Finite Group Databasebeta

← #14418162

Subgroups — #14418162

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
1C5×#5819C211yesmaximal, characteristic, complemented
2C3×#66156C211yesmaximal, characteristic
3#11754120C211yesmaximal, characteristic, complemented
4C2×#91121C211yesmaximal, characteristic, complemented
5#11749437C214yesmaximal, complemented
6#11749436C214yesmaximal, complemented
7#11748476C211yesmaximal, characteristic, complemented
8C2×#90976C211yesmaximal, characteristic, complemented
9#11748328C211yesmaximal, characteristic, complemented
10#10615542—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C5×#948—22no—
16C5×#948C2214yescomplemented
17C2×C5×#208—22no—
18C2×C5×#208C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C3×#4097C412yescomplemented
21C3×#4096C2214yes—
22C3×#4095C412yescomplemented
23C3×#4088C412yescomplemented
24C3×#4078C412yescomplemented
25C2×C3×#681C2211yescharacteristic
26#91284—22no—
27#91283C2214yescomplemented
28D5×#208—22no—
29#91121C2212yescomplemented
30#91121C2212yescomplemented
31#90991C2214yescomplemented
32#90976C2212yescomplemented
33#90976C2212yescomplemented
34#90954C2212yescomplemented
35#90951C2212yescomplemented
36#84000—51nomaximal, Hall
37C5×#568—31no—
38#66156D311yescharacteristic
39#66079—31no—
40C2×#3969—31no—
41#65434—34no—
42#65433—34no—
43C2×#3957—31no—
44#65413—31no—
45M16×Dic5—31no—
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
55C22×Dic15—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
64C4×Dic15—21no—
65C4×Dic15C2311yescharacteristic
66C4×Dic15C2311yescharacteristic
67#6710—21no—
68#6710C2312yes—
69C2×C3⋊#168—21no—
70C5×#208—21no—
71C5×#208—24no—
72C5×#208D412yes—
73C5×#208D412yes—
74C5×#208C2312yes—
75C2×C5×C3⋊C8—21no—
76C2×C5×C3⋊C8—24no—
77C2×C5×C3⋊C8C2312yes—
78C3×#689C2×C414yescomplemented
79C3×#688C2×C414yescomplemented
80C3×#687C2×C414yescomplemented
81C3×#686C2×C414yescomplemented
82C3×#681C2×C412yes—
83C3×#681C2×C412yes—
84C2×C3×#168C2312yes—
85#6649—24no—
86D5×C3⋊C8—24no—
87C3×#575—51no—
88#5819—51no—
89#5819D511yescharacteristic, complemented
90C2×#837—51no—
91C2×#837—51no—
92#5197—54no—
93#5196—54no—
94#5125—51no—
95Dic3×M16—51no—
96C2×C5×#41C2×D311yescharacteristic
97C2×#709C2×D311yescharacteristic
98C5×#131—34no—
99C5×#131—62no—
100C2×C5×M16—31no—
101C2×C5×M16—31no—
102C2×C5×M16—62no—
103#4097Dic312yescomplemented
104#4096C2×D314yes—
105#4095Dic312yescomplemented
106#4088Dic312yescomplemented
107#4078Dic312yescomplemented
108C2×C4×Dic5—31no—
109C2×#681—31no—
110C2×#681C2×D311yescharacteristic
111#4053—62no—
112D5×M16—62no—
113#4047—34no—
114#3969—32no—
115#3969—32no—
116#3957—32no—
117#3957—32no—
118#3954—34no—
119#3947—32no—
120C8×Dic5—32no—
121#2956—151noSylow
122C23×C3×C5—21no—
123C23×C3×C5#4111yescharacteristic
124C22×C3×D5—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
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—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⋊#168—22no—
153C3×#168C22×C414yes—
154C5×C3⋊C8—22no—
155C5×C3⋊C8C2×D414yes—
156C2×C3×#41—51no—
157C2×C3×#41C2×D511yescharacteristic
158C3×#137—52no—
159C3×#137—52no—
160C3×AGL(1,ℤ/8)—52no—
161C3×AGL(1,ℤ/8)—52no—
162C3×#135—54no—
163C2×C3×M16—51no—
164#948—22no—
165#948—54no—
166#948—102no—
167#948C2×D514yescomplemented
168C2×C4×Dic3—51no—
169C2×#208—22no—
170C2×#208—51no—
171C2×#208—102no—
172C2×#208C2×D511yescharacteristic
173C2×#208C2×D511yescharacteristic
174#837—52no—
175#837—52no—
176#837—52no—
177#837—52no—
178#819—54no—
179#815—52no—
180C8×Dic3—52no—
181C5×#41—21no—
182C5×#41—21no—
183C5×#41C2×Dic312yes—
184C5×#41C22×D312yes—
185C2×C5×Q8C2×Dic311yescharacteristic
186C2×C5×D4—21no—
187C2×C5×D4C2×Dic311yescharacteristic
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—21no—
191C22×Dic5—61no—
192#709—21no—
193#709—21no—
194#709C2×Dic312yes—
195#709C22×D312yes—
