Finite Group Databasebeta

← #14418170

Subgroups — #14418170

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#11754154C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic, complemented
3#11754120C211yesmaximal, characteristic, complemented
4C2×#91089C211yesmaximal, characteristic, complemented
5C4×C5×#208C211yesmaximal, characteristic, complemented
6C2×C3×#3937C211yesmaximal, characteristic, complemented
7#11748480C211yesmaximal, characteristic, complemented
8#11747017C214yesmaximal, complemented
9#11747016C214yesmaximal, complemented
10#10610272—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18#91315C412yescomplemented
19#91313C412yescomplemented
20#91312C412yescomplemented
21#91311C2214yes—
22#91301C412yescomplemented
23#91292—22no—
24#91291C2214yescomplemented
25#91290—22no—
26#91284—22no—
27#91283C2214yescomplemented
28D5×#208—22no—
29#91089C2212yescomplemented
30#91089C2212yescomplemented
31C5×#803C2212yescomplemented
32C4×C5×C3⋊C8C2212yescomplemented
33C3×#3937C2212yescomplemented
34C3×#3937C2212yescomplemented
35#90993C2214yescomplemented
36#78980—51nomaximal, Hall
37#66082—31no—
38#66079—31no—
39#66079—31no—
40C4×C5×M16—31no—
41#65414—31no—
42C2×#3937—31no—
43C2×#3937D311yescharacteristic, complemented
44#65006—34no—
45#64989—34no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5C2311yescharacteristic
48C2×#1220—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×C42×C5—21no—
65C3×C42×C5C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67#6710—21no—
68#6710C2312yes—
69C2×C3⋊#168—21no—
70C5×#208C2×C412yes—
71C5×#208C2×C412yes—
72C5×#208D412yes—
73C5×#208D412yes—
74C2×C5×C3⋊C8C2312yes—
75C2×C5×C3⋊C8C2312yes—
76C3×#681—21no—
77C3×#681C2312yes—
78C2×C3×#168—21no—
79#6662C2×C414yescomplemented
80#6658C2×C414yescomplemented
81#6657C2×C414yescomplemented
82#6653C2×C414yescomplemented
83#6651—24no—
84#6649—24no—
85#6648—24no—
86D5×C3⋊C8—24no—
87#5822—51no—
88#5819—51no—
89#5745—51no—
90C2×C3×#104—51no—
91#5124—51no—
92C2×#805—51no—
93C4×#208D511yescharacteristic, complemented
94#4824—54no—
95#4823—54no—
96C2×#709—31no—
97C2×#709C2×D311yescharacteristic
98C2×C5×M16—31no—
99C2×C5×M16—31no—
100C2×C42×C5C2×D311yescharacteristic
101C2×#681—31no—
102C2×#681C2×D311yescharacteristic
103#4055—32no—
104#4055—32no—
105#4054—32no—
106#4054—32no—
107#4053—62no—
108#4053—62no—
109D5×M16—62no—
110D5×M16—62no—
111#4050—34no—
112#4047—34no—
113#4047—34no—
114C5×#97—32no—
115C4×C5×C8—32no—
116#3951—34no—
117#3937—32no—
118#3937—32no—
119#3937C2×D312yescomplemented
120#3937C2×D312yescomplemented
121#2956—151noSylow
122C23×C3×C5#4111yescharacteristic
123C22×D15—21no—
124C22×C3×D5—21no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—42no—
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×C3×C4×C5C22×C411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134#1220—22no—
135#1220—22no—
136C2×Dic15—21no—
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⋊#168—22no—
153C3×#168—22no—
154C5×C3⋊C8C22×C414yes—
155C5×C3⋊C8C2×D414yes—
156C2×C3×#41—51no—
157C2×#235—51no—
158C2×C3×M16—51no—
159C2×C3×C42C2×D511yescharacteristic
160#951—52no—
161#950—54no—
162#949—52no—
163#948—54no—
164#948—102no—
165#942—52no—
166#932—52no—
167C2×#208—51no—
168C2×#208—102no—
169C2×#208C2×D511yescharacteristic
170C2×#208C2×D511yescharacteristic
171#907—54no—
172D3×M16—102no—
173#901—102no—
174C3×#104—52no—
175C3×#104—52no—
176#822—54no—
177#805—52no—
178#805—52no—
179#803C2×D512yescomplemented
180C4×C3⋊C8C2×D512yescomplemented
181C22×C4×C5—21no—
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—32no—
202C5×M16—32no—
203C2×C5×C8—32no—
204C2×C5×C8—32no—
205C42×C5—21no—
206C42×C5C22×D311yescharacteristic
207C42×C5C22×D311yescharacteristic
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—64no—
219#676—64no—
220C8×D5—64no—
221C8×D5—64no—
222#575—151no—
223#568—151no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—51no—
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×C5—22no—
240C3×C4×C5—41no—
241C3×C4×C5C4×D411yescharacteristic
242C3×C4×C5C4×D411yescharacteristic
243C3×C4×C5C23×C411yescharacteristic
244C3×C4×C5C22×D411yescharacteristic
245Dic15—22no—
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—21no—
255C22×C3×C4—101no—
256C22×C3×C4C22×D511yescharacteristic
257C2×#67—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—52no—
266C3×M16—101no—
267C2×C3×C8—101no—
268C3×C42—21no—
269C3×C42C22×D511yescharacteristic
270C3×C42C22×D511yescharacteristic
271#216—54no—
272#215—54no—
273#214—54no—
274#213—54no—
275#208—52no—
276#208—101no—
277#208—104no—
278#208C4×D512yes—
279#208C4×D512yes—
280#208D2012yes—
281#208D2012yes—
282C2×C3⋊C8—101no—
283C2×C3⋊C8—104no—
284C2×C3⋊C8C22×D512yes—
285C2×C3⋊C8C22×D512yes—
286ΓL(1,𝔽25)—104no—
