Finite Group Databasebeta

← #14418112

Subgroups — #14418112

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#568C211yesmaximal, characteristic, complemented
2#11756581C211yesmaximal, characteristic
3#11756504C211yesmaximal, characteristic, complemented
4C2×#91121C211yesmaximal, characteristic, complemented
5#11751246C214yesmaximal, complemented
6#11751245C214yesmaximal, complemented
7C2×#91109C211yesmaximal, characteristic, complemented
8#11751225C211yesmaximal, characteristic, complemented
9M16×Dic15C211yesmaximal, characteristic, complemented
10#10615542—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×#6817C2211yescharacteristic
13C3×C5×#131—22no—
14C3×C5×#131C2214yescomplemented
15C2×C3×C5×M16—22no—
16C2×C3×C5×M16C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91840C412yescomplemented
19#91839C2214yes—
20#91838C412yescomplemented
21#91831C412yescomplemented
22#91821C412yescomplemented
23C2×C4×Dic15C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25C2×#6710C2211yescharacteristic
26#91796—22no—
27M16×D15—22no—
28#91790C2214yescomplemented
29#91121C2212yescomplemented
30#91121C2212yescomplemented
31#91109C2212yescomplemented
32#91109C2212yescomplemented
33#91106C2214yescomplemented
34#91099C2212yescomplemented
35C8×Dic15C2212yescomplemented
36#83811—51nomaximal, Hall
37C5×#568D311yescharacteristic, complemented
38#66156—31no—
39#66079—31no—
40C2×#3969—31no—
41#65434—34no—
42#65433—34no—
43C2×#3957—31no—
44#65413—31no—
45M16×Dic5—31no—
46C3×C5×#41—21no—
47C3×C5×#41—21no—
48C3×C5×#41C2×C412yes—
49C3×C5×#41C2312yes—
50C2×C3×C5×Q8C2×C411yescharacteristic
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2×C411yescharacteristic
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—21no—
56C22×Dic15—21no—
57#6817—21no—
58#6817—21no—
59#6817C2×C412yes—
60#6817C2312yes—
61C2×D60C2×C411yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2×C411yescharacteristic
64C3×C5×M16—21no—
65C3×C5×M16—24no—
66C3×C5×M16D412yes—
67C3×C5×M16D412yes—
68C3×C5×M16C2312yes—
69C2×C3×C5×C8—21no—
70C2×C3×C5×C8—24no—
71C2×C3×C5×C8C2312yes—
72#6718C2×C414yescomplemented
73#6717C2×C414yescomplemented
74#6716C2×C414yescomplemented
75#6715C2×C414yescomplemented
76C4×Dic15—21no—
77C4×Dic15C2311yescharacteristic
78C4×Dic15C2311yescharacteristic
79#6710—21no—
80#6710C2×C412yes—
81#6710C2×C412yes—
82#6710C2312yes—
83C2×C3⋊#168—21no—
84C2×C3⋊#168C2312yes—
85#6705—24no—
86C8×D15—24no—
87C3×#568D511yescharacteristic, complemented
88#5822—51no—
89#5745—51no—
90C2×#837—51no—
91#5145—54no—
92#5144—54no—
93C2×#825—51no—
94#5124—51no—
95Dic3×M16—51no—
96C2×C5×#41C2×D311yescharacteristic
97C2×#709—31no—
98C5×#131—22no—
99C5×#131C2×D314yescomplemented
100C2×C5×M16—22no—
101C2×C5×M16C2×D311yescharacteristic
102C2×C5×M16C2×D311yescharacteristic
103#4097—32no—
104#4096—34no—
105#4095—32no—
106#4088—32no—
107#4078—32no—
108C2×C4×Dic5—31no—
109C2×#681—31no—
110C2×#681—31no—
111#4053—62no—
112D5×M16—62no—
113#4047—34no—
114#3969—32no—
115#3969—32no—
116#3957—32no—
117#3957—32no—
118#3954—34no—
119#3947—32no—
120C8×Dic5—32no—
121#2956—151noSylow
