Finite Group Databasebeta

← #14418159

Subgroups — #14418159

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#11756581C211yesmaximal, characteristic
2C3×#66153C211yesmaximal, characteristic, complemented
3#11754130C211yesmaximal, characteristic, complemented
4C2×C5×#837C211yesmaximal, characteristic, complemented
5#11749435C214yesmaximal, complemented
6#11749434C214yesmaximal, complemented
7#11748478C211yesmaximal, characteristic, complemented
8C2×#90980C211yesmaximal, characteristic, complemented
9Dic3×#681C211yesmaximal, characteristic, complemented
10#10610711—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×#6817C2211yescharacteristic
13#91840C412yescomplemented
14#91839C2214yes—
15#91838C412yescomplemented
16#91831C412yescomplemented
17#91821C412yescomplemented
18C2×#6710C2211yescharacteristic
19C2×C4×C5×Dic3C2211yescharacteristic
20C2×C5×#208C2211yescharacteristic
21C3×#4094—22no—
22C3×#4094C2214yescomplemented
23C2×C3×#681—22no—
24C2×C3×#681C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91292—22no—
27#91291—22no—
28#91290C2214yescomplemented
29C5×#837C2212yescomplemented
30C5×#837C2212yescomplemented
31#90992C2214yescomplemented
32#90980C2212yescomplemented
33#90980C2212yescomplemented
34#90953C2212yescomplemented
35Dic3×#168C2212yescomplemented
36#83811—51nomaximal, Hall
37#66156—31no—
38#66153D311yescharacteristic, complemented
39#66079—31no—
40C2×C5×#104—31no—
41#65413—31no—
42C2×#3937—31no—
43C4×#681—31no—
44#65113—34no—
45#65112—34no—
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—
56#6817—21no—
57#6817—21no—
58#6817C2×C412yes—
59#6817C2312yes—
60C2×D60C2×C411yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30C2×C411yescharacteristic
63C22×C5×Dic3—21no—
64#6718C2×C414yescomplemented
65#6717C2×C414yescomplemented
66#6716C2×C414yescomplemented
67#6715C2×C414yescomplemented
68#6710C2×C412yes—
69#6710C2×C412yes—
70C2×C3⋊#168C2312yes—
71C4×C5×Dic3—21no—
72C4×C5×Dic3C2311yescharacteristic
73C4×C5×Dic3C2311yescharacteristic
74C5×#208—21no—
75C5×#208C2312yes—
76C2×C5×C3⋊C8—21no—
77C3×#681—21no—
78C3×#681—24no—
79C3×#681D412yes—
80C3×#681D412yes—
81C3×#681C2312yes—
82C2×C3×#168—21no—
83C2×C3×#168—24no—
84C2×C3×#168C2312yes—
85#6651—24no—
86#6648—24no—
87C3×#568—51no—
88#5822—51no—
89#5745—51no—
90C2×#837D511yescharacteristic, complemented
91#5145—54no—
92#5144—54no—
93C2×#825—51no—
94#5124—51no—
95Dic3×M16—51no—
96C2×C5×#41C2×D311yescharacteristic
97C2×#709—31no—
98C2×C5×M16—31no—
99C2×C42×C5—31no—
100#4097—32no—
101#4096—34no—
102#4095—32no—
103#4094—22no—
104#4094C2×D314yescomplemented
105#4088—32no—
106#4078—32no—
107C2×#681—22no—
108C2×#681—31no—
109C2×#681C2×D311yescharacteristic
110C2×#681C2×D311yescharacteristic
111#4053—34no—
112D5×M16—62no—
113#4047—62no—
114C5×#104—32no—
115C5×#104—32no—
116#3954—34no—
117#3937—32no—
118#3937—32no—
119#3935—32no—
120C4×#168—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—
143D60—21no—
144D60C22×C412yes—
145C4×D15—22no—
146C4×D15—22no—
147Dic30—21no—
148Dic30C22×C412yes—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—42no—
152C3⋊#168C22×C414yes—
153C3×#168—22no—
154C3×#168C2×D414yes—
155C5×C3⋊C8—22no—
156C2×C3×#41C2×D511yescharacteristic
157C2×#235—51no—
158C3×#131—54no—
159C3×#131—102no—
160C2×C3×M16—51no—
161C2×C3×M16—51no—
162C2×C3×M16—102no—
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#837C2×D512yescomplemented
175#837C2×D512yescomplemented
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×C5—61no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—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—32no—
200C5×M16—61no—
201C2×C5×C8—61no—
202C42×C5—31no—
203C42×C5—31no—
204C42×C5—61no—
205#689—34no—
206#688—34no—
207#687—34no—
208#686—34no—
209#681—21no—
210#681—24no—
211#681—32no—
212#681—32no—
213#681#6712yes—
214#681#6712yes—
215#681C22×D312yes—
216C2×#168—21no—
217C2×#168—24no—
218C2×#168—32no—
219C2×#168C22×D312yes—
220#676—64no—
221C8×D5—64no—
222#575—151no—
223#568—51no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—31no—
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—
245C5×Dic3—22no—
246C5×Dic3—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—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—52no—
267C3×M16—52no—
268C3×M16—104no—
269C3×M16—101no—
270C2×C3×C8—52no—
271C2×C3×C8—104no—
272C2×C3×C8—101no—
273#216—54no—
274#215—54no—
275#214—54no—
276#213—54no—
277C4×Dic3—21no—
278C4×Dic3C22×D511yescharacteristic
279C4×Dic3C22×D511yescharacteristic
280#208—21no—
281#208—52no—
282#208—52no—
283#208C22×D512yes—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—52no—
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×C5—61no—
301C2×C4×C5—61no—
302C2×C4×C5—122no—
