Finite Group Databasebeta

← #14458451

Subgroups — #14458451

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756489C211yesmaximal, characteristic, complemented
2#11756476C211yesmaximal, characteristic
3C3×C5×#486C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751176C211yesmaximal, characteristic, complemented
6#11750879C212yesmaximal, complemented
7#11750878C212yesmaximal, complemented
8#11750877C212yesmaximal, complemented
9D15×#102C212yesmaximal, complemented
10C4×#6706C211yesmaximal, characteristic, complemented
11C8×D60C211yesmaximal, characteristic, complemented
12#10613308—31nomaximal, Hall
13C2×D4×D15—21no—
14C2×D4×D15C2212yes—
15C3×C5×C4⋊Q8C2211yescharacteristic, complemented
16C3×C5×#127C2211yescharacteristic
17#91835—22no—
18#91827—21no—
19#91827C2212yes—
20#91826—22no—
21C2×#6716C2212yescomplemented
22C2×#6706C2211yescharacteristic
23C2×C8×D15C2212yescomplemented
24#91786C2212yescomplemented
25#91782—21no—
26C4⋊C4×D15C2212yescomplemented
27#91779—21no—
28C4×D60C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C4×Dic30C2211yescharacteristic, complemented
31C3×C5×#102C2212yescomplemented
32C3×C5×#102C2212yescomplemented
33C3×C4×C5×C8C2211yescharacteristic, complemented
34#91116C2212yescomplemented
35#91105C2211yescharacteristic
36#91104C2212yescomplemented
37#91101C2211yescharacteristic, complemented
38#91100C2211yescharacteristic, complemented
39#91093C2212yes—
40#91092C2212yescomplemented
41C4⋊(C3⋊#168)C2211yescharacteristic, complemented
42#81577—51nomaximal, Hall
43#66064—31no—
44#66051—31no—
45C5×#486D311yescharacteristic, complemented
46#65373—31no—
47#65364—31no—
48#65067—32no—
49#65066—32no—
50#65065—32no—
51D5×#102—32no—
52C4×#677—31no—
53C8×D20—31no—
54C23×D15—22no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4—21no—
58C2×C3×C5×D4C2312yes—
59C2×#1220—22no—
60C2×#1220—22no—
61D4×D15—24no—
62D4×D15—42no—
63D4×D15—44no—
64C2×D60D411yescharacteristic
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×C4×D15—22no—
68C2×C4×D15C2312yes—
69C2×Dic30C2311yescharacteristic
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4C2312yes—
74C3×C42×C5C2311yescharacteristic
75#6719—22no—
76#6716—42no—
77#6714—22no—
78#6714—21no—
79#6714D412yes—
80C4⋊Dic15—22no—
81C4⋊Dic15D411yescharacteristic
82C4⋊Dic15C2311yescharacteristic
83C4⋊Dic15C2311yescharacteristic
84#6712—21no—
85#6712—22no—
86C4×Dic15—21no—
87C2×C3⋊#168C2312yes—
88#6706—22no—
89C8×D15—42no—
90#5730—51no—
91#5717—51no—
92C3×#486D511yescharacteristic, complemented
93#5084—51no—
94#5075—51no—
95#4778—52no—
96#4777—52no—
97#4776—52no—
98D3×#102—52no—
99C4×#204—51no—
100C8×D12—51no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C5×C4⋊Q8C2×D311yescharacteristic, complemented
104C5×#127C2×D311yescharacteristic
105#4092—62no—
106#4084—32no—
107#4084—61no—
108#4083—62no—
109C2×#687—32no—
110C2×#677—31no—
111C2×C8×D5—32no—
112#4043—32no—
113#4039—61no—
114D5×C4⋊C4—32no—
115#4036—61no—
116C4×D20—31no—
117C4×D20—31no—
118C4×Dic10—31no—
119C5×#102C2×D312yescomplemented
120C5×#102C2×D312yescomplemented
121C4×C5×C8C2×D311yescharacteristic, complemented
122#3964—32no—
123#3953—31no—
124#3952—32no—
125#3949—31no—
126#3948—31no—
127#3941—32no—
128#3940—32no—
129C4⋊#168—31no—
130#3295—151noSylow
131C23×C3×C5—22no—
132C22×D15—21no—
133C22×D15—44no—
134C22×D15—44no—
135C22×D15—82no—
136C22×D15C2×D412yes—
137C3×C5×Q8—81no—
138C3×C5×D4—22no—
139C3×C5×D4—22no—
140C3×C5×D4—42no—
141C3×C5×D4—81no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—44no—
147#1220—44no—
