Finite Group Databasebeta

← #14418167

Subgroups — #14418167

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
1#11756504C211yesmaximal, characteristic, complemented
2C3×#66079C211yesmaximal, characteristic, complemented
3#11754154C211yesmaximal, characteristic
4C5×Dic3×M16C211yesmaximal, characteristic, complemented
5#11748480C211yesmaximal, characteristic, complemented
6C2×#90980C211yesmaximal, characteristic, complemented
7C2×#90977C211yesmaximal, characteristic, complemented
8#11748077C214yesmaximal, complemented
9#11748076C214yesmaximal, complemented
10#10610272—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15#91796—22no—
16M16×D15—22no—
17#91790C2214yescomplemented
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C3×#4053—22no—
22C3×D5×M16—22no—
23C3×#4047C2214yescomplemented
24#91315C412yescomplemented
25#91313C412yescomplemented
26#91312C412yescomplemented
27#91311C2214yes—
28#91301C412yescomplemented
29C5×#815C2212yescomplemented
30C5×C8×Dic3C2212yescomplemented
31#90993C2214yescomplemented
32#90980C2212yescomplemented
33#90980C2212yescomplemented
34#90977C2212yescomplemented
35#90977C2212yescomplemented
36#83811—51nomaximal, Hall
37#66082—31no—
38#66079—31no—
39#66079D311yescharacteristic, complemented
40C4×C5×M16—31no—
41#65414—31no—
42C2×#3937—31no—
43C2×#3937—31no—
44#65006—34no—
45#64989—34no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48#6817—21no—
49#6817—21no—
50#6817C2×C412yes—
51#6817C2312yes—
52C2×D60C2×C411yescharacteristic
53C2×C4×D15—21no—
54C2×Dic30C2×C411yescharacteristic
55C22×C5×Dic3—21no—
56C2×C3×C22⋊D5—21no—
57C3×#709—21no—
58C3×#709—21no—
59C3×#709C2×C412yes—
60C3×#709C2312yes—
61C2×C3×D20C2×C411yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×Dic10C2×C411yescharacteristic
64C3×C5×M16D412yes—
65C3×C5×M16D412yes—
66C2×C3×C5×C8C2312yes—
67#6710—21no—
68#6710C2312yes—
69C2×C3⋊#168—21no—
70#6705—24no—
71C8×D15—24no—
72C4×C5×Dic3—21no—
73C4×C5×Dic3C2311yescharacteristic
74C4×C5×Dic3C2311yescharacteristic
75C5×#208C2×C412yes—
76C5×#208C2×C412yes—
77C2×C5×C3⋊C8C2312yes—
78C3×#681—21no—
79C3×#681C2312yes—
80C2×C3×#168—21no—
81C3×#676—24no—
82C3×C8×D5—24no—
83#6662C2×C414yescomplemented
84#6658C2×C414yescomplemented
85#6657C2×C414yescomplemented
86#6653C2×C414yescomplemented
87C3×#568—51no—
88#5822—51no—
89#5745—51no—
90C2×#837—51no—
91#5145—54no—
92#5144—54no—
93C2×#825—51no—
94#5124—51no—
95Dic3×M16D511yescharacteristic, complemented
96C2×#709—31no—
97C2×#709C2×D311yescharacteristic
98C2×C5×M16—31no—
99C2×C5×M16C2×D311yescharacteristic
100C2×C42×C5—31no—
101C2×#681—31no—
102C2×#681C2×D311yescharacteristic
103#4055—32no—
104#4055—32no—
105#4054—32no—
106#4054—32no—
107#4053—22no—
108#4053—62no—
109D5×M16—22no—
110D5×M16—62no—
111#4050—34no—
112#4047—34no—
113#4047C2×D314yescomplemented
114C5×#97—32no—
115C4×C5×C8—32no—
116#3951—34no—
117#3937—32no—
118#3937—32no—
119#3937—32no—
120#3937—32no—
121#2956—151noSylow
122C23×C3×C5#4111yescharacteristic
123C22×D15—21no—
124C22×C3×D5—21no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C22×C411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131#1220—22no—
132#1220—22no—
133C2×Dic15—21no—
134D60—21no—
135D60C22×C412yes—
136C4×D15—22no—
137C4×D15—22no—
138Dic30—21no—
139Dic30C22×C412yes—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—42no—
143C3×C22⋊D5—22no—
144C3×C22⋊D5—22no—
145C2×C3×Dic5—21no—
146C3×D20—21no—
147C3×D20C22×C412yes—
148C3×C4×D5—22no—
149C3×C4×D5—22no—
150C3×Dic10—21no—
151C3×Dic10C22×C412yes—
152C3×C5×C8C2×D414yes—
153C3⋊#168—22no—
154C3×#168—22no—
155C5×C3⋊C8C22×C414yes—
156C2×C3×#41—51no—
157C2×#235—51no—
158C3×#131—54no—
159C3×#131—102no—
160C2×C3×M16—51no—
161C2×C3×M16—102no—
162C2×C3×M16C2×D511yescharacteristic
163#951—52no—
164#950—54no—
165#949—52no—
166#942—52no—
167#932—52no—
168C2×C4×Dic3C2×D511yescharacteristic
169C2×#208—51no—
170C2×#208C2×D511yescharacteristic