122C23×C3×C5—21no—
123C23×C3×C5#4111yescharacteristic
124C22×D15—21no—
125C3×C5×Q8—21no—
126C3×C5×Q8C22×C412yes—
127C3×C5×D4—22no—
128C3×C5×D4—22no—
129C3×C5×D4—21no—
130C3×C5×D4C22×C412yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C22×C411yescharacteristic
135C2×C3×C4×C5C22×C411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5#4111yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140#1220—22no—
141#1220—22no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15—42no—
146D60—21no—
147D60C22×C412yes—
148C4×D15—22no—
149C4×D15—22no—
150Dic30—21no—
151Dic30C22×C412yes—
152C3×C5×C8—22no—
153C3×C5×C8C2×D414yes—
154C3⋊#168—22no—
155C3⋊#168C22×C414yes—
156C2×C3×#41C2×D511yescharacteristic
157C2×#235—51no—
158C3×#131—22no—
159C3×#131C2×D514yescomplemented
160C2×C3×M16—22no—
161C2×C3×M16C2×D511yescharacteristic
162C2×C3×M16C2×D511yescharacteristic
163#951—52no—
164#950—54no—
165#949—52no—
166#942—52no—
167#932—52no—
168C2×C4×Dic3—51no—
169C2×#208—51no—
170C2×#208—51no—
171#907—102no—
172D3×M16—102no—
173#901—54no—
174#837—52no—
175#837—52no—
176#825—52no—
177#825—52no—
178#822—54no—
179#815—52no—
180C8×Dic3—52no—
181C5×#41—21no—
182C5×#41—21no—
183C5×#41C4×D312yes—
184C5×#41C22×D312yes—
185C2×C5×Q8C4×D311yescharacteristic
186C2×C5×D4—21no—
187C2×C5×D4C4×D311yescharacteristic
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—61no—
191C22×Dic5—61no—
192#709—32no—
193#709—32no—
194#709—61no—
195#709—61no—
196C2×D20—31no—
197C2×C4×D5—61no—
198C2×Dic10—31no—
199C5×M16—21no—
200C5×M16—24no—
201C5×M16#6712yes—
202C5×M16#6712yes—
203C5×M16C22×D312yes—
204C2×C5×C8—21no—
205C2×C5×C8—24no—
206C2×C5×C8C22×D312yes—
207#689—34no—
208#688—34no—
209#687—34no—
210#686—34no—
211C4×Dic5—31no—
212C4×Dic5—31no—
213C4×Dic5—61no—
214#681—32no—
215#681—32no—
216#681—32no—
217#681—61no—
218C2×#168—32no—
219C2×#168—61no—
220#676—64no—
221C8×D5—64no—
222#575—151no—
223#568—151no—
224#568D1511yescharacteristic, complemented
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—151no—
229C2×#104—151no—
230C4×M16—151no—
231C22×C3×C5—22no—
232C22×C3×C5—41no—
233C22×C3×C5—81no—
234C22×C3×C5C4×D411yescharacteristic
235C22×C3×C5C4×D411yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C2×D15—22no—
238C2×D15—81no—
239C3×C4×C5—22no—
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C4×D411yescharacteristic
242C3×C4×C5C23×C411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—22no—
245Dic15—22no—
246Dic15—41no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41C4×D512yes—
250C3×#41C22×D512yes—
251C2×C3×Q8C4×D511yescharacteristic
252C2×C3×D4—21no—
253C2×C3×D4C4×D511yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—101no—
257C22×Dic3—101no—
258#235—52no—
259#235—52no—
260#235—101no—
261#235—101no—
262C2×D12—51no—
263C2×C4×D3—101no—
264C2×Dic6—51no—
265C3×M16—21no—
266C3×M16—24no—
267C3×M16C22⋊D512yes—
268C3×M16C22⋊D512yes—
269C3×M16C22×D512yes—
270C2×C3×C8—21no—
271C2×C3×C8—24no—
272C2×C3×C8C22×D512yes—
273#216—54no—
274#215—54no—
275#214—54no—
276#213—54no—
277C4×Dic3—51no—
278C4×Dic3—51no—
279C4×Dic3—101no—
280#208—52no—
