Finite Group Databasebeta

← #14471827

Subgroups — #14471827

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756344C211yesmaximal, characteristic, complemented
2C3×#65913C211yesmaximal, characteristic, complemented
3C5×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#11747063C212yesmaximal, complemented
5C4×#6657C211yesmaximal, characteristic, complemented
6#11747028C211yesmaximal, characteristic
7C4×#6653C212yesmaximal, complemented
8#11746951C212yesmaximal, complemented
9#11746933C212yesmaximal, complemented
10#11746917C211yesmaximal, characteristic, complemented
11#11746910C211yesmaximal, characteristic, complemented
12#10611658—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91836—21no—
15#91783—22no—
16#91782—21no—
17#91764C2212yes—
18#91763C2211yescharacteristic
19C4×D60C2212yes—
20C4×Dic30C2211yescharacteristic
21C3×#4092—21no—
22C3×#4042—22no—
23C3×D5×C4⋊C4—21no—
24C3×C4×D20C2212yes—
25C3×C4×D20C2211yescharacteristic
26C3×#4016C2212yes—
27C3×#4015C2211yescharacteristic
28C2×#6657C2211yescharacteristic
29C2×#6653C2212yes—
30C5×C4⋊(C3⋊C8)C2211yescharacteristic
31C5×C4⋊(C3⋊C8)C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C4×C5×C3⋊C8C2212yes—
34#90990C2212yes—
35#90987C2211yescharacteristic
36#90974C2212yes—
37#90974C2211yescharacteristic
38#90968C2212yes—
39#90968C2212yes—
40#90968C2212yes—
41#90965C2211yescharacteristic
42#83643—51nomaximal, Hall
43#65919—31no—
44#65913D311yescharacteristic, complemented
45C5×C8×Q8—31no—
46#65139—31no—
47#65136—32no—
48#65133—32no—
49#65132—31no—
50#64986—32no—
51#64983—31no—
52C4×D40—32no—
53C4×#677—31no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×C4×D15—22no—
59C2×Dic30C2311yescharacteristic
60C2×C3×D20C2311yescharacteristic
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—22no—
63C2×C3×Dic10—21no—
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D412yes—
66C3×C42×C5C2311yescharacteristic
67C3×C42×C5C2312yes—
68#6714—22no—
69#6714—22no—
70#6714—22no—
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73C4×Dic15—21no—
74C2×C5×C3⋊C8C2311yescharacteristic
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2312yes—
77C3×#685—22no—
78C3×#685—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2312yes—
82C3×#683—22no—
83C3×#683—22no—
84#6657—22no—
85#6653—24no—
86C3×#554—51no—
87#5585—51no—
88#5091—51no—
89#5088—51no—
90#5068—52no—
91#5066—52no—
92Q8×C3⋊C8D511yescharacteristic, complemented
93C4×#214—51no—
94#5016—52no—
95#5015—51no—
96C4×#213—52no—
97C4×C5×Q8C2×D311yescharacteristic
98#4093—61no—
99#4092—21no—
100C2×D40—32no—
101C2×#677—31no—
102#4042—22no—
103#4040—62no—
104#4039—61no—
105D5×C4⋊C4—21no—
106#4021—32no—
107#4020—31no—
108C4×D20—32no—
109C4×D20C2×D311yescharacteristic
110C4×D20C2×D312yes—
111#4016C2×D312yes—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×C4⋊C8—31no—
115C5×C4⋊C8—32no—
116C4×C5×C8—31no—
117C4×C5×C8—32no—
118#3953—31no—
119#3953—32no—
120#3953—32no—
121#3953—32no—
122#3950—32no—
123#3949—31no—
124#3948—32no—
125#3948—31no—
126#3361—151noSylow
127C22×D15—22no—
128C22×C3×D5—21no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—21no—
137D60—22no—
138D60—22no—
139D60—42no—
140D60—81no—
141C4×D15—82no—
142Dic30—21no—
143Dic30—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C3×D20—21no—
147C3×D20#4112yes—
148C3×C4×D5—42no—
149C3×C4×D5—82no—
150C3×Dic10—81no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—22no—
153C5×C3⋊C8—21no—
154C3×C4⋊Q8—51no—
