Finite Group Databasebeta

← #14418158

Subgroups — #14418158

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×#66079C211yesmaximal, characteristic, complemented
2#11754154C211yesmaximal, characteristic
3#11754130C211yesmaximal, characteristic, complemented
4C2×#91109C211yesmaximal, characteristic, complemented
5C5×#5124C211yesmaximal, characteristic, complemented
6C2×#90976C211yesmaximal, characteristic, complemented
7#11748328C211yesmaximal, characteristic, complemented
8#11748207C214yesmaximal, complemented
9#11748206C214yesmaximal, complemented
10#10610989—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×C4×Dic15C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18C3×#4053C2214yescomplemented
19C3×D5×M16—22no—
20C3×#4047—22no—
21#91315C412yescomplemented
22#91313C412yescomplemented
23#91312C412yescomplemented
24#91311C2214yes—
25#91301C412yescomplemented
26#91292—22no—
27#91291—22no—
28#91290C2214yescomplemented
29#91109C2212yescomplemented
30#91109C2212yescomplemented
31C5×#822C2214yescomplemented
32#90976C2212yescomplemented
33#90976C2212yescomplemented
34#90954C2212yescomplemented
35#90951C2212yescomplemented
36#83811—51nomaximal, Hall
37#66082—31no—
38#66079—31no—
39#66079D311yescharacteristic, complemented
40C5×#430—31no—
41C2×#3957—31no—
42C2×#3957—31no—
43M16×Dic5—31no—
44#65184—34no—
45#65183—34no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48C22×Dic15—21no—
49#6817—21no—
50#6817—21no—
51#6817C2×C412yes—
52#6817C2312yes—
53C2×D60C2×C411yescharacteristic
54C2×C4×D15—21no—
55C2×Dic30C2×C411yescharacteristic
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×M16—21no—
65C3×C5×M16C2312yes—
66C2×C3×C5×C8—21no—
67C4×Dic15—21no—
68C4×Dic15C2311yescharacteristic
69C4×Dic15C2311yescharacteristic
70C5×#208—21no—
71C5×#208C2×C412yes—
72C5×#208C2×C412yes—
73C5×#208C2312yes—
74C2×C5×C3⋊C8—21no—
75C2×C5×C3⋊C8C2312yes—
76C3×#681D412yes—
77C3×#681D412yes—
78C2×C3×#168C2312yes—
79C3×#676—24no—
80C3×C8×D5—24no—
81#6662C2×C414yescomplemented
82#6658C2×C414yescomplemented
83#6657C2×C414yescomplemented
84#6653C2×C414yescomplemented
85#6651—24no—
86#6648—24no—
87C3×#568—51no—
88#5822—51no—
89#5745—51no—
90C2×#837—51no—
91#5145—54no—
92#5144—54no—
93C2×#825—51no—
94#5124D511yescharacteristic, complemented
95Dic3×M16—51no—
96C2×#709—31no—
97C2×#709C2×D311yescharacteristic
98C2×C5×M16—31no—
99C2×C5×M16—31no—
100C2×C5×M16C2×D311yescharacteristic
101C2×C4×Dic5—31no—
102C2×#681C2×D311yescharacteristic
103#4055—32no—
104#4055—32no—
105#4054—32no—
106#4054—32no—
107#4053—34no—
108#4053C2×D314yescomplemented
109D5×M16—22no—
110D5×M16—62no—
111#4050—34no—
112#4047—22no—
113#4047—62no—
114C5×#108—34no—
115#3957—32no—
116#3957—32no—
117#3957—32no—
118#3957—32no—
119#3947—32no—
120C8×Dic5—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—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—42no—
137D60—21no—
138D60C22×C412yes—
139C4×D15—22no—
140C4×D15—22no—
141Dic30—21no—
142Dic30C22×C412yes—
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×C8—22no—
153C3×#168C2×D414yes—
154C5×C3⋊C8—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×Dic3—51no—
169C2×#208C2×D511yescharacteristic
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#822C2×D514yescomplemented
179#815—52no—
180C8×Dic3—52no—
181C22×C4×C5C22×D311yescharacteristic
182C2×C22⋊D5—21no—
183C2×C22⋊D5—61no—
184C22×Dic5—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—21no—
200C5×M16—32no—
201C5×M16—32no—
202C5×M16—32no—
203C5×M16—61no—
204C5×M16C22×D312yes—
205C2×C5×C8—21no—
206C2×C5×C8—32no—
207C2×C5×C8—61no—
208C4×Dic5—31no—
209C4×Dic5—31no—
210C4×Dic5—61no—
211#681#6712yes—
212#681#6712yes—
213C2×#168C22×D312yes—
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—31no—
228C2×#104—151no—
229C2×#104—151no—
230C4×M16—151no—
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—
244Dic15—22no—
245Dic15—41no—
246C3×Dic5—22no—
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—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—52no—
267C3×M16—52no—
268C3×M16—104no—
269C3×M16C22×D512yes—
270C2×C3×C8—21no—
271C2×C3×C8—52no—
272C2×C3×C8—104no—
273#216—54no—
274#215—54no—
275#214—54no—
276#213—54no—
277C4×Dic3—51no—
278C4×Dic3—51no—
279C4×Dic3—101no—
280#208—21no—
281#208C4×D512yes—
282#208C4×D512yes—
283#208C22×D512yes—
284C2×C3⋊C8—21no—
285C2×C3⋊C8C22×D512yes—
286ΓL(1,𝔽25)—104no—
287D3×C8—104no—
288C23×C5#23511yescharacteristic
289C22×D5—21no—
290C22×D5—61no—
