Finite Group Databasebeta

← #14471821

Subgroups — #14471821

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
2#11752648C211yesmaximal, characteristic, complemented
3C5×#5021C211yesmaximal, characteristic, complemented
4C3×C4×#688C211yesmaximal, characteristic, complemented
5#11749230C212yesmaximal, complemented
6#11749190C212yesmaximal, complemented
7#11747226C212yesmaximal, complemented
8#11747185C212yesmaximal, complemented
9#11747028C211yesmaximal, characteristic
10#11746912C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612865—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91836C2212yes—
15#91783—22no—
16#91782C2212yes—
17#91764—21no—
18#91763C2211yescharacteristic
19C4×D60—21no—
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C2×C3×#688C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91434C2212yes—
25#91421—22no—
26D5×C4⋊Dic3—21no—
27#91384C2212yes—
28#91360—21no—
29C2×#6653C2212yes—
30C5×#835C2212yes—
31C5×#807C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3967C2211yescharacteristic
34C3×#3941C2211yescharacteristic
35C3×#3940C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90983C2212yes—
38#90969C2212yes—
39#90969C2212yes—
40#90968C2212yes—
41#90951C2212yes—
42#79621—51nomaximal, Hall
43#66064—31no—
44#65919—31no—
45C5×#477—31no—
46#65377—31no—
47C4×#688D311yescharacteristic, complemented
48#65180—32no—
49#65161—32no—
50#65132—31no—
51#65119—31no—
52#65108—32no—
53#65089—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×C4×D15—22no—
59C2×Dic30D411yescharacteristic
60C2×C5×Dic6—21no—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×D5×Dic3—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C42×C5—21no—
67C3×C42×C5C2311yescharacteristic
68#6714—22no—
69#6714—22no—
70#6714—22no—
71C4⋊Dic15D411yescharacteristic
72#6712D412yes—
73C4×Dic15C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8C2312yes—
77C3×#688—22no—
78C3×#685—21no—
79C3×C4⋊Dic5C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6665—22no—
85#6653—24no—
86#5585—51no—
87#5543—51no—
88C3×C4×SD16—51no—
89#5165—52no—
90#5021D511yescharacteristic, complemented
91#5015—51no—
92#4871—52no—
93#4800—52no—
94#4756—52no—
95#4694—51no—
96C8×Dic6—51no—
97C5×C4⋊Q8—31no—
98C4×C5×Q8C2×D311yescharacteristic
99#4093—32no—
100#4092—62no—
101C2×#688C2×D311yescharacteristic
102C2×D40—32no—
103#4043—61no—
104#4040—62no—
105#4039—32no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4021—61no—
110#4020—31no—
111C4×D20—61no—
112C4×D20C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×#107—32no—
115C5×C4⋊C8—31no—
116C5×#103—32no—
117#3967C2×D311yescharacteristic
118#3953—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3941—32no—
122#3941—32no—
123#3941C2×D311yescharacteristic
124#3940C2×D311yescharacteristic
125C4×#168C2×D311yescharacteristic
126#3361—151noSylow
127C22×D15—22no—
128C22×C3×D5—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15C2×D412yes—
137C2×Dic15C2×D412yes—
138D60—22no—
139D60—22no—
140D60—42no—
141D60—81no—
142C4×D15—82no—
143Dic30—22no—
144C2×C5×Dic3—22no—
145C5×Dic6—81no—
146C2×C3×Dic5—21no—
147C3×D20—21no—
148C3×D20#4112yes—
149C3×C4×D5—42no—
150D5×Dic3—82no—
151C3×#168—21no—
152C3×#168—21no—
153C5×C3⋊C8—22no—
154C2×C3×SD16—51no—
155C3×C4×Q8C2×D511yescharacteristic
156C3×C4×D4—51no—
157#947—52no—
158D4×Dic3—52no—
159C2×#213—52no—
160C2×C4⋊Dic3—101no—
161#924—101no—
162#894—102no—
163#893—52no—
164#890—52no—
165#878—102no—
166#875—101no—
167#874—51no—
168C4×D12—101no—
169#869C2×D511yescharacteristic
170C4×Dic6—51no—
171C3×#106—51no—
172C3×#103—51no—
173C3×#102—51no—
174C3×C4×C8—51no—
175#835C2×D512yes—
176#821—52no—
177#821—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#809—52no—
181#807C2×D512yes—
182C4⋊(C3⋊C8)C2×D511yescharacteristic
183C2×C5×Q8—61no—
184C2×C5×Q8C22×D311yescharacteristic
185C2×D20—32no—
186C2×D20—61no—
187C2×D20—61no—
188C2×D20C22×D311yescharacteristic
189C2×C4×D5—21no—
190C2×C4×D5—62no—
191C2×C4×D5—62no—
192C2×Dic10—31no—
193C2×C5×C8—32no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4—61no—
197C5×C4⋊C4C22×D311yescharacteristic
198C42×C5—21no—
199C42×C5C22×D311yescharacteristic
200#688—22no—
201#685—21no—
202#685—62no—
203#685—62no—
204#685—62no—
205#685—62no—
206C4⋊Dic5—31no—
207C4⋊Dic5—62no—
208C4⋊Dic5C22×D311yescharacteristic
209#683—32no—
210#683—62no—
211C4×Dic5—32no—
212C2×#168C22×D311yescharacteristic
213C2×#168C22×D311yescharacteristic
214D40—64no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—31no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—51no—
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—21no—
234C3×C4×C5—41no—
235C3×C4×C5—41no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—22no—
240Dic15—22no—
241C3×Dic5—41no—
242C5×Dic3—42no—
243C2×C3×Q8C22×D511yescharacteristic
244C2×C3×D4—51no—
245C22×C3×C4—101no—