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#815C2×D512yescomplemented
180C8×Dic3C2×D512yescomplemented
181C22×C4×C5—61no—
182C22×C4×C5C22×D311yescharacteristic
183C2×C22⋊D5—21no—
184C2×C22⋊D5—61no—
185#709—21no—
186#709—21no—
187#709—32no—
188#709—32no—
189#709—61no—
190#709—61no—
191#709C4×D312yes—
192#709C22×D312yes—
193C2×D20—31no—
194C2×D20C4×D311yescharacteristic
195C2×C4×D5—21no—
196C2×C4×D5—61no—
197C2×Dic10—31no—
198C2×Dic10C4×D311yescharacteristic
199C5×M16—32no—
200C5×M16—32no—
201C5×M16#6712yes—
202C5×M16#6712yes—
203C2×C5×C8—32no—
204C2×C5×C8C22×D312yes—
205C42×C5—31no—
206C42×C5—31no—
207C42×C5—61no—
208#681—21no—
209#681—32no—
210#681—61no—
211#681C22×D312yes—
212C2×#168—21no—
213C2×#168—61no—
214Dic20—34no—
215D40—34no—
216#677—34no—
217#677—34no—
218#676—24no—
219#676—64no—
220C8×D5—24no—
221C8×D5—64no—
222#575—151no—
223#568—51no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—151no—
229C2×#104—151no—
230C4×M16—31no—
231C22×C3×C5—41no—
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C2×D15—22no—
236C2×D15—81no—
237C2×C3×D5—22no—
238C2×C3×D5—81no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243Dic15—22no—
244C3×Dic5—22no—
245C5×Dic3—22no—
246C5×Dic3—41no—
247C3×#41—52no—
248C3×#41—52no—
249C3×#41—101no—
250C3×#41—101no—
251C2×C3×Q8—51no—
252C2×C3×D4—51no—
253C2×C3×D4—101no—
254C22×C3×C4—101no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—101no—
257C22×Dic3—21no—
258#235—52no—
259#235—52no—
260#235—101no—
261#235—101no—
262C2×D12—51no—
263C2×C4×D3—101no—
264C2×Dic6—51no—
265C3×M16—52no—
266C3×M16—101no—
267C3×M16—104no—
268C3×M16D2012yes—
269C3×M16D2012yes—
270C2×C3×C8—101no—
271C2×C3×C8—104no—
272C2×C3×C8C22×D512yes—
273#216—54no—
274#215—54no—
275#214—54no—
276#213—54no—
277C4×Dic3—21no—
278C4×Dic3C22×D511yescharacteristic
279C4×Dic3C22×D511yescharacteristic
280#208—52no—
281#208—101no—
282#208C4×D512yes—
283#208C4×D512yes—
284C2×C3⋊C8—101no—
285C2×C3⋊C8C22×D512yes—
286ΓL(1,𝔽25)—104no—
287D3×C8—104no—
288C23×C5#23511yescharacteristic
289C22×D5—21no—
290C22×D5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—122no—
294C2×C4×C5C2×C4×D311yescharacteristic
295C2×C4×C5C2×C4×D311yescharacteristic
296C2×C4×C5#23511yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C22⋊D5—22no—
301C22⋊D5—22no—
302C22⋊D5—62no—
303C22⋊D5—62no—
304C2×Dic5—21no—
305C2×Dic5—61no—
306D20—21no—
307D20—32no—
308D20—61no—
309D20C2×C4×D312yes—
310C4×D5—22no—
311C4×D5—22no—
312C4×D5—62no—
313C4×D5—62no—
314Dic10—21no—
315Dic10—32no—
316Dic10—61no—
317Dic10C2×C4×D312yes—
318C5×C8—34no—
319C5×C8C2×#6714yes—
320#168—22no—
321#168—62no—
322C2×#41—51no—
323C2×#41—151no—
324#137—152no—
325#137—152no—
326AGL(1,ℤ/8)—152no—
327AGL(1,ℤ/8)—152no—
328#135—154no—
329#131—54no—
330#131—102no—
331#131—154no—
332#131—302no—
333C2×M16—31no—
334C2×M16—51no—
335C2×M16—102no—
336C2×M16—151no—
337C2×M16—302no—
338C2×M16D3×D511yescharacteristic
339C2×C42—31no—
340#108—154no—
341#104—152no—
342#104—152no—
343#104—152no—
344#104—152no—
345#97—32no—
346C4×C8—32no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5—21no—
350C2×C3×C5C2×C4×D411yescharacteristic
351D15—42no—
352C3×D5—42no—
353C23×C3—101no—
354C23×C3#70911yescharacteristic
355C22×D3—101no—
356C3×Q8—52no—
357C3×Q8—101no—
358C3×D4—52no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—101no—
362C2×C3×C4—101no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4C2×C4×D511yescharacteristic
366C2×C3×C4C2×C4×D511yescharacteristic
367C2×C3×C4C2×D2011yescharacteristic
368C2×C3×C4C2×D2011yescharacteristic
369C2×C3×C4#70911yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—102no—
372#67—102no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—42no—
376C2×Dic3—101no—
377D12—52no—
378D12—101no—
379C4×D3—102no—
380C4×D3—102no—
381Dic6—52no—
382Dic6—101no—
383C3×C8—102no—
384C3×C8C2×D2014yes—
385C3⋊C8—102no—
386C3⋊C8C2×C4×D514yes—
387C22×C5—41no—
388C22×C5C4×#6711yescharacteristic