155C3×#125—52no—
156C3×C22⋊Q8—101no—
157C3×C22⋊Q8—102no—
158C3×C4×Q8C2×D511yescharacteristic
159C3×C4×D4—52no—
160C3×C4×D4—51no—
161C2×C3×C4⋊C4—101no—
162#947—101no—
163C2×#214—51no—
164C2×#213—52no—
165#894—102no—
166#893—101no—
167#875—52no—
168#874—51no—
169C4×D12—52no—
170C4×Dic6—51no—
171#832—51no—
172#810—52no—
173#810—51no—
174#809—52no—
175#809—52no—
176#809—52no—
177#808—51no—
178#807—52no—
179C4⋊(C3⋊C8)C2×D511yescharacteristic
180C4⋊(C3⋊C8)C2×D512yes—
181C4×C3⋊C8C2×D512yes—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8#6711yescharacteristic
184C2×D20—32no—
185C2×D20—61no—
186C2×D20—61no—
187C2×D20C22×D311yescharacteristic
188C2×C4×D5—21no—
189C2×C4×D5—22no—
190C2×C4×D5—62no—
191C2×Dic10—21no—
192C2×Dic10—31no—
193C2×C5×C8—32no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C5×C4⋊C4#6711yescharacteristic
197C5×C4⋊C4#6712yes—
198C42×C5C22×D311yescharacteristic
199C42×C5C22×D312yes—
200#685—21no—
201#685—22no—
202#685—62no—
203#685—62no—
204#685—62no—
205C4⋊Dic5—21no—
206C4⋊Dic5—31no—
207C4⋊Dic5C22×D311yescharacteristic
208C4⋊Dic5C22×D312yes—
209#683—22no—
210#683—22no—
211#683—61no—
212C4×Dic5—61no—
213D40—64no—
214#677—62no—
215#559—151no—
216#554—51no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—31no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—42no—
228C2×D15—42no—
229C2×D15—42no—
230C2×C3×D5—22no—
231C2×C3×D5—41no—
232C2×C3×D5—41no—
233C3×C4×C5—22no—
234C3×C4×C5—21no—
235C3×C4×C5—22no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—41no—
240Dic15—41no—
241C3×Dic5—41no—
242C3×Dic5—42no—
243C2×C3×Q8—101no—
244C2×C3×Q8D2011yescharacteristic
245C2×C3×D4—51no—
246C22×C3×C4—101no—
247C22×C3×C4—102no—
248C2×D12—52no—
249C2×D12—101no—
250C2×D12—101no—
251C2×C4×D3—102no—
252C2×Dic6—51no—
253C3×C4⋊C4—52no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—102no—
256C3×C4⋊C4—102no—
257C3×C4⋊C4—101no—
258C3×C4⋊C4D2011yescharacteristic
259C3×C4⋊C4D2012yes—
260C3×C22⋊C4—101no—
261C3×C22⋊C4—102no—
262C3×C42C22×D511yescharacteristic
263C3×C42C22×D512yes—
264#214—102no—
265#213—104no—
266(C2×D3)⋊C4—102no—
267(C2×D3)⋊C4—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—51no—
270Dic3⋊C4—101no—
271C4×Dic3—101no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D512yes—
274C2×C3⋊C8C22×D511yescharacteristic
275C22×D5—21no—
276C22×D5—62no—
277C5×Q8—22no—
278C2×C4×C5C2×#6712yes—
279C2×C4×C5C2×#6712yes—
280C2×C4×C5C2×#6711yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—22no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287D20—21no—
288D20—62no—
289D20—62no—
290D20—122no—
291D20—241no—
292D20#23912yes—
293C4×D5—42no—
294C4×D5—82no—
295C4×D5—242no—
296Dic10—61no—
297Dic10—61no—
298Dic10—81no—
299C5×C8—61no—
300C5×C8—62no—
301C5×C8—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—151no—
306#125—52no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—101no—
311C22⋊Q8—102no—
312C4×Q8—151no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—52no—
315C4×D4—51no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—101no—
319#107—152no—
320#106—151no—
321C4⋊C8—31no—
322C4⋊C8—32no—
323#103—151no—
324#103—152no—
325#102—152no—
326#102—152no—
327#102—152no—
328#102—151no—
329C4×C8—32no—
330C4×C8—31no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—82no—
335C3×D5—42no—
336C23×C3—101no—
337C22×D3—102no—
338C3×Q8—22no—
339C3×Q8—401no—
340C3×D4—52no—
341C3×D4—101no—
342C2×C3×C4—101no—
343C2×C3×C4—102no—
344C2×C3×C4—202no—
345C2×C3×C4—402no—
