Finite Group Databasebeta

← #14418168

Subgroups — #14418168

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#11754145C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic, complemented
3#11754125C211yesmaximal, characteristic, complemented
4C2×#91089C211yesmaximal, characteristic, complemented
5C2×C5×#805C211yesmaximal, characteristic, complemented
6C3×C4×#681C211yesmaximal, characteristic, complemented
7#11748476C211yesmaximal, characteristic, complemented
8#11747019C214yesmaximal, complemented
9#11747018C214yesmaximal, complemented
10#10610711—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18#91322C412yescomplemented
19#91321C412yescomplemented
20#91305C412yescomplemented
21#91304C412yescomplemented
22#91303C2214yes—
23#91292—22no—
24#91291—22no—
25#91290C2214yescomplemented
26#91288—22no—
27D3×#681—22no—
28#91286C2214yescomplemented
29#91089C2212yescomplemented
30#91089C2212yescomplemented
31C5×#805C2212yescomplemented
32C5×#805C2212yescomplemented
33C3×#3935C2212yescomplemented
34C3×C4×#168C2212yescomplemented
35#90991C2214yescomplemented
36#78541—51nomaximal, Hall
37#66156—31no—
38#66153—31no—
39#66079—31no—
40C2×C5×#104—31no—
41#65413—31no—
42C2×#3937—31no—
43C4×#681D311yescharacteristic, complemented
44#65113—34no—
45#65112—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×C5×#67—21no—
57C5×#235—21no—
58C5×#235—21no—
59C5×#235C2×C412yes—
60C5×#235C2312yes—
61C2×C5×D12C2×C411yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2×C411yescharacteristic
64C3×C42×C5—21no—
65C3×C42×C5C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67#6710—21no—
68#6710C2312yes—
69C2×C3⋊#168—21no—
70C5×#208—21no—
71C5×#208C2312yes—
72C2×C5×C3⋊C8—21no—
73C3×#681C2×C412yes—
74C3×#681C2×C412yes—
75C3×#681D412yes—
76C3×#681D412yes—
77C2×C3×#168C2312yes—
78C2×C3×#168C2312yes—
79#6663C2×C414yescomplemented
80#6660C2×C414yescomplemented
81#6659C2×C414yescomplemented
82#6654C2×C414yescomplemented
83#6651—24no—
84#6650—24no—
85#6648—24no—
86D3×#168—24no—
87#5748—51no—
88#5745—51no—
89#5745—51no—
90C3×C4×M16—51no—
91#5125—51no—
92C2×#805—51no—
93C2×#805D511yescharacteristic, complemented
94#4717—54no—
95#4700—54no—
96C2×C5×#41—31no—
97C2×#709—31no—
98C2×C5×M16—31no—
99C2×C42×C5C2×D311yescharacteristic
100#4097—32no—
101#4096—34no—
102#4095—32no—
103#4094—34no—
104#4094—62no—
105#4088—32no—
106#4078—32no—
107C2×#681—31no—
108C2×#681—62no—
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#3935C2×D312yescomplemented
120C4×#168C2×D312yescomplemented
121#2956—151noSylow
122C23×C3×C5#4111yescharacteristic
123C22×D15—21no—
124C22×C5×D3—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—
143C5×#67—22no—
144C5×#67—22no—
145C2×C5×Dic3—21no—
146C5×D12—21no—
147C5×D12C22×C412yes—
148C4×C5×D3—22no—
149C4×C5×D3—22no—
150C5×Dic6—21no—
151C5×Dic6C22×C412yes—
152C3⋊#168—22no—
153C3×#168C22×C414yes—
154C3×#168C2×D414yes—
155C5×C3⋊C8—22no—
156C2×#235—51no—
157C2×#235C2×D511yescharacteristic
158C2×C3×M16—51no—
159C2×C3×M16—51no—
160C2×C3×C42C2×D511yescharacteristic
161C2×#208—51no—
162C2×#208C2×D511yescharacteristic
163#909—52no—
164#909—52no—
165#908—52no—
166#908—52no—
167#907—102no—
168#907—102no—
169D3×M16—102no—
170D3×M16—102no—
171#904—54no—
172#901—54no—
173#901—54no—
174C3×#97—52no—
175C3×C4×C8—52no—
176#819—54no—
177#805—52no—
178#805—52no—
179#805C2×D512yescomplemented
180#805C2×D512yescomplemented
181C5×#41—32no—
182C5×#41—32no—
183C5×#41—61no—
184C5×#41—61no—
