Finite Group Databasebeta

← #14484785

Subgroups — #14484785

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2#11756576C212yesmaximal, complemented
3#11756344C213yesmaximal, complemented
4#11756343C213yesmaximal, complemented
5#11756339C216yesmaximal, complemented
6#11756336C211yesmaximal, characteristic, complemented
7C4×#6821C212yesmaximal, complemented
8#11756329C211yesmaximal, characteristic, complemented
9#11756273C216yesmaximal, complemented
10#11756236C213yesmaximal, complemented
11C4×#6817C213yesmaximal, complemented
12#10617703—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6821C2212yes—
15C2×#6817C2213yes—
16C3×C4×C5×Q8C2211yescharacteristic
17C3×C4×C5×Q8C2211yescharacteristic
18C3×C4×C5×Q8C2213yes—
19C3×C4×C5×Q8C2213yes—
20C2×C3×C5×C4⋊C4C2213yes—
21C2×C3×C42×C5C2213yes—
22#91836C2216yes—
23#91835C2216yes—
24Q8×Dic15C2212yes—
25#91819C2216yes—
26#91819C2216yes—
27C4×#1220C2216yes—
28C4×#1220C2216yes—
29#91815C2211yescharacteristic
30#91787C22112yes—
31#91784C2216yes—
32#91783C22112yes—
33#91782C2216yes—
34#91781C2216yes—
35#91779C2216yes—
36#91764C2216yes—
37#91763C2213yes—
38C4×D60C2216yes—
39C4×D60C2213yes—
40C4×D60C2216yes—
41C4×D60C2213yes—
42#91761C2216yes—
43C42×D15C2216yes—
44#91758C2213yes—
45C4×Dic30C2213yes—
46C4×Dic30C2213yes—
47#85802—51nomaximal, Hall
48C2×C4×C5×Q8D311yescharacteristic, complemented
49#66151—32no—
50#65919—33no—
51#65918—33no—
52#65914—36no—
53#65911—31no—
54C4×#713—32no—
55#65904—31no—
56#65848—36no—
57#65811—33no—
58C4×#709—33no—
59C2×C3×C5×Q8—24no—
60C2×C3×C5×Q8C2313yes—
61C2×C3×C5×Q8C2311yescharacteristic
62C22×C3×C4×C5C2313yes—
63C22×C3×C4×C5C2313yes—
64C22×C3×C4×C5C2311yescharacteristic
65C2×#1220C2316yes—
66#6821—28no—
67#6817—212no—
68C2×D60C2313yes—
69C2×D60C2316yes—
70C2×D60C2316yes—
71C2×C4×D15C2316yes—
72C2×C4×D15C2316yes—
73C2×C4×D15C2316yes—
74C2×Dic30C2313yes—
75C3×C5×C4⋊C4C2313yes—
76C3×C5×C4⋊C4C2313yes—
77C3×C5×C4⋊C4C2316yes—
78C3×C42×C5C2313yes—
79C3×C42×C5C2313yes—
80C3×C42×C5C2313yes—
81C3×C42×C5C2313yes—
82#6719C2312yes—
83#6714C2316yes—
84#6714C2316yes—
85#6714C23112yes—
86#6714C23112yes—
87C4⋊Dic15C2311yescharacteristic
88C4⋊Dic15C2311yescharacteristic
89C4⋊Dic15C2316yes—
90C4⋊Dic15C2316yes—
91#6712C2316yes—
92#6712C2316yes—
93C4×Dic15C2316yes—
94C4×Dic15C2316yes—
95C4×Dic15C2312yes—
96C2×C3×C4×Q8D511yescharacteristic, complemented
97#5817—52no—
98#5585—53no—
99#5584—53no—
100#5580—56no—
101#5577—51no—
102C4×#239—52no—
103#5570—51no—
104#5514—56no—
105#5477—53no—
106C4×#235—53no—
107C22×C5×Q8C2×D311yescharacteristic
108C2×#713—32no—
109C2×#709—33no—
110C4×C5×Q8C2×D311yescharacteristic
111C4×C5×Q8C2×D311yescharacteristic
112C4×C5×Q8C2×D313yes—
113C4×C5×Q8C2×D313yes—
114C2×C5×C4⋊C4C2×D313yes—
115C2×C42×C5C2×D313yes—
116#4093—36no—
117#4092—36no—
118Q8×Dic5—32no—
119#4076—36no—
120#4076—36no—
121C4×C22⋊D5—36no—
122C4×C22⋊D5—36no—
123#4072—31no—
124#4044—312no—
125#4041—36no—