196C2×D20C2×Dic311yescharacteristic
197C2×C4×D5—21no—
198C2×Dic10C2×Dic311yescharacteristic
199C5×M16—32no—
200C5×M16—32no—
201C5×M16—32no—
202C5×M16—64no—
203C5×M16—61no—
204C2×C5×C8—32no—
205C2×C5×C8—64no—
206C2×C5×C8—61no—
207#689C2×Dic314yescomplemented
208#688C2×Dic314yescomplemented
209#687C2×Dic314yescomplemented
210#686C2×Dic314yescomplemented
211C4×Dic5—31no—
212C4×Dic5—31no—
213C4×Dic5—61no—
214#681—32no—
215#681—61no—
216#681C2×Dic312yes—
217#681C2×Dic312yes—
218C2×#168—61no—
219C2×#168C22×D312yes—
220#676—64no—
221C8×D5—64no—
222#575—51no—
223#568—31no—
224#568—151no—
225#444—154no—
226#443—154no—
227#430—151no—
228C2×#104—151no—
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×C3×D5—22no—
238C2×C3×D5—81no—
239C3×C4×C5—22no—
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C4×D411yescharacteristic
242C3×C4×C5C23×C411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—22no—
245Dic15—41no—
246C3×Dic5—22no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41—52no—
250C3×#41—52no—
251C3×#41—101no—
252C3×#41—101no—
253C3×#41C4×D512yes—
254C3×#41C22×D512yes—
255C2×C3×Q8—51no—
256C2×C3×Q8C4×D511yescharacteristic
257C2×C3×D4—21no—
258C2×C3×D4—51no—
259C2×C3×D4—101no—
260C2×C3×D4C4×D511yescharacteristic
261C22×C3×C4—21no—
262C22×C3×C4—101no—
263C22×C3×C4C22×D511yescharacteristic
264C22×Dic3—101no—
265C3×Q16—54no—
266C3×SD16—54no—
267C3×SD16—54no—
268C3×D8—54no—
269C3×M16—52no—
270C3×M16—52no—
271C2×C3×C8—52no—
272C4×Dic3—51no—
273C4×Dic3—51no—
274C4×Dic3—101no—
275#208—21no—
276#208—24no—
277#208—52no—
278#208—101no—
279#208—104no—
280#208C22⋊D512yes—
281#208C22⋊D512yes—
282#208C22×D512yes—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—24no—
285C2×C3⋊C8—101no—
286C2×C3⋊C8—104no—
287C2×C3⋊C8C22×D512yes—
288C23×C5—21no—
289C23×C5#23711yescharacteristic
290C22×D5—21no—
291C5×Q8—21no—
292C5×Q8C22×Dic312yes—
293C5×D4—22no—
294C5×D4—22no—
295C5×D4—21no—
296C5×D4C22×Dic312yes—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5#23711yescharacteristic
303C2×C4×C5C22×Dic311yescharacteristic
304C2×C4×C5C22×Dic311yescharacteristic
305C2×C4×C5C23×D311yescharacteristic
306C22⋊D5—22no—
307C22⋊D5—22no—
308C2×Dic5—21no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—122no—
312D20—21no—
313D20C22×Dic312yes—
314C4×D5—22no—
315C4×D5—22no—
316Dic10—21no—
317Dic10C22×Dic312yes—
318C5×C8—34no—
319C5×C8—62no—
320#168—62no—
321#168C22×Dic314yes—
322C2×#41—51no—
323C2×#41D3×D511yescharacteristic
324#137—52no—
325#137—52no—
326AGL(1,ℤ/8)—52no—
327AGL(1,ℤ/8)—52no—
328#135—54no—
329#131—34no—
330#131—62no—
331#131—154no—
332#131—302no—
333C2×M16—31no—
334C2×M16—31no—
335C2×M16—51no—
336C2×M16—62no—
337C2×M16—151no—
338C2×M16—302no—
339C2×C42—151no—
340#108—154no—
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×C5—42no—
351C2×C3×C5C2×C4×D411yescharacteristic
352C3×D5—42no—
353C23×C3—21no—
354C23×C3—101no—
355C23×C3#70911yescharacteristic
356C3×Q8—21no—
357C3×Q8—52no—
358C3×Q8—101no—
359C3×Q8C2×C4×D512yes—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—21no—
363C3×D4—52no—
364C3×D4—102no—
365C3×D4—102no—
366C3×D4—101no—
367C3×D4C2×C4×D512yes—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—101no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4C2×C4×D511yescharacteristic
375C2×C3×C4C2×C4×D511yescharacteristic
376C2×C3×C4#70911yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380C2×Dic3—101no—
381C2×Dic3—101no—
382C2×Dic3—202no—
383C3×C8—54no—
384C3⋊C8—22no—
385C3⋊C8—102no—
386C3⋊C8C2×C22⋊D514yes—
387C22×C5—22no—
388C22×C5—41no—
389C22×C5—81no—
390C22×C5D4×Dic311yescharacteristic
391C22×C5D4×Dic311yescharacteristic
392C22×C5C2×#23711yescharacteristic
393C2×D5—22no—
394C2×D5—81no—
395C4×C5—22no—
396C4×C5D4×Dic311yescharacteristic
397C4×C5D4×Dic311yescharacteristic
398C4×C5C2×D3×D411yescharacteristic
399C4×C5C23×Dic311yescharacteristic