185C2×C5×Q8—31no—
186C2×C5×D4—31no—
187C2×C5×D4—61no—
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—21no—
203C42×C5C22×D311yescharacteristic
204C42×C5C22×D311yescharacteristic
205#689—34no—
206#688—34no—
207#687—34no—
208#686—34no—
209#681—32no—
210#681—61no—
211#681—64no—
212#681C4×D312yes—
213#681C4×D312yes—
214#681D1212yes—
215#681D1212yes—
216C2×#168—61no—
217C2×#168—64no—
218C2×#168C22×D312yes—
219C2×#168C22×D312yes—
220#676—64no—
221C8×D5—64no—
222#575—151no—
223#568—151no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—31no—
229C2×#104—151no—
230C4×M16—51no—
231C22×C3×C5—41no—
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C2×D15—22no—
236C2×D15—81no—
237C2×C5×D3—22no—
238C2×C5×D3—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—
246C5×Dic3—22no—
247C22×C3×C4—21no—
248C22×C3×C4C22×D511yescharacteristic
249C2×#67—21no—
250C2×#67—101no—
251#235—21no—
252#235—21no—
253#235—52no—
254#235—52no—
255#235—101no—
256#235—101no—
257#235C4×D512yes—
258#235C22×D512yes—
259C2×D12—51no—
260C2×D12C4×D511yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—101no—
263C2×Dic6—51no—
264C2×Dic6C4×D511yescharacteristic
265C3×M16—52no—
266C3×M16—52no—
267C3×M16—52no—
268C3×M16—52no—
269C2×C3×C8—52no—
270C2×C3×C8—52no—
271C3×C42—21no—
272C3×C42C22×D511yescharacteristic
273C3×C42C22×D511yescharacteristic
274#208—21no—
275#208—52no—
276#208—101no—
277#208C22×D512yes—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—101no—
280Dic12—54no—
281D24—54no—
282#204—54no—
283#204—54no—
284ΓL(1,𝔽25)—104no—
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287D3×C8—104no—
288C23×C5—61no—
289C23×C5#23511yescharacteristic
290C22×D5—61no—
291C5×Q8—32no—
292C5×Q8—61no—
293C5×D4—32no—
294C5×D4—62no—
295C5×D4—62no—
296C5×D4—61no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—42no—
300C2×C4×C5—61no—
301C2×C4×C5—62no—
302C2×C4×C5—62no—
303C2×C4×C5C2×C4×D311yescharacteristic
304C2×C4×C5C2×C4×D311yescharacteristic
305C2×C4×C5C2×D1211yescharacteristic
306C2×C4×C5C2×D1211yescharacteristic
307C2×C4×C5#23511yescharacteristic
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—62no—
320#168C2×C4×D314yes—
321#168C2×D1214yes—
322C2×#41—31no—
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—51no—
335C2×M16—51no—
336C2×M16—151no—
337C2×M16—302no—
338C2×M16—302no—
339C2×C42D3×D511yescharacteristic
340#108—154no—
341#104—32no—
342#104—32no—
343#104—152no—
344#104—152no—
345#97—52no—
346C4×C8—52no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5—21no—
350C2×C3×C5C2×C4×D411yescharacteristic
351D15—42no—
352C5×D3—42no—
353C23×C3#71111yescharacteristic
354C22×D3—21no—
355C22×D3—101no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—42no—
359C2×C3×C4C2×C4×D511yescharacteristic
360C2×C3×C4C2×C4×D511yescharacteristic
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4#71111yescharacteristic
364C2×C3×C4C23×D511yescharacteristic
365#67—22no—
366#67—22no—
367#67—102no—
368#67—102no—
369C2×Dic3—21no—
370C2×Dic3—101no—
371D12—21no—
372D12—52no—
373D12—101no—
374D12C2×C4×D512yes—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—102no—
378C4×D3—102no—
379Dic6—21no—
380Dic6—52no—
381Dic6—101no—
382Dic6C2×C4×D512yes—
383C3×C8—54no—
384C3×C8—54no—
385C3⋊C8—22no—
386C3⋊C8—102no—
387C22×C5—41no—
388C22×C5—62no—
389C22×C5—241no—
390C22×C5C4×D1211yescharacteristic
391C22×C5C4×D1211yescharacteristic
392C22×C5C2×#23511yescharacteristic
393C2×D5—62no—
394C2×D5—241no—
395C4×C5—22no—