126#4040—312no—
127#4039—36no—
128#4038—36no—
129#4036—36no—
130#4021—36no—
131#4020—33no—
132C4×D20—33no—
133C4×D20—33no—
134C4×D20—36no—
135C4×D20—36no—
136#4018—36no—
137C42×D5—36no—
138#4015—33no—
139C4×Dic10—33no—
140C4×Dic10—33no—
141#3480—151noSylow
142C23×C3×C5C2411yescharacteristic
143C22×D15C2416yes—
144C3×C5×Q8—26no—
145C3×C5×Q8#4114yescomplemented
146C2×C3×C4×C5—26no—
147C2×C3×C4×C5—43no—
148C2×C3×C4×C5#4114yescomplemented
149C2×C3×C4×C5C2413yes—
150C2×C3×C4×C5C2413yes—
151C2×C3×C4×C5C2413yes—
152C2×C3×C4×C5C2413yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×C3×C4×C5C2411yescharacteristic
155#1220—212no—
156C2×Dic15C2412yes—
157C2×Dic15C2412yes—
158C2×Dic15C2416yes—
159D60—26no—
160D60—212no—
161D60—46no—
162C4×D15—212no—
163C4×D15—212no—
164C4×D15—46no—
165Dic30—26no—
166C22×C3×Q8C2×D511yescharacteristic
167C2×#239—52no—
168C2×#235—53no—
169C3×C4×Q8C2×D511yescharacteristic
170C3×C4×Q8C2×D511yescharacteristic
171C3×C4×Q8C2×D513yes—
172C3×C4×Q8C2×D513yes—
173C2×C3×C4⋊C4C2×D513yes—
174C2×C3×C42C2×D513yes—
175#947—56no—
176#946—56no—
177Q8×Dic3—52no—
178#930—56no—
179#930—56no—
180C4×#67—56no—
181C4×#67—56no—
182#926—51no—
183#898—512no—
184#895—56no—
185#894—512no—
186#893—56no—
187#892—56no—
188#890—56no—
189#875—56no—
190#874—53no—
191C4×D12—53no—
192C4×D12—53no—
193C4×D12—56no—
194C4×D12—56no—
195#872—56no—
196C42×D3—56no—
197#869—53no—
198C4×Dic6—53no—
199C4×Dic6—53no—
200C2×C5×Q8—24no—
201C2×C5×Q8C22×D313yes—
202C2×C5×Q8C22×D311yescharacteristic
203C22×C4×C5C22×D313yes—
204C22×C4×C5C22×D313yes—
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—36no—
207#713—68no—
208#709—612no—
209C2×D20—33no—
210C2×D20—36no—
211C2×D20—36no—
212C2×C4×D5—36no—
213C2×C4×D5—36no—
214C2×C4×D5—36no—
215C2×Dic10—33no—
216C5×C4⋊C4C22×D313yes—
217C5×C4⋊C4C22×D313yes—
218C5×C4⋊C4C22×D316yes—
219C42×C5C22×D313yes—
220C42×C5C22×D313yes—
221C42×C5C22×D313yes—
222C42×C5C22×D313yes—
223C22⋊Dic5—32no—
224#685—36no—
225#685—36no—
226#685—312no—
227#685—312no—
228C4⋊Dic5—31no—
229C4⋊Dic5—31no—
230C4⋊Dic5—36no—
231C4⋊Dic5—36no—
232#683—36no—
233#683—36no—
234C4×Dic5—36no—
235C4×Dic5—36no—
236C4×Dic5—32no—
237#559—153no—
238#557—151no—
239#556—153no—
240#553—156no—
241#550—151no—
242#548—152no—
243#532—153no—
244#529—156no—
245C4×#41—152no—
246C4×#41—153no—
247C2×C4×Q8D1511yescharacteristic, complemented
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C2×#4112yes—
251C22×C3×C5C2511yescharacteristic
252C2×D15—26no—
253C2×D15—26no—
254C2×D15—26no—
255C3×C4×C5—23no—
256C3×C4×C5—23no—
257C3×C4×C5—23no—
258C3×C4×C5C2×#4116yes—
259C3×C4×C5C2×#4112yes—
260C3×C4×C5C2×#4112yes—
261Dic15—26no—
262Dic15—22no—
263Dic15—22no—
264C2×C3×Q8—24no—
265C2×C3×Q8C22×D513yes—
266C2×C3×Q8C22×D511yescharacteristic
267C22×C3×C4C22×D513yes—
268C22×C3×C4C22×D513yes—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—56no—
271#239—108no—
272#235—1012no—
273C2×D12—53no—
274C2×D12—56no—