291C2×C4×C5C2×C4×D311yescharacteristic
292C2×C4×C5C2×C4×D311yescharacteristic
293C2×C4×C5#23511yescharacteristic
294C2×C4×C5C2×#6711yescharacteristic
295C2×C4×C5C2×#6711yescharacteristic
296C2×C4×C5C23×D311yescharacteristic
297C22⋊D5—22no—
298C22⋊D5—22no—
299C22⋊D5—62no—
300C22⋊D5—62no—
301C2×Dic5—21no—
302C2×Dic5—61no—
303C2×Dic5—61no—
304C2×Dic5—61no—
305C2×Dic5—122no—
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—22no—
319C5×C8—34no—
320C5×C8—62no—
321#168C2×#6714yes—
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—31no—
335C2×M16—51no—
336C2×M16—102no—
337C2×M16—302no—
338C2×M16D3×D511yescharacteristic
339C2×C42—151no—
340#108—34no—
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×C5C2×C4×D411yescharacteristic
351D15—42no—
352C3×D5—42no—
353C23×C3—101no—
354C23×C3#71311yescharacteristic
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×C4D4×D511yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4#71311yescharacteristic
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×C8—54no—
385C3⋊C8—22no—
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×C5C4×#6711yescharacteristic
396C4×C5C4×#6711yescharacteristic
397C4×C5C22×C4×D311yescharacteristic
398C4×C5C22×#6711yescharacteristic
399Dic5—22no—
400Dic5—62no—
401Dic5—62no—
402Dic5—121no—
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—101no—
418C22×C4—301no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—21no—
426M16—32no—
427M16—32no—
428M16—32no—
429M16—52no—
430M16—52no—
431M16—61no—
432M16—104no—
433M16—304no—
434M16C2×D3×D512yes—
435C2×C8—21no—
436C2×C8—32no—
437C2×C8—52no—
438C2×C8—61no—
439C2×C8—104no—
440C2×C8—304no—
441C42—151no—
442C42—151no—
443C42—301no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—41no—
446C22×C3—102no—
447C22×C3—401no—
448C22×C3#403911yescharacteristic
449C22×C3#403911yescharacteristic
450C22×C3C2×#71311yescharacteristic
451C2×D3—102no—
452C2×D3—401no—
453C3×C4—102no—
454C3×C4#403911yescharacteristic
455C3×C4#403911yescharacteristic
456C3×C4C22×C4×D511yescharacteristic
457C3×C4C2×D4×D511yescharacteristic
458Dic3—102no—
459Dic3—102no—
460Dic3—201no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5C2×C4×#6711yescharacteristic
465D5—42no—
466D5—122no—
467C23—101no—
468C23—301no—
469C23#677311yescharacteristic
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—101no—
483C2×C4—102no—
484C2×C4—102no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4#677311yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4C4×D3×D511yescharacteristic
494C2×C4D5×#6711yescharacteristic
495C2×C4D5×#6711yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—22no—
498C8—34no—
499C8—54no—
500C8—62no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—202no—
505C2×C3C2×#403911yescharacteristic
506D3—202no—
507C5#8381111yescharacteristic, complemented, Sylow
508C22—41no—
509C22—102no—
510C22—302no—
511C22—401no—
512C22—1201no—
513C22#9144411yescharacteristic
514C22#9144411yescharacteristic
515C22C2×#677311yescharacteristic
516C4—102no—
517C4—302no—
518C4—302no—
519C4—601no—
520C4#9144411yescharacteristic
521C4#9144411yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×D5×#6711yescharacteristic
524C3#1061098911yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—202no—
529C2—602no—
530C2C2×#9144411yescharacteristic
subgroupG/H
centerC4C2×D5×#67
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 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#66079C2semidirect
3. #11754130C2semidirect
4. C2×#91109C2semidirect
5. C5×#5124C2semidirect
6. C2×#90976C2semidirect
7. #11748328C2semidirect
8. #11748207C2semidirect
9. #11748206C2semidirect
18. C3×#4053C22semidirect
21. #91315C4semidirect
22. #91313C4semidirect
23. #91312C4semidirect
25. #91301C4semidirect
28. #91290C22semidirect
29. #91109C22semidirect
30. #91109C22semidirect
31. C5×#822C22semidirect
32. #90976C22semidirect
33. #90976C22semidirect
34. #90954C22semidirect
35. #90951C22semidirect
39. #66079D3semidirect
81. #6662C2×C4semidirect
82. #6658C2×C4semidirect
83. #6657C2×C4semidirect
84. #6653C2×C4semidirect
94. #5124D5semidirect
108. #4053C2×D3semidirect
178. #822C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#83811semidirect
524. C3#10610989semidirect

Maximal subgroups

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

subgroupindex
C3×#660792
#117541542
#117541302
C2×#911092
C5×#51242
C2×#909762
#117483282
#117482072
#117482062
#106109893
#838115