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15C2×D412yes—
152D60—21no—
153D60SD1614yescomplemented
154D60#4112yes—
155C4×D15—22no—
156C4×D15—22no—
157C4×D15—42no—
158C4×D15—82no—
159Dic30—21no—
160Dic30—21no—
161C3×C5×C8—21no—
162C3×C5×C8—21no—
163C3⋊#168—22no—
164C2×D3×D4—52no—
165C2×D3×D4—101no—
166C3×C4⋊Q8C2×D511yescharacteristic, complemented
167C3×#127C2×D511yescharacteristic
168#946—102no—
169#938—52no—
170#938—101no—
171#937—102no—
172C2×#214—52no—
173C2×#204—51no—
174C2×D3×C8—52no—
175#897—52no—
176#893—101no—
177D3×C4⋊C4—52no—
178#890—101no—
179C4×D12—51no—
180C4×D12—51no—
181C4×Dic6—51no—
182C3×#102C2×D512yescomplemented
183C3×#102C2×D512yescomplemented
184C3×C4×C8C2×D511yescharacteristic, complemented
185#832—52no—
186#821—51no—
187(C2×D3)⋊C8—52no—
188#817—51no—
189#816—51no—
190#809—52no—
191#808—52no—
192C4⋊(C3⋊C8)—51no—
193C23×D5—62no—
194C2×C5×Q8—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4C22×D312yes—
198C2×C22⋊D5—62no—
199C2×C22⋊D5—62no—
200D4×D5—64no—
201D4×D5—122no—
202D4×D5—124no—
203C2×D20—31no—
204C2×D20—31no—
205C2×C4×D5—32no—
206C2×C4×D5—61no—
207C2×C4×D5—62no—
208C2×Dic10—31no—
209C2×C5×C8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211C5×C4⋊C4—21no—
212C5×C4⋊C4C22×D312yes—
213C42×C5C22×D311yescharacteristic
214C22⋊Dic5—62no—
215#687—122no—
216#685—32no—
217#685—62no—
218#685—61no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5—31no—
222C4⋊Dic5—62no—
223#683—62no—
224#683—61no—
225C4×Dic5—61no—
226C2×#168—32no—
227#677—62no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486D1511yescharacteristic, complemented
232#481—152no—
233#476—151no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5C22×D411yescharacteristic
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C2×D15—88no—
250C2×D15C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5—42no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—22no—
257Dic15—41no—
258Dic15—41no—
259Dic15—41no—
260C23×D3—102no—
261C2×C3×Q8—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4C22×D512yes—
265C2×#67—102no—
266C2×#67—102no—
267D3×D4—104no—
268D3×D4—202no—
269D3×D4—204no—
270C2×D12—51no—
271C2×D12—51no—
272C2×C4×D3—52no—
273C2×C4×D3—101no—
274C2×C4×D3—102no—
275C2×Dic6—51no—
276C2×C3×C8C22×D511yescharacteristic
277C2×C3×C8C22×D511yescharacteristic
278C3×C4⋊C4—21no—
279C3×C4⋊C4C22×D512yes—
280C3×C42C22×D511yescharacteristic
281#217—102no—
282#214—202no—
283(C2×D3)⋊C4—52no—
284(C2×D3)⋊C4—102no—
285(C2×D3)⋊C4—101no—
286C4⋊Dic3—51no—
287C4⋊Dic3—51no—
288C4⋊Dic3—51no—
289C4⋊Dic3—102no—
290Dic3⋊C4—102no—
291Dic3⋊C4—101no—
292C4×Dic3—101no—
293C2×C3⋊C8—52no—
294#204—102no—
295D3×C8—202no—
296C23×C5—22no—
297C22×D5—32no—
298C22×D5—61no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—81no—
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—42no—
306C5×D4—81no—
307C2×C4×C5—22no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C22⋊D5—124no—
313C2×Dic5—32no—
314C2×Dic5—61no—
315C2×Dic5—61no—
316C2×Dic5—61no—
317D20—34no—
318D20—32no—
319D20—61no—
320C4×D5—62no—
321C4×D5—62no—
322C4×D5—122no—
323C4×D5—242no—
324Dic10—61no—
325Dic10—61no—
326C5×C8—21no—
327C5×C8—21no—
328#168—62no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—152no—
332C2×SD16—151no—
333C22×C8—152no—
334C4⋊Q8C2×D1511yescharacteristic, complemented
335#127C2×D1511yescharacteristic
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—151no—
343C4×D4—151no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—151no—
348#106—152no—
349C4⋊C8—151no—