287D3×C8—104no—
288C23×C5#23711yescharacteristic
289C22×D5—21no—
290C22×D5—61no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—42no—
294C2×C4×C5C2×C4×D311yescharacteristic
295C2×C4×C5C2×C4×D311yescharacteristic
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5#23711yescharacteristic
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×C8—34no—
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—154no—
330#131—154no—
331#131—302no—
332#131—302no—
333C2×M16—31no—
334C2×M16—31no—
335C2×M16—51no—
336C2×M16—151no—
337C2×M16—302no—
338C2×M16—302no—
339C2×C42D3×D511yescharacteristic
340#108—154no—
341#104—52no—
342#104—52no—
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—21no—
363C2×C3×C4—21no—
364C2×C3×C4—42no—
365C2×C3×C4—101no—
366C2×C3×C4—102no—
367C2×C3×C4—102no—
368C2×C3×C4C2×C4×D511yescharacteristic
369C2×C3×C4C2×C4×D511yescharacteristic
370C2×C3×C4C2×D2011yescharacteristic
371C2×C3×C4C2×D2011yescharacteristic
372C2×C3×C4#70911yescharacteristic
373C2×C3×C4C23×D511yescharacteristic
374#67—102no—
375#67—102no—
376C2×Dic3—101no—
377D12—52no—
378D12—101no—
379C4×D3—102no—
380C4×D3—102no—
381Dic6—52no—
382Dic6—101no—
383C3×C8—102no—
384C3⋊C8—102no—
385C3⋊C8C2×C4×D514yes—
386C3⋊C8C2×D2014yes—
387C22×C5—41no—
388C22×C5#67⋊C411yescharacteristic
389C22×C5#67⋊C411yescharacteristic
390C22×C5C2×#23711yescharacteristic
391C2×D5—22no—
392C2×D5—62no—
393C2×D5—81no—
394C2×D5—241no—
395C4×C5—22no—
396C4×C5—41no—
397C4×C5#67⋊C411yescharacteristic
398C4×C5#67⋊C411yescharacteristic
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×D3×D411yescharacteristic
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—21no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—32no—
426M16—32no—
427M16—32no—
428M16—32no—
429M16—52no—
430M16—101no—
431M16—152no—
432M16—304no—
433M16—304no—
434M16—301no—
435C2×C8—32no—
436C2×C8—32no—
437C2×C8—101no—
438C2×C8—304no—
439C2×C8—304no—
440C2×C8—301no—
441C42—21no—
442C42C2×D3×D511yescharacteristic
443C42C2×D3×D511yescharacteristic
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—22no—
454C3×C4—41no—
455C3×C4—102no—
456C3×C4C4×D2011yescharacteristic
457C3×C4C4×D2011yescharacteristic
458C3×C4C22×C4×D511yescharacteristic
459C3×C4C22×D2011yescharacteristic
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5C2×#67⋊C411yescharacteristic
465D5—42no—
466D5—122no—
467C23—101no—
468C23—301no—
469C23#677911yescharacteristic
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—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—101no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—301no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4C4×D3×D511yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4D3×D2011yescharacteristic
494C2×C4D3×D2011yescharacteristic
495C2×C4#677911yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—34no—
498C8—34no—
499C8—102no—
500C8—302no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—202no—
505C2×C3C2×C4×D2011yescharacteristic
506D3—202no—
507C5#7898011yescharacteristic, complemented, Sylow
508C22—41no—
509C22—102no—
510C22—302no—
511C22—401no—
512C22—1201no—
513C22#9139511yescharacteristic
514C22#9139511yescharacteristic
515C22C2×#677911yescharacteristic
516C4—22no—
517C4—41no—
518C4—102no—
519C4—302no—
520C4#9139511yescharacteristic
521C4#9139511yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×D3×D2011yescharacteristic
524C3#1061027211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—202no—
529C2—602no—
530C2C2×#9139511yescharacteristic
subgroupG/H
centerC4C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5C2×C4×D4
prime radical#11754154C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11754130C2semidirect
3. #11754120C2semidirect
4. C2×#91089C2semidirect
5. C4×C5×#208C2semidirect
6. C2×C3×#3937C2semidirect
7. #11748480C2semidirect
8. #11747017C2semidirect
9. #11747016C2semidirect
18. #91315C4semidirect
19. #91313C4semidirect
20. #91312C4semidirect
22. #91301C4semidirect
24. #91291C22semidirect
27. #91283C22semidirect
29. #91089C22semidirect
30. #91089C22semidirect
31. C5×#803C22semidirect
32. C4×C5×C3⋊C8C22semidirect
33. C3×#3937C22semidirect
34. C3×#3937C22semidirect
35. #90993C22semidirect
43. C2×#3937D3semidirect
79. #6662C2×C4semidirect
80. #6658C2×C4semidirect
81. #6657C2×C4semidirect
82. #6653C2×C4semidirect
93. C4×#208D5semidirect
119. #3937C2×D3semidirect
120. #3937C2×D3semidirect
179. #803C2×D5semidirect
180. C4×C3⋊C8C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#78980semidirect
524. C3#10610272semidirect

Maximal subgroups

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

subgroupindex
#117541542
#117541302
#117541202
C2×#910892
C4×C5×#2082
C2×C3×#39372
#117484802
#117470172
#117470162
#106102723
#789805