389C22×C5C4×#6711yescharacteristic
390C22×C5C2×#23511yescharacteristic
391C2×D5—22no—
392C2×D5—62no—
393C2×D5—81no—
394C2×D5—241no—
395C4×C5—62no—
396C4×C5—121no—
397C4×C5C4×#6711yescharacteristic
398C4×C5C4×#6711yescharacteristic
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C22×#6711yescharacteristic
401Dic5—22no—
402Dic5—62no—
403#41—52no—
404#41—52no—
405#41—101no—
406#41—101no—
407#41—152no—
408#41—152no—
409#41—301no—
410#41—301no—
411C2×Q8—51no—
412C2×Q8—151no—
413C2×D4—51no—
414C2×D4—101no—
415C2×D4—151no—
416C2×D4—301no—
417C22×C4—61no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—32no—
426M16—32no—
427M16—52no—
428M16—101no—
429M16—104no—
430M16—152no—
431M16—301no—
432M16—304no—
433M16#120212yes—
434M16#120212yes—
435C2×C8—32no—
436C2×C8—101no—
437C2×C8—104no—
438C2×C8—301no—
439C2×C8—304no—
440C2×C8C2×D3×D512yes—
441C42—31no—
442C42—31no—
443C42—61no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—41no—
446C22×C3—102no—
447C22×C3—401no—
448C22×C3C4×D2011yescharacteristic
449C22×C3C4×D2011yescharacteristic
450C22×C3C2×#70911yescharacteristic
451C2×D3—102no—
452C2×D3—401no—
453C3×C4—102no—
454C3×C4C4×D2011yescharacteristic
455C3×C4C4×D2011yescharacteristic
456C3×C4C22×C4×D511yescharacteristic
457C3×C4C22×D2011yescharacteristic
458Dic3—22no—
459Dic3—41no—
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5C2×C4×#6711yescharacteristic
465D5—42no—
466D5—122no—
467C23—101no—
468C23—301no—
469C23#677111yescharacteristic
470Q8—52no—
471Q8—101no—
472Q8—152no—
473Q8—301no—
474D4—52no—
475D4—102no—
476D4—102no—
477D4—101no—
478D4—152no—
479D4—302no—
480D4—302no—
481D4—301no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—101no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—122no—
488C2×C4—301no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4#677111yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4C4×D3×D511yescharacteristic
494C2×C4C2×#120211yescharacteristic
495C2×C4C2×#120211yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—34no—
498C8—102no—
499C8—302no—
500C8C2×#120214yes—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—202no—
505C2×C3C2×C4×D2011yescharacteristic
506D3—202no—
507C5#8381111yescharacteristic, complemented, Sylow
508C22—41no—
509C22—102no—
510C22—302no—
511C22—401no—
512C22—1201no—
513C22C4×#120211yescharacteristic
514C22C4×#120211yescharacteristic
515C22C2×#677111yescharacteristic
516C4—62no—
517C4—102no—
518C4—121no—
519C4—302no—
520C4C4×#120211yescharacteristic
521C4C4×#120211yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C22×#120211yescharacteristic
524C3#1061027211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—202no—
529C2—602no—
530C2C2×C4×#120211yescharacteristic
subgroupG/H
centerC4C22×#1202
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C2×C4×D4
prime radical#11754154C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #11756504C2semidirect
2. C3×#66079C2semidirect
4. C5×Dic3×M16C2semidirect
5. #11748480C2semidirect
6. C2×#90980C2semidirect
7. C2×#90977C2semidirect
8. #11748077C2semidirect
9. #11748076C2semidirect
17. #91790C22semidirect
23. C3×#4047C22semidirect
24. #91315C4semidirect
25. #91313C4semidirect
26. #91312C4semidirect
28. #91301C4semidirect
29. C5×#815C22semidirect
30. C5×C8×Dic3C22semidirect
31. #90993C22semidirect
32. #90980C22semidirect
33. #90980C22semidirect
34. #90977C22semidirect
35. #90977C22semidirect
39. #66079D3semidirect
83. #6662C2×C4semidirect
84. #6658C2×C4semidirect
85. #6657C2×C4semidirect
86. #6653C2×C4semidirect
95. Dic3×M16D5semidirect
113. #4047C2×D3semidirect
179. #815C2×D5semidirect
180. C8×Dic3C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#83811semidirect
524. C3#10610272semidirect

Maximal subgroups

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

subgroupindex
#117565042
C3×#660792
#117541542
C5×Dic3×M162
#117484802
C2×#909802
C2×#909772
#117480772
#117480762
#106102723
#838115