275C2×D12—56no—
276C2×C4×D3—56no—
277C2×C4×D3—56no—
278C2×C4×D3—56no—
279C2×Dic6—53no—
280C3×C4⋊C4C22×D513yes—
281C3×C4⋊C4C22×D513yes—
282C3×C4⋊C4C22×D516yes—
283C3×C42C22×D513yes—
284C3×C42C22×D513yes—
285C3×C42C22×D513yes—
286C3×C42C22×D513yes—
287#217—52no—
288(C2×D3)⋊C4—56no—
289(C2×D3)⋊C4—56no—
290(C2×D3)⋊C4—512no—
291(C2×D3)⋊C4—512no—
292C4⋊Dic3—51no—
293C4⋊Dic3—51no—
294C4⋊Dic3—56no—
295C4⋊Dic3—56no—
296Dic3⋊C4—56no—
297Dic3⋊C4—56no—
298C4×Dic3—56no—
299C4×Dic3—56no—
300C4×Dic3—52no—
301C23×C5C23×D311yescharacteristic
302C22×D5—36no—
303C5×Q8—26no—
304C5×Q8#23514yescomplemented
305C2×C4×C5—26no—
306C2×C4×C5—43no—
307C2×C4×C5#23914yescomplemented
308C2×C4×C5C23×D313yes—
309C2×C4×C5C23×D313yes—
310C2×C4×C5C23×D313yes—
311C2×C4×C5C23×D313yes—
312C2×C4×C5C23×D311yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—612no—
315C2×Dic5—32no—
316C2×Dic5—32no—
317C2×Dic5—36no—
318D20—612no—
319D20—66no—
320D20—126no—
321C4×D5—612no—
322C4×D5—612no—
323C4×D5—126no—
324Dic10—66no—
325C2×#41—152no—
326C2×#41—153no—
327C22×Q8C2×D1511yescharacteristic
328C4⋊Q8—153no—
329#127—153no—
330#126—1512no—
331#125—156no—
332#124—156no—
333#124—156no—
334#123—1512no—
335C22⋊Q8—156no—
336#121—156no—
337#121—156no—
338#121—156no—
339C4×Q8—152no—
340C4×Q8—153no—
341C4×Q8—153no—
342C4×Q8C2×D1511yescharacteristic
343C4×Q8C2×D1513yes—
344C4×Q8C2×D1511yescharacteristic
345C4×Q8C2×D1513yes—
346C4×D4—156no—
347C4×D4—156no—
348C4×D4—156no—
349C4×D4—156no—
350C4×D4—153no—
351C4×D4—153no—
352C4×D4—156no—
353#117—151no—
354#117—156no—
355#117—156no—
356C2×C4⋊C4C2×D1513yes—
357C2×C42—156no—
358C2×C42C2×D1513yes—
359C2×C3×C5—22no—
360C2×C3×C5C22×#4111yescharacteristic
361C2×C3×C5C22×#4111yescharacteristic
362C2×C3×C5#58511yescharacteristic
363D15—46no—
364C23×C3C23×D511yescharacteristic
365C22×D3—56no—
366C3×Q8—26no—
367C3×Q8#70914yescomplemented
368C2×C3×C4—26no—
369C2×C3×C4—43no—
370C2×C3×C4#71314yescomplemented
371C2×C3×C4C23×D513yes—
372C2×C3×C4C23×D513yes—
373C2×C3×C4C23×D513yes—
374C2×C3×C4C23×D513yes—
375C2×C3×C4C23×D511yescharacteristic
376C2×C3×C4C23×D511yescharacteristic
377#67—1012no—
378C2×Dic3—52no—
379C2×Dic3—52no—
380C2×Dic3—56no—
381D12—1012no—
382D12—106no—
383D12—206no—
384C4×D3—1012no—
385C4×D3—1012no—
386C4×D3—206no—
387Dic6—106no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5C2×#23912yes—
391C22×C5C24×D311yescharacteristic
392C2×D5—66no—
393C2×D5—66no—
394C2×D5—66no—
395C4×C5—23no—
396C4×C5—23no—
397C4×C5—23no—
398C4×C5C2×#23516yes—
399C4×C5C2×#23912yes—
400C4×C5C2×#23912yes—
401Dic5—62no—
402Dic5—66no—
403Dic5—62no—
404#41—308no—
405#41—3012no—
406C2×Q8—24no—
407C2×Q8—153no—
408C2×Q8C22×D1513yes—
409C2×Q8C22×D1511yescharacteristic
410C2×D4—156no—
411C2×D4—156no—
412C2×D4—153no—
413C2×D4—156no—
414C22×C4—156no—
415C22×C4—156no—
416C22×C4—156no—
417C22×C4C22×D1513yes—
418C22×C4C22×D1513yes—
419C22×C4C22×D1511yescharacteristic
420C4⋊C4—151no—
421C4⋊C4—151no—