281#208—52no—
282#208—52no—
283#208—101no—
284C2×C3⋊C8—52no—
285C2×C3⋊C8—101no—
286ΓL(1,𝔽25)—104no—
287D3×C8—104no—
288C23×C5—21no—
289C23×C5#23511yescharacteristic
290C22×D5—61no—
291C5×Q8—21no—
292C5×Q8C2×C4×D312yes—
293C5×D4—22no—
294C5×D4—22no—
295C5×D4—21no—
296C5×D4C2×C4×D312yes—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5C2×C4×D311yescharacteristic
301C2×C4×C5C2×C4×D311yescharacteristic
302C2×C4×C5#23511yescharacteristic
303C2×C4×C5C2×#6711yescharacteristic
304C2×C4×C5C2×#6711yescharacteristic
305C2×C4×C5C23×D311yescharacteristic
306C22⋊D5—62no—
307C22⋊D5—62no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—122no—
312D20—32no—
313D20—61no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—32no—
317Dic10—61no—
318C5×C8—22no—
319C5×C8C2×#6714yes—
320#168—34no—
321#168—62no—
322C2×#41—151no—
323C2×#41C2×D1511yescharacteristic
324#137—152no—
325#137—152no—
326AGL(1,ℤ/8)—152no—
327AGL(1,ℤ/8)—152no—
328#135—154no—
329#131—22no—
330#131—154no—
331#131—302no—
332#131C2×D1514yescomplemented
333C2×M16—22no—
334C2×M16—151no—
335C2×M16—151no—
336C2×M16—302no—
337C2×M16C2×D1511yescharacteristic
338C2×M16C2×D1511yescharacteristic
339C2×C42—151no—
340#108—154no—
341#104—152no—
342#104—152no—
343#104—152no—
344#104—152no—
345#97—152no—
346C4×C8—152no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5—21no—
350C2×C3×C5—42no—
351C2×C3×C5C2×C4×D411yescharacteristic
352D15—42no—
353C23×C3—21no—
354C23×C3#70911yescharacteristic
355C22×D3—101no—
356C3×Q8—21no—
357C3×Q8C2×C4×D512yes—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4C2×C4×D512yes—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4C2×C4×D511yescharacteristic
366C2×C3×C4C2×C4×D511yescharacteristic
367C2×C3×C4#70911yescharacteristic
368C2×C3×C4C2×C22⋊D511yescharacteristic
369C2×C3×C4C2×C22⋊D511yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—102no—
372#67—102no—
373C2×Dic3—101no—
374C2×Dic3—101no—
375C2×Dic3—101no—
376C2×Dic3—202no—
377D12—52no—
378D12—101no—
379C4×D3—102no—
380C4×D3—102no—
381Dic6—52no—
382Dic6—101no—
383C3×C8—22no—
384C3×C8C2×C22⋊D514yes—
385C3⋊C8—54no—
386C3⋊C8—102no—
387C22×C5—22no—
388C22×C5—41no—
389C22×C5—81no—
390C22×C5C4×#6711yescharacteristic
391C22×C5C4×#6711yescharacteristic
392C22×C5C2×#23511yescharacteristic
393C2×D5—62no—
394C2×D5—241no—
395C4×C5—22no—
396C4×C5C4×#6711yescharacteristic
397C4×C5C4×#6711yescharacteristic
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C22×#6711yescharacteristic
400Dic5—62no—
401Dic5—62no—
402Dic5—121no—
403#41—21no—
404#41—21no—
405#41—152no—
406#41—152no—
407#41—301no—
408#41—301no—
409#41C4×D1512yes—
410#41C22×D1512yes—
411C2×Q8—151no—
412C2×Q8C4×D1511yescharacteristic
413C2×D4—21no—
414C2×D4—151no—
415C2×D4—301no—
416C2×D4C4×D1511yescharacteristic
417C22×C4—21no—
418C22×C4—301no—
419C22×C4—301no—
420C22×C4C22×D1511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—21no—
426M16—24no—
427M16—152no—
428M16—152no—
429M16—152no—
430M16—301no—
431M16—304no—
432M16#122012yes—
433M16#122012yes—
434M16C22×D1512yes—
435C2×C8—21no—
436C2×C8—24no—
437C2×C8—152no—
