Finite Group Databasebeta

← #14418164

Subgroups — #14418164

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×#5822C211yesmaximal, characteristic
2C3×#66153C211yesmaximal, characteristic, complemented
3#11754125C211yesmaximal, characteristic, complemented
4C2×#91121C211yesmaximal, characteristic, complemented
5#11749433C214yesmaximal, complemented
6#11749432C214yesmaximal, complemented
7#11748480C211yesmaximal, characteristic, complemented
8C2×#90978C211yesmaximal, characteristic, complemented
9#11748328C211yesmaximal, characteristic, complemented
10#10615731—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C5×#951C412yescomplemented
16C5×#950C2214yes—
17C5×#949C412yescomplemented
18C5×#942C412yescomplemented
19C5×#932C412yescomplemented
20C2×C5×#208C2211yescharacteristic
21C3×#4094—22no—
22C3×#4094C2214yescomplemented
23C2×C3×#681—22no—
24C2×C3×#681C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91288—22no—
27D3×#681—22no—
28#91286C2214yescomplemented
29#91121C2212yescomplemented
30#91121C2212yescomplemented
31#90993C2214yescomplemented
32#90978C2212yescomplemented
33#90978C2212yescomplemented
34#90954C2212yescomplemented
35#90951C2212yescomplemented
36#83811—51nomaximal, Hall
37C5×#575—31no—
38#66153—31no—
39#66153D311yescharacteristic, complemented
40C2×#3969—31no—
41C2×#3969—31no—
42#65486—34no—
43#65485—34no—
44#65414—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×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
64C4×Dic15—21no—
65C4×Dic15C2311yescharacteristic
66C4×Dic15C2311yescharacteristic
67#6710—21no—
68#6710C2312yes—
69C2×C3⋊#168—21no—
70C5×#216C2×C414yescomplemented
71C5×#215C2×C414yescomplemented
72C5×#214C2×C414yescomplemented
73C5×#213C2×C414yescomplemented
74C5×#208C2×C412yes—
75C5×#208C2×C412yes—
76C2×C5×C3⋊C8C2312yes—
77C3×#681—21no—
78C3×#681—24no—
79C3×#681D412yes—
80C3×#681D412yes—
81C3×#681C2312yes—
82C2×C3×#168—21no—
83C2×C3×#168—24no—
84C2×C3×#168C2312yes—
85#6650—24no—
86D3×#168—24no—
87C3×#568—51no—
88#5822D511yescharacteristic
89#5745—51no—
90C2×#837—51no—
91#5145—54no—
92#5144—54no—
93C2×#825—51no—
94#5124—51no—
95Dic3×M16—51no—
96C2×C5×#41—31no—
97C2×C5×#41C2×D311yescharacteristic
98C5×#137—32no—
99C5×#137—32no—
100C5×AGL(1,ℤ/8)—32no—
101C5×AGL(1,ℤ/8)—32no—
102C5×#135—34no—
103C2×C5×M16—31no—
104#4094—22no—
105#4094—34no—
106#4094—62no—
107#4094C2×D314yescomplemented
108C2×C4×Dic5—31no—
109C2×#681—22no—
110C2×#681—31no—
111C2×#681—62no—
112C2×#681C2×D311yescharacteristic
113C2×#681C2×D311yescharacteristic
114#3969—32no—
115#3969—32no—
116#3969—32no—
117#3969—32no—
118#3951—34no—
119#3947—32no—
120C8×Dic5—32no—
121#2956—151noSylow
122C23×C3×C5—21no—
123C23×C3×C5#4111yescharacteristic
124C22×C5×D3—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—
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×#168—22no—
154C3×#168C2×D414yes—
155C5×C3⋊C8C22×C414yes—
156C2×C3×#41C2×D511yescharacteristic
157C2×#235C2×D511yescharacteristic
158C3×#131—54no—
159C3×#131—102no—
160C2×C3×M16—51no—
161C2×C3×M16—51no—
162C2×C3×M16—102no—
163#951Dic512yescomplemented
164#950C2×D514yes—
165#949Dic512yescomplemented
166#942Dic512yescomplemented
167#932Dic512yescomplemented
168C2×C4×Dic3—51no—
169C2×#208—51no—
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#822—54no—
179#815—52no—
180C8×Dic3—52no—
181C5×#41—21no—
182C5×#41—21no—
183C5×#41—32no—
184C5×#41—32no—
185C5×#41—61no—
186C5×#41—61no—
187C5×#41C4×D312yes—
188C5×#41C22×D312yes—
189C2×C5×Q8—31no—
190C2×C5×Q8C4×D311yescharacteristic
191C2×C5×D4—21no—