400Dic5—22no—
401Dic5—62no—
402Dic5—121no—
403#41—21no—
404#41—21no—
405#41—52no—
406#41—52no—
407#41—101no—
408#41—101no—
409#41D5×Dic312yes—
410#41C2×D3×D512yes—
411C2×Q8—51no—
412C2×Q8D5×Dic311yescharacteristic
413C2×D4—21no—
414C2×D4—51no—
415C2×D4—101no—
416C2×D4D5×Dic311yescharacteristic
417C22×C4—21no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—54no—
422SD16—54no—
423SD16—54no—
424D8—54no—
425M16—32no—
426M16—32no—
427M16—32no—
428M16—52no—
429M16—52no—
430M16—64no—
431M16—61no—
432M16—152no—
433M16—304no—
434M16—301no—
435C2×C8—32no—
436C2×C8—52no—
437C2×C8—64no—
438C2×C8—61no—
439C2×C8—304no—
440C2×C8—301no—
441C42—151no—
442C42—151no—
443C42—301no—
444C3×C5#295611yescharacteristic, complemented, Hall
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—81no—
448C22×C3—102no—
449C22×C3—401no—
450C22×C3C4×C22⋊D511yescharacteristic
451C22×C3C4×C22⋊D511yescharacteristic
452C22×C3C2×#70911yescharacteristic
453C3×C4—22no—
454C3×C4—102no—
455C3×C4C4×C22⋊D511yescharacteristic
456C3×C4C4×C22⋊D511yescharacteristic
457C3×C4C22×C4×D511yescharacteristic
458C3×C4C22×C22⋊D511yescharacteristic
459Dic3—102no—
460Dic3—201no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—42no—
465C2×C5C2×D4×Dic311yescharacteristic
466D5—42no—
467C23—21no—
468C23—101no—
469C23#677911yescharacteristic
470Q8—21no—
471Q8—52no—
472Q8—101no—
473Q8C2×D5×Dic312yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—52no—
478D4—102no—
479D4—102no—
480D4—101no—
481D4C2×D5×Dic312yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—101no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4C2×D5×Dic311yescharacteristic
492C2×C4C2×D5×Dic311yescharacteristic
493C2×C4#677911yescharacteristic
494C2×C4D3×C22⋊D511yescharacteristic
495C2×C4D3×C22⋊D511yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—34no—
498C8—54no—
499C8—62no—
500C8—302no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3—202no—
506C2×C3C2×C4×C22⋊D511yescharacteristic
507C5#8400011yescharacteristic, complemented, Sylow
508C22—22no—
509C22—41no—
510C22—81no—
511C22—102no—
512C22—401no—
513C22Dic3×C22⋊D511yescharacteristic
514C22Dic3×C22⋊D511yescharacteristic
515C22C2×#677911yescharacteristic
516C4—22no—
517C4—102no—
518C4—302no—
519C4—601no—
520C4Dic3×C22⋊D511yescharacteristic
521C4Dic3×C22⋊D511yescharacteristic
522C4C22×D5×Dic311yescharacteristic
523C4C2×D3×C22⋊D511yescharacteristic
524C3#1061554211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—42no—
529C2—202no—
530C2C2×Dic3×C22⋊D511yescharacteristic
subgroupG/H
centerC4C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×C4×D4
prime radicalC3×#66156C2
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
1. C5×#5819C2semidirect
3. #11754120C2semidirect
4. C2×#91121C2semidirect
5. #11749437C2semidirect
6. #11749436C2semidirect
7. #11748476C2semidirect
8. C2×#90976C2semidirect
9. #11748328C2semidirect
16. C5×#948C22semidirect
20. C3×#4097C4semidirect
22. C3×#4095C4semidirect
23. C3×#4088C4semidirect
24. C3×#4078C4semidirect
27. #91283C22semidirect
29. #91121C22semidirect
30. #91121C22semidirect
31. #90991C22semidirect
32. #90976C22semidirect
33. #90976C22semidirect
34. #90954C22semidirect
35. #90951C22semidirect
78. C3×#689C2×C4semidirect
79. C3×#688C2×C4semidirect
80. C3×#687C2×C4semidirect
81. C3×#686C2×C4semidirect
89. #5819D5semidirect
103. #4097Dic3semidirect
105. #4095Dic3semidirect
106. #4088Dic3semidirect
107. #4078Dic3semidirect
167. #948C2×D5semidirect
207. #689C2×Dic3semidirect
208. #688C2×Dic3semidirect
209. #687C2×Dic3semidirect
210. #686C2×Dic3semidirect
444. C3×C5#2956semidirect
507. C5#84000semidirect
524. C3#10615542semidirect

Maximal subgroups

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

subgroupindex
C5×#58192
C3×#661562
#117541202
C2×#911212
#117494372
#117494362
#117484762
C2×#909762
#117483282
#106155423
#840005