438C2×C8—301no—
439C2×C8—304no—
440C2×C8C22×D1512yes—
441C42—151no—
442C42—151no—
443C42—301no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—81no—
448C22×C3C4×C22⋊D511yescharacteristic
449C22×C3C4×C22⋊D511yescharacteristic
450C22×C3C2×#70911yescharacteristic
451C2×D3—102no—
452C2×D3—401no—
453C3×C4—22no—
454C3×C4C4×C22⋊D511yescharacteristic
455C3×C4C4×C22⋊D511yescharacteristic
456C3×C4C22×C4×D511yescharacteristic
457C3×C4C22×C22⋊D511yescharacteristic
458Dic3—102no—
459Dic3—102no—
460Dic3—201no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—42no—
465C2×C5C2×C4×#6711yescharacteristic
466D5—122no—
467C23—21no—
468C23—301no—
469C23#681711yescharacteristic
470Q8—21no—
471Q8—152no—
472Q8—301no—
473Q8C2×C4×D1512yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—152no—
478D4—302no—
479D4—302no—
480D4—301no—
481D4C2×C4×D1512yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4C2×C4×D1511yescharacteristic
492C2×C4C2×C4×D1511yescharacteristic
493C2×C4#681711yescharacteristic
494C2×C4C2×#122011yescharacteristic
495C2×C4C2×#122011yescharacteristic
496C2×C4C23×D1511yescharacteristic
497C8—22no—
498C8—154no—
499C8—302no—
500C8C2×#122014yes—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3C2×C4×C22⋊D511yescharacteristic
506D3—202no—
507C5#8381111yescharacteristic, complemented, Sylow
508C22—22no—
509C22—41no—
510C22—81no—
511C22—302no—
512C22—1201no—
513C22C4×#122011yescharacteristic
514C22C4×#122011yescharacteristic
515C22C2×#681711yescharacteristic
516C4—22no—
517C4—302no—
518C4—302no—
519C4—601no—
520C4C4×#122011yescharacteristic
521C4C4×#122011yescharacteristic
522C4C22×C4×D1511yescharacteristic
523C4C22×#122011yescharacteristic
524C3#1061554211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—42no—
529C2—602no—
530C2C2×C4×#122011yescharacteristic
subgroupG/H
centerC4C22×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#568C2
socleC2×C3×C5C2×C4×D4
prime radical#11756581C2
cosocleC2×C3×C4×C5C24
hypercenter#568D15
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×M16 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C3×C5×#568C2semidirect
3. #11756504C2semidirect
4. C2×#91121C2semidirect
5. #11751246C2semidirect
6. #11751245C2semidirect
7. C2×#91109C2semidirect
8. #11751225C2semidirect
9. M16×Dic15C2semidirect
14. C3×C5×#131C22semidirect
18. #91840C4semidirect
20. #91838C4semidirect
21. #91831C4semidirect
22. #91821C4semidirect
28. #91790C22semidirect
29. #91121C22semidirect
30. #91121C22semidirect
31. #91109C22semidirect
32. #91109C22semidirect
33. #91106C22semidirect
34. #91099C22semidirect
35. C8×Dic15C22semidirect
37. C5×#568D3semidirect
72. #6718C2×C4semidirect
73. #6717C2×C4semidirect
74. #6716C2×C4semidirect
75. #6715C2×C4semidirect
87. C3×#568D5semidirect
99. C5×#131C2×D3semidirect
159. C3×#131C2×D5semidirect
224. #568D15semidirect
332. #131C2×D15semidirect
444. C3×C5#2956semidirect
507. C5#83811semidirect
524. C3#10615542semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5682
#117565812
#117565042
C2×#911212
#117512462
#117512452
C2×#911092
#117512252
M16×Dic152
#106155423
#838115