192C2×C5×D4—31no—
193C2×C5×D4—61no—
194C2×C5×D4C4×D311yescharacteristic
195C22×C4×C5—21no—
196C22×C4×C5—61no—
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—61no—
199C5×Q16—34no—
200C5×SD16—34no—
201C5×SD16—34no—
202C5×D8—34no—
203C5×M16—32no—
204C5×M16—32no—
205C2×C5×C8—32no—
206C4×Dic5—31no—
207C4×Dic5—31no—
208C4×Dic5—61no—
209#681—21no—
210#681—24no—
211#681—32no—
212#681—61no—
213#681—64no—
214#681#6712yes—
215#681#6712yes—
216#681C22×D312yes—
217C2×#168—21no—
218C2×#168—24no—
219C2×#168—61no—
220C2×#168—64no—
221C2×#168C22×D312yes—
222#575—31no—
223#568—51no—
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×C5×D3—22no—
238C2×C5×D3—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—
246C5×Dic3—22no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41C2×Dic512yes—
250C3×#41C22×D512yes—
251C2×C3×Q8C2×Dic511yescharacteristic
252C2×C3×D4—21no—
253C2×C3×D4C2×Dic511yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—21no—
257C22×Dic3—101no—
258#235—21no—
259#235—21no—
260#235C2×Dic512yes—
261#235C22×D512yes—
262C2×D12C2×Dic511yescharacteristic
263C2×C4×D3—21no—
264C2×Dic6C2×Dic511yescharacteristic
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#216C2×Dic514yescomplemented
274#215C2×Dic514yescomplemented
275#214C2×Dic514yescomplemented
276#213C2×Dic514yescomplemented
277C4×Dic3—51no—
278C4×Dic3—51no—
279C4×Dic3—101no—
280#208—52no—
281#208—101no—
282#208C2×Dic512yes—
283#208C2×Dic512yes—
284C2×C3⋊C8—101no—
285C2×C3⋊C8C22×D512yes—
286ΓL(1,𝔽25)—104no—
287D3×C8—104no—
288C23×C5—21no—
289C23×C5—61no—
290C23×C5#23511yescharacteristic
291C5×Q8—21no—
292C5×Q8—32no—
293C5×Q8—61no—
294C5×Q8C2×C4×D312yes—
295C5×D4—22no—
296C5×D4—22no—
297C5×D4—21no—
298C5×D4—32no—
299C5×D4—62no—
300C5×D4—62no—
301C5×D4—61no—
302C5×D4C2×C4×D312yes—
303C2×C4×C5—21no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—61no—
307C2×C4×C5—62no—
308C2×C4×C5—62no—
309C2×C4×C5C2×C4×D311yescharacteristic
310C2×C4×C5C2×C4×D311yescharacteristic
311C2×C4×C5#23511yescharacteristic
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—61no—
316C2×Dic5—61no—
317C2×Dic5—122no—
318C5×C8—34no—
319#168—22no—
320#168—62no—
321#168C2×#6714yes—
322C2×#41—31no—
323C2×#41D3×D511yescharacteristic
324#137—32no—
325#137—32no—
326AGL(1,ℤ/8)—32no—
327AGL(1,ℤ/8)—32no—
328#135—34no—
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—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
352C5×D3—42no—
353C23×C3—21no—
354C23×C3#71111yescharacteristic
355C22×D3—21no—
356C3×Q8—21no—
357C3×Q8C22×Dic512yes—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4C22×Dic512yes—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4D4×D511yescharacteristic
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4#71111yescharacteristic
368C2×C3×C4C22×Dic511yescharacteristic
369C2×C3×C4C22×Dic511yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—22no—
372#67—22no—
373C2×Dic3—21no—
374C2×Dic3—101no—
375C2×Dic3—101no—
376C2×Dic3—202no—
377D12—21no—
378D12C22×Dic512yes—
379C4×D3—22no—
380C4×D3—22no—
381Dic6—21no—
382Dic6C22×Dic512yes—
383C3×C8—54no—
384C3×C8—102no—
385C3⋊C8—102no—
386C3⋊C8C22×Dic514yes—
387C22×C5—22no—
388C22×C5—41no—
389C22×C5—62no—
390C22×C5—81no—
391C22×C5—241no—
392C22×C5C4×#6711yescharacteristic
393C22×C5C4×#6711yescharacteristic
394C22×C5C2×#23511yescharacteristic
395C4×C5—22no—
396C4×C5—62no—
397C4×C5C4×#6711yescharacteristic
398C4×C5C4×#6711yescharacteristic
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C22×#6711yescharacteristic
401Dic5—62no—
402Dic5—121no—
403#41—21no—