246C22×Dic3—102no—
247C2×D12—52no—
248C2×D12—101no—
249C2×D12—101no—
250C2×C4×D3—102no—
251C2×Dic6—21no—
252C2×Dic6—51no—
253C3×SD16—102no—
254C2×C3×C8—51no—
255C2×C3×C8—51no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—51no—
258C3×C4⋊C4C22×D511yescharacteristic
259C3×C22⋊C4—101no—
260C3×C42—21no—
261C3×C42C22×D511yescharacteristic
262#217—102no—
263#213—104no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22×D512yes—
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273C4×Dic3—52no—
274C2×C3⋊C8C22×D512yes—
275C22×D5—21no—
276C22×D5—62no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—241no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—62no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—32no—
288C2×Dic5—32no—
289D20—21no—
290D20—62no—
291D20—62no—
292D20—122no—
293D20—241no—
294D20#23512yes—
295C4×D5—42no—
296C4×D5—242no—
297C4×D5—242no—
298Dic10—62no—
299C5×C8—62no—
300#168—21no—
301#168—21no—
302C2×SD16—51no—
303C2×D8—152no—
304C4⋊Q8—31no—
305#127—151no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—151no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—51no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—32no—
320#106—51no—
321C4⋊C8—31no—
322C4⋊C8—152no—
323#103—32no—
324#103—51no—
325#102—51no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—51no—
330C4×C8—152no—
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—21no—
339C3×Q8—21no—
340C3×D4—52no—
341C3×D4—101no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—101no—
345C2×C3×C4—202no—
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—52no—
351C2×Dic3—52no—
352C2×Dic3—402no—
353D12—102no—
354D12—102no—
355D12—202no—
356D12—401no—
357C4×D3—402no—
358Dic6—81no—
359Dic6—102no—
360C3×C8—101no—
361C3×C8—101no—
362C3⋊C8—22no—
363C22×C5C2×D3×D411yescharacteristic
364C2×D5—22no—
365C2×D5—41no—
366C2×D5—41no—
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—41no—
373C4×C5—122no—
374C4×C5#91612yes—
375C4×C5C2×#23511yescharacteristic
376C4×C5#101011yescharacteristic
377Dic5—41no—
378Dic5—62no—
379Dic5—62no—
380C2×Q8—61no—
381C2×Q8—151no—
382C2×Q8C2×D3×D511yescharacteristic
383C2×D4—51no—
384C2×D4—152no—
385C2×D4—301no—
386C2×D4—301no—
387C22×C4—101no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—102no—
391D8—304no—
392C2×C8—32no—
393C2×C8—51no—
394C2×C8—51no—
395C4⋊C4—21no—
396C4⋊C4—32no—
397C4⋊C4—51no—
398C4⋊C4—61no—
399C4⋊C4—151no—
400C4⋊C4—152no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—101no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—21no—
410C42—152no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—102no—
414C22×C3—201no—
415C22×C3—201no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—201no—
424C3×C4#406512yes—
425C3×C4#414711yescharacteristic
426C3×C4D5×#4111yescharacteristic
427Dic3—42no—
428Dic3—102no—
429Dic3—102no—
430C2×C5#555211yescharacteristic
431C2×C5C2×#91611yescharacteristic
432C2×C5#576911yescharacteristic
433D5—42no—
434D5—242no—
435C23—101no—
436C23—302no—
437Q8—21no—
438Q8—21no—
439Q8—241no—
440Q8—302no—
441D4—52no—
442D4—101no—
443D4—302no—
444D4—302no—
445D4—602no—
446D4—1201no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—62no—
450C2×C4—101no—
451C2×C4—152no—
452C2×C4—152no—
453C2×C4—202no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#679011yescharacteristic
457C2×C4#679011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—62no—
460C8—101no—
461C8—101no—
462C2×C3—202no—
463C2×C3#6596711yescharacteristic
464C2×C3C2×#406511yescharacteristic
465C2×C3#6610811yescharacteristic
466D3—402no—
467C5#7962111yescharacteristic, complemented, Sylow
468C22—102no—
469C22—201no—
470C22—201no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×#679011yescharacteristic
475C4—21no—
476C4—41no—
477C4—41no—
478C4—122no—
479C4—201no—
480C4—302no—
481C4—302no—
482C4#9152112yes—
483C4#9200011yescharacteristic
484C4D5×#23511yescharacteristic
485C3#1061286511yescharacteristic, complemented, Sylow
486C2—202no—
487C2—1202no—
488C2#1175436711yescharacteristic
489C2C2×#9152111yescharacteristic
490C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
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 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756344C2semidirect
2. #11752648C2semidirect
3. C5×#5021C2semidirect
4. C3×C4×#688C2semidirect
5. #11749230C2semidirect
6. #11749190C2semidirect
7. #11747226C2semidirect
8. #11747185C2semidirect
10. #11746912C2semidirect
11. #11746851C2semidirect
47. C4×#688D3semidirect
90. #5021D5semidirect
412. C3×C5#3361semidirect
467. C5#79621semidirect
485. C3#10612865semidirect

Maximal subgroups

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

subgroupindex
#117563442
#117526482
C5×#50212
C3×C4×#6882
#117492302
#117491902
#117472262
#117471852
#117470282
#117469122
#117468512
#106128653
#796215