—241no—
372C23—21no—
373C23—301no—
374C23—301no—
375C23—1201no—
376C23—1201no—
377C23—1201no—
378Q8—41no—
379Q8—41no—
380Q8—41no—
381Q8—601no—
382Q8—601no—
383D4—41no—
384D4—601no—
385D4—601no—
386D4—1201no—
387D4—1201no—
388D4—1201no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—301no—
392C2×C4—301no—
393C2×C4D4×D1511yescharacteristic
394C2×C4D4×D1511yescharacteristic
395C2×C4C2×#122011yescharacteristic
396C8—41no—
397C8—302no—
398C8—601no—
399C2×C3—81no—
400C2×C3#6535011yescharacteristic
401C2×C3#6548711yescharacteristic
402C2×C3#6549111yescharacteristic
403D3—401no—
404D3—401no—
405C5#7124411yescharacteristic, complemented, Sylow
406C22—41no—
407C22—41no—
408C22—41no—
409C22—601no—
410C22—601no—
411C22—601no—
412C22—601no—
413C22—601no—
414C22—601no—
415C22—1204no—
416C22#9182611yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—41no—
421C4—81no—
422C4—601no—
423C4—601no—
424C3#1060203711yescharacteristic, complemented, Sylow
425C2—81no—
426C2—1201no—
427C2—1201no—
428C2#1175116211yescharacteristic
429C2#1175129911yescharacteristic
430C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#489C2
socleC22×C3×C5#120
prime radical#11756442C2
hypercenter#489D15
hypocenterC3×C5#1659
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. C3×C5×#489C2semidirect
3. #11751190C2semidirect
4. #11751187C2semidirect
5. #11746361C2semidirect
6. #11746285C2semidirect
7. #11746285C2semidirect
9. C3×C5×C4⋊Q8C22semidirect
23. C3×C5×#97C22semidirect
26. #91087C22semidirect
27. #91087C22semidirect
30. C5×#489D3semidirect
66. C3×#489D5semidirect
72. C5×C4⋊Q8C2×D3semidirect
86. C5×#97C2×D3semidirect
119. C3×C4⋊Q8C2×D5semidirect
133. C3×#97C2×D5semidirect
170. #489D15semidirect
250. C4⋊Q8C2×D15semidirect
266. #97C2×D15semidirect
347. C3×C5#1659semidirect
405. C5#71244semidirect
424. C3#10602037semidirect

Maximal subgroups

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

subgroupindex
#117564422
C3×C5×#4892
#117511902
#117511872
#117463612
#117462852
#106020373
#712445