346C2×C3×C4C2×D2011yescharacteristic
347C2×C3×C4C2×D2012yes—
348C2×C3×C4C2×D2012yes—
349C2×C3×C4C2×D2011yescharacteristic
350C2×C3×C4C23×D511yescharacteristic
351C2×Dic3—101no—
352C2×Dic3—101no—
353D12—102no—
354D12—102no—
355D12—202no—
356D12—401no—
357C4×D3—402no—
358Dic6—101no—
359Dic6—101no—
360C3⋊C8—21no—
361C3⋊C8—22no—
362C3⋊C8—21no—
363C22×C5C22×#6711yescharacteristic
364C2×D5—22no—
365C2×D5—41no—
366C2×D5—41no—
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—22no—
371C4×C5—21no—
372C4×C5—22no—
373C4×C5#95012yes—
374C4×C5C2×#23911yescharacteristic
375C4×C5#100711yescharacteristic
376Dic5—41no—
377Dic5—42no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—101no—
381C2×Q8—151no—
382C2×Q8#120211yescharacteristic
383C2×D4—51no—
384C2×D4—152no—
385C2×D4—301no—
386C2×D4—301no—
387C22×C4—101no—
388C22×C4—102no—
389C22×C4—302no—
390SD16—302no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—32no—
395C4⋊C4—51no—
396C4⋊C4—52no—
397C4⋊C4—102no—
398C4⋊C4—101no—
399C4⋊C4—102no—
400C4⋊C4—151no—
401C4⋊C4—301no—
402C4⋊C4#120211yescharacteristic
403C4⋊C4#120212yes—
404C22⋊C4—101no—
405C22⋊C4—102no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—301no—
410C42C2×D3×D512yes—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—102no—
414C22×C3—201no—
415C22×C3—201no—
416C22×C3C22×D2011yescharacteristic
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—201no—
424C3×C4—202no—
425C3×C4#405012yes—
426C3×C4#414711yescharacteristic
427C3×C4D5×#4111yescharacteristic
428Dic3—201no—
429Dic3—201no—
430C2×C5#581711yescharacteristic
431C2×C5C2×#95011yescharacteristic
432C2×C5#583511yescharacteristic
433D5—42no—
434D5—242no—
435C23—101no—
436C23—302no—
437Q8—22no—
438Q8—301no—
439Q8—301no—
440Q8—401no—
441D4—52no—
442D4—101no—
443D4—302no—
444D4—302no—
445D4—602no—
446D4—1201no—
447C2×C4—101no—
448C2×C4—102no—
449C2×C4—202no—
450C2×C4—301no—
451C2×C4—301no—
452C2×C4—402no—
453C2×C4—1202no—
454C2×C4C2×#120212yes—
455C2×C4C2×#120211yescharacteristic
456C2×C4C2×#120212yes—
457C2×C4C2×#120211yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—62no—
461C8—61no—
462C2×C3—202no—
463C2×C3#6591011yescharacteristic
464C2×C3C2×#405011yescharacteristic
465C2×C3#6608611yescharacteristic
466D3—402no—
467C5#8364311yescharacteristic, complemented, Sylow
468C22—102no—
469C22—201no—
470C22—201no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C22×#120211yescharacteristic
475C4—22no—
476C4—21no—
477C4—22no—
478C4—202no—
479C4—201no—
480C4—601no—
481C4—601no—
482C4#9131112yes—
483C4#9202911yescharacteristic
484C4D5×#23911yescharacteristic
485C3#1061165811yescharacteristic, complemented, Sylow
486C2—202no—
487C2—1202no—
488C2C2×#9131111yescharacteristic
489C2#1175512811yescharacteristic
490C2#1175531111yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11747028C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756344C2semidirect
2. C3×#65913C2semidirect
3. C5×Q8×C3⋊C8C2semidirect
4. #11747063C2semidirect
5. C4×#6657C2semidirect
7. C4×#6653C2semidirect
8. #11746951C2semidirect
9. #11746933C2semidirect
10. #11746917C2semidirect
11. #11746910C2semidirect
44. #65913D3semidirect
92. Q8×C3⋊C8D5semidirect
412. C3×C5#3361semidirect
467. C5#83643semidirect
485. C3#10611658semidirect

Maximal subgroups

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

subgroupindex
#117563442
C3×#659132
C5×Q8×C3⋊C82
#117470632
C4×#66572
#117470282
C4×#66532
#117469512
#117469332
#117469172
#117469102
#106116583
#836435