404#41—21no—
405#41—32no—
406#41—32no—
407#41—61no—
408#41—61no—
409#41D3×Dic512yes—
410#41C2×D3×D512yes—
411C2×Q8—31no—
412C2×Q8D3×Dic511yescharacteristic
413C2×D4—21no—
414C2×D4—31no—
415C2×D4—61no—
416C2×D4D3×Dic511yescharacteristic
417C22×C4—21no—
418C22×C4—61no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—34no—
422SD16—34no—
423SD16—34no—
424D8—34no—
425M16—32no—
426M16—32no—
427M16—52no—
428M16—52no—
429M16—52no—
430M16—104no—
431M16—101no—
432M16—152no—
433M16—304no—
434M16—301no—
435C2×C8—32no—
436C2×C8—52no—
437C2×C8—104no—
438C2×C8—101no—
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×C3D4×Dic511yescharacteristic
449C22×C3D4×Dic511yescharacteristic
450C22×C3C2×#71111yescharacteristic
451C2×D3—22no—
452C2×D3—81no—
453C3×C4—22no—
454C3×C4D4×Dic511yescharacteristic
455C3×C4D4×Dic511yescharacteristic
456C3×C4C2×D4×D511yescharacteristic
457C3×C4C23×Dic511yescharacteristic
458Dic3—22no—
459Dic3—102no—
460Dic3—201no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—42no—
465C2×C5—122no—
466C2×C5C2×C4×#6711yescharacteristic
467C23—21no—
468C23—61no—
469C23#678211yescharacteristic
470Q8—21no—
471Q8—32no—
472Q8—61no—
473Q8C2×D3×Dic512yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—32no—
478D4—62no—
479D4—62no—
480D4—61no—
481D4C2×D3×Dic512yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4C2×D3×Dic511yescharacteristic
492C2×C4C2×D3×Dic511yescharacteristic
493C2×C4#678211yescharacteristic
494C2×C4D5×#6711yescharacteristic
495C2×C4D5×#6711yescharacteristic
496C2×C4C22×D3×D511yescharacteristic
497C8—34no—
498C8—54no—
499C8—102no—
500C8—302no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3C2×D4×Dic511yescharacteristic
506D3—42no—
507C5#8381111yescharacteristic, complemented, Sylow
508C22—22no—
509C22—41no—
510C22—62no—
511C22—81no—
512C22—241no—
513C22Dic5×#6711yescharacteristic
514C22Dic5×#6711yescharacteristic
515C22C2×#678211yescharacteristic
516C4—22no—
517C4—62no—
518C4—302no—
519C4—601no—
520C4Dic5×#6711yescharacteristic
521C4Dic5×#6711yescharacteristic
522C4C22×D3×Dic511yescharacteristic
523C4C2×D5×#6711yescharacteristic
524C3#1061573111yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—21no—
528C2—42no—
529C2—122no—
530C2C2×Dic5×#6711yescharacteristic
subgroupG/H
centerC4C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×C4×D4
prime radicalC5×#5822C2
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. #11754125C2semidirect
4. C2×#91121C2semidirect
5. #11749433C2semidirect
6. #11749432C2semidirect
7. #11748480C2semidirect
8. C2×#90978C2semidirect
9. #11748328C2semidirect
15. C5×#951C4semidirect
17. C5×#949C4semidirect
18. C5×#942C4semidirect
19. C5×#932C4semidirect
22. C3×#4094C22semidirect
28. #91286C22semidirect
29. #91121C22semidirect
30. #91121C22semidirect
31. #90993C22semidirect
32. #90978C22semidirect
33. #90978C22semidirect
34. #90954C22semidirect
35. #90951C22semidirect
39. #66153D3semidirect
70. C5×#216C2×C4semidirect
71. C5×#215C2×C4semidirect
72. C5×#214C2×C4semidirect
73. C5×#213C2×C4semidirect
107. #4094C2×D3semidirect
163. #951Dic5semidirect
165. #949Dic5semidirect
166. #942Dic5semidirect
167. #932Dic5semidirect
273. #216C2×Dic5semidirect
274. #215C2×Dic5semidirect
275. #214C2×Dic5semidirect
276. #213C2×Dic5semidirect
444. C3×C5#2956semidirect
507. C5#83811semidirect
524. C3#10615731semidirect

Maximal subgroups

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

subgroupindex
C5×#58222
C3×#661532
#117541252
C2×#911212
#117494332
#117494322
#117484802
C2×#909782
#117483282
#106157313
#838115