422C4⋊C4—156no—
423C4⋊C4—156no—
424C4⋊C4—156no—
425C4⋊C4—156no—
426C4⋊C4C22×D1513yes—
427C4⋊C4C22×D1513yes—
428C4⋊C4C22×D1516yes—
429C22⋊C4—152no—
430C22⋊C4—156no—
431C22⋊C4—1512no—
432C22⋊C4—156no—
433C22⋊C4—1512no—
434C42—156no—
435C42—156no—
436C42—152no—
437C42C22×D1513yes—
438C42C22×D1513yes—
439C42C22×D1513yes—
440C42C22×D1513yes—
441C3×C5#348011yescharacteristic, complemented, Hall
442C22×C3—21no—
443C22×C3—21no—
444C22×C3C2×#71312yes—
445C22×C3C24×D511yescharacteristic
446C2×D3—106no—
447C2×D3—106no—
448C2×D3—106no—
449C3×C4—23no—
450C3×C4—23no—
451C3×C4—23no—
452C3×C4C2×#70916yes—
453C3×C4C2×#71312yes—
454C3×C4C2×#71312yes—
455Dic3—102no—
456Dic3—106no—
457Dic3—102no—
458C2×C5—22no—
459C2×C5C22×#23511yescharacteristic
460C2×C5C22×#23911yescharacteristic
461C2×C5#596411yescharacteristic
462D5—126no—
463C23—156no—
464C23C23×D1511yescharacteristic
465Q8—26no—
466Q8—306no—
467Q8#681714yescomplemented
468D4—3012no—
469D4—3012no—
470D4—306no—
471D4—606no—
472C2×C4—26no—
473C2×C4—43no—
474C2×C4—152no—
475C2×C4—152no—
476C2×C4—156no—
477C2×C4—3012no—
478C2×C4—3012no—
479C2×C4—606no—
480C2×C4#682114yescomplemented
481C2×C4C23×D1513yes—
482C2×C4C23×D1513yes—
483C2×C4C23×D1513yes—
484C2×C4C23×D1513yes—
485C2×C4C23×D1511yescharacteristic
486C2×C4C23×D1511yescharacteristic
487C2×C3—22no—
488C2×C3C22×#70911yescharacteristic
489C2×C3C22×#71311yescharacteristic
490C2×C3#6628311yescharacteristic
491D3—206no—
492C5#8580211yescharacteristic, complemented, Sylow
493C22—21no—
494C22—21no—
495C22—306no—
496C22—306no—
497C22—306no—
498C22C2×#682112yes—
499C22C24×D1511yescharacteristic
500C4—23no—
501C4—23no—
502C4—23no—
503C4—302no—
504C4—306no—
505C4—302no—
506C4C2×#681716yes—
507C4C2×#682112yes—
508C4C2×#682112yes—
509C3#1061770311yescharacteristic, complemented, Sylow
510C2—22no—
511C2—606no—
512C2C22×#681711yescharacteristic
513C2C22×#682111yescharacteristic
514C2#1175714611yescharacteristic
subgroupG/H
centerC2×C4C23×D15
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×Q8C2
hypercenterC2×C4×Q8D15
hypocenterC3×C5#3480
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
2. #11756576C2semidirect
3. #11756344C2semidirect
4. #11756343C2semidirect
5. #11756339C2semidirect
6. #11756336C2semidirect
7. C4×#6821C2semidirect
8. #11756329C2semidirect
9. #11756273C2semidirect
10. #11756236C2semidirect
11. C4×#6817C2semidirect
48. C2×C4×C5×Q8D3semidirect
96. C2×C3×C4×Q8D5semidirect
145. C3×C5×Q8#41semidirect
148. C2×C3×C4×C5#41semidirect
247. C2×C4×Q8D15semidirect
304. C5×Q8#235semidirect
307. C2×C4×C5#239semidirect
367. C3×Q8#709semidirect
370. C2×C3×C4#713semidirect
441. C3×C5#3480semidirect
467. Q8#6817semidirect
480. C2×C4#6821semidirect
492. C5#85802semidirect
509. C3#10617703semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
#117565762
#117563442
#117563432
#117563392
#117563362
C4×#68212
#117563292
#117562732
#117562362
C4×#68172
#106177033
#858025