303C2×C4×C5C2×C4×D311yescharacteristic
304C2×C4×C5C2×C4×D311yescharacteristic
305C2×C4×C5#23511yescharacteristic
306C2×C4×C5C2×#6711yescharacteristic
307C2×C4×C5C2×#6711yescharacteristic
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—62no—
310C22⋊D5—62no—
311C2×Dic5—61no—
312D20—32no—
313D20—61no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—32no—
317Dic10—61no—
318C5×C8—62no—
319#168—22no—
320#168—34no—
321#168C2×#6714yes—
322C2×#41—151no—
323C2×#41D3×D511yescharacteristic
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—51no—
336C2×M16—102no—
337C2×M16—151no—
338C2×M16—302no—
339C2×C42—31no—
340#108—154no—
341#104—32no—
342#104—32no—
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#71111yescharacteristic
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×C4D4×D511yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4#71111yescharacteristic
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—54no—
384C3×C8—102no—
385C3⋊C8—22no—
386C3⋊C8—54no—
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×C5—62no—
397C4×C5—121no—
398C4×C5C4×#6711yescharacteristic
399C4×C5C4×#6711yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C22×#6711yescharacteristic
402Dic5—62no—
403#41—21no—
404#41—21no—
405#41—152no—
406#41—152no—
407#41—301no—
408#41—301no—
409#41#120012yes—
410#41C2×D3×D512yes—
411C2×Q8—151no—
412C2×Q8#120011yescharacteristic
413C2×D4—21no—
414C2×D4—151no—
415C2×D4—301no—
416C2×D4#120011yescharacteristic
417C22×C4—21no—
418C22×C4—61no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—32no—
426M16—52no—
427M16—52no—
428M16—52no—
429M16—61no—
430M16—104no—
431M16—101no—
432M16—152no—
433M16—152no—
434M16—304no—
435C2×C8—52no—
436C2×C8—61no—
437C2×C8—104no—
438C2×C8—101no—
439C2×C8—152no—
440C2×C8—304no—
441C42—31no—
442C42—31no—
443C42—61no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—81no—
448C22×C3#402711yescharacteristic
449C22×C3#402711yescharacteristic
450C22×C3C2×#71111yescharacteristic
451C2×D3—102no—
452C2×D3—401no—
453C3×C4—22no—
454C3×C4#402711yescharacteristic
455C3×C4#402711yescharacteristic
456C3×C4C22×C4×D511yescharacteristic
457C3×C4C2×D4×D511yescharacteristic
458Dic3—22no—
459Dic3—41no—
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—42no—
465C2×C5C2×C4×#6711yescharacteristic
466D5—122no—
467C23—21no—
468C23—301no—
469C23#678211yescharacteristic
470Q8—21no—
471Q8—152no—
472Q8—301no—
473Q8C2×#120012yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—152no—
478D4—302no—
479D4—302no—
480D4—301no—
481D4C2×#120012yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—122no—
488C2×C4—301no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4#678211yescharacteristic
492C2×C4C2×#120011yescharacteristic
493C2×C4C2×#120011yescharacteristic
494C2×C4D5×#6711yescharacteristic
495C2×C4D5×#6711yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—54no—
498C8—62no—
499C8—102no—
500C8—154no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3C2×#402711yescharacteristic
506D3—202no—
507C5#8381111yescharacteristic, complemented, Sylow
508C22—22no—
509C22—41no—
510C22—81no—
511C22—302no—
512C22—1201no—
513C22#9155211yescharacteristic
514C22#9155211yescharacteristic
515C22C2×#678211yescharacteristic
516C4—22no—
517C4—62no—
518C4—121no—
519C4—302no—
520C4#9155211yescharacteristic
521C4#9155211yescharacteristic
522C4C22×#120011yescharacteristic
523C4C2×D5×#6711yescharacteristic
524C3#1061071111yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—42no—
529C2—602no—
530C2C2×#9155211yescharacteristic
subgroupG/H
centerC4C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×C4×D4
prime radical#11756581C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#66153C2semidirect
3. #11754130C2semidirect
4. C2×C5×#837C2semidirect
5. #11749435C2semidirect
6. #11749434C2semidirect
7. #11748478C2semidirect
8. C2×#90980C2semidirect
9. Dic3×#681C2semidirect
13. #91840C4semidirect
15. #91838C4semidirect
16. #91831C4semidirect
17. #91821C4semidirect
22. C3×#4094C22semidirect
28. #91290C22semidirect
29. C5×#837C22semidirect
30. C5×#837C22semidirect
31. #90992C22semidirect
32. #90980C22semidirect
33. #90980C22semidirect
34. #90953C22semidirect
35. Dic3×#168C22semidirect
38. #66153D3semidirect
64. #6718C2×C4semidirect
65. #6717C2×C4semidirect
66. #6716C2×C4semidirect
67. #6715C2×C4semidirect
90. C2×#837D5semidirect
104. #4094C2×D3semidirect
174. #837C2×D5semidirect
175. #837C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#83811semidirect
524. C3#10610711semidirect

Maximal subgroups

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

subgroupindex
#117565812
C3×#661532
#117541302
C2×C5×#8372
#117494352
#117494342
#117484782
C2×#909802
Dic3×#6812
#106107113
#838115