396C4×C5—41no—
397C4×C5—62no—
398C4×C5C4×D1211yescharacteristic
399C4×C5C4×D1211yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C22×D1211yescharacteristic
402Dic5—62no—
403#41—32no—
404#41—32no—
405#41—61no—
406#41—61no—
407#41—152no—
408#41—152no—
409#41—301no—
410#41—301no—
411C2×Q8—31no—
412C2×Q8—151no—
413C2×D4—31no—
414C2×D4—61no—
415C2×D4—151no—
416C2×D4—301no—
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—52no—
430M16—61no—
431M16—152no—
432M16—304no—
433M16—304no—
434M16—301no—
435C2×C8—52no—
436C2×C8—52no—
437C2×C8—61no—
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#402711yescharacteristic
447C22×C3#402711yescharacteristic
448C22×C3C2×#71111yescharacteristic
449C2×D3—22no—
450C2×D3—81no—
451C2×D3—102no—
452C2×D3—401no—
453C3×C4—22no—
454C3×C4—41no—
455C3×C4#402711yescharacteristic
456C3×C4#402711yescharacteristic
457C3×C4C22×C4×D511yescharacteristic
458C3×C4C2×D4×D511yescharacteristic
459Dic3—22no—
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—122no—
465C2×C5C2×C4×D1211yescharacteristic
466D5—122no—
467C23—61no—
468C23—301no—
469C23#678211yescharacteristic
470Q8—32no—
471Q8—61no—
472Q8—152no—
473Q8—301no—
474D4—32no—
475D4—62no—
476D4—62no—
477D4—61no—
478D4—152no—
479D4—302no—
480D4—302no—
481D4—301no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—301no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4C4×D3×D511yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4D5×D1211yescharacteristic
494C2×C4D5×D1211yescharacteristic
495C2×C4#678211yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—54no—
498C8—54no—
499C8—62no—
500C8—302no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3C2×#402711yescharacteristic
505D3—42no—
506D3—202no—
507C5#7854111yescharacteristic, complemented, Sylow
508C22—41no—
509C22—62no—
510C22—241no—
511C22—302no—
512C22—1201no—
513C22#9140511yescharacteristic
514C22#9140511yescharacteristic
515C22C2×#678211yescharacteristic
516C4—22no—
517C4—41no—
518C4—62no—
519C4—302no—
520C4#9140511yescharacteristic
521C4#9140511yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×D5×D1211yescharacteristic
524C3#1061071111yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—122no—
529C2—602no—
530C2C2×#9140511yescharacteristic
subgroupG/H
centerC4C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5C2×C4×D4
prime radical#11754145C2
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. #11754125C2semidirect
4. C2×#91089C2semidirect
5. C2×C5×#805C2semidirect
6. C3×C4×#681C2semidirect
7. #11748476C2semidirect
8. #11747019C2semidirect
9. #11747018C2semidirect
18. #91322C4semidirect
19. #91321C4semidirect
20. #91305C4semidirect
21. #91304C4semidirect
25. #91290C22semidirect
28. #91286C22semidirect
29. #91089C22semidirect
30. #91089C22semidirect
31. C5×#805C22semidirect
32. C5×#805C22semidirect
33. C3×#3935C22semidirect
34. C3×C4×#168C22semidirect
35. #90991C22semidirect
43. C4×#681D3semidirect
79. #6663C2×C4semidirect
80. #6660C2×C4semidirect
81. #6659C2×C4semidirect
82. #6654C2×C4semidirect
93. C2×#805D5semidirect
119. #3935C2×D3semidirect
120. C4×#168C2×D3semidirect
179. #805C2×D5semidirect
180. #805C2×D5semidirect
444. C3×C5#2956semidirect
507. C5#78541semidirect
524. C3#10610711semidirect

Maximal subgroups

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

subgroupindex
#117541452
#117541302
#117541252
C2×#910892
C2×C5×#8052
C3×C4×#6812
#117484762
#117470192
#117470182
#106107113
#785415