350#103—151no—
351#102—152no—
352#102—151no—
353#102—152no—
354#102C2×D1512yescomplemented
355#102C2×D1512yescomplemented
356C22⋊C8—152no—
357C4×C8C2×D1511yescharacteristic, complemented
358C2×C3×C5—82no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362D15—24no—
363D15—42no—
364C23×C3—22no—
365C22×D3—52no—
366C22×D3—101no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—81no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—42no—
374C3×D4—81no—
375C2×C3×C4—22no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—204no—
380#67—204no—
381C2×Dic3—52no—
382C2×Dic3—101no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385D12—52no—
386D12—54no—
387D12—101no—
388C4×D3—102no—
389C4×D3—102no—
390C4×D3—202no—
391C4×D3—402no—
392Dic6—101no—
393Dic6—101no—
394C3×C8—21no—
395C3×C8—21no—
396C3⋊C8—102no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—34no—
402C2×D5—62no—
403C2×D5—62no—
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—42no—
410C4×C5D3×SD1612yes—
411C4×C5D3×#4111yescharacteristic
412C4×C5#100911yescharacteristic
413Dic5—62no—
414Dic5—121no—
415Dic5—121no—
416Dic5—121no—
417C24—302no—
418C2×Q8—21no—
419C2×Q8—151no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—151no—
423C2×D4—151no—
424C2×D4—302no—
425C2×D4—304no—
426C2×D4—302no—
427C2×D4—602no—
428C2×D4—604no—
429C2×D4C22×D1512yes—
430C22×C4—152no—
431C22×C4—302no—
432C22×C4—301no—
433SD16—302no—
434SD16—602no—
435C2×C8—152no—
436C2×C8—602no—
437C2×C8C22×D1511yescharacteristic
438C2×C8C22×D1511yescharacteristic
439C4⋊C4—21no—
440C4⋊C4—151no—
441C4⋊C4—151no—
442C4⋊C4—151no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C22×D1512yes—
447C22⋊C4—152no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—301no—
452C42C22×D1511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—54no—
459C2×D3—102no—
460C2×D3—102no—
461C2×D3—102no—
462C2×D3—201no—
463C2×D3—201no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—42no—
467C3×C4D5×SD1612yes—
468C3×C4D5×#4111yescharacteristic
469C3×C4#414911yescharacteristic
470Dic3—102no—
471Dic3—201no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—82no—
475C2×C5#567611yescharacteristic
476C2×C5#575711yescharacteristic
477C2×C5C2×D3×SD1611yescharacteristic
478D5—64no—
479D5—122no—
480C23—22no—
481C23—152no—
482C23—301no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—81no—
487Q8—301no—
488Q8—301no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—81no—
493D4—154no—
494D4—152no—
495D4—301no—
496D4—604no—
497D4—604no—
498C2×C4—22no—
499C2×C4—152no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—301no—
503C2×C4—301no—
504C2×C4—301no—
505C2×C4—602no—
506C2×C4—1202no—
507C2×C4D4×D1511yescharacteristic
508C2×C4D4×D1511yescharacteristic
509C2×C4C23×D1511yescharacteristic
510C8—21no—
511C8—21no—
512C8—302no—
513C2×C3—82no—
514C2×C3#6601011yescharacteristic
515C2×C3#6609111yescharacteristic
516C2×C3C2×D5×SD1611yescharacteristic
517D3—104no—
518D3—202no—
519C5#8157711yescharacteristic, complemented, Sylow
520C22—42no—
521C22—42no—
522C22—42no—
523C22—154no—
524C22—302no—
525C22—302no—
526C22—302no—
527C22—601no—
528C22—601no—
529C22—1208no—
530C22C2×D4×D1511yescharacteristic
531C4—21no—
532C4—42no—
533C4—302no—
534C4—601no—
535C4—601no—
536C4—601no—
537C4SD16×D1512yes—
538C4#41×D1511yescharacteristic
539C4#9210011yescharacteristic
540C3#1061330811yescharacteristic, complemented, Sylow
541C2—82no—
542C2—304no—
543C2—602no—
544C2#1175643511yescharacteristic
545C2#1175651611yescharacteristic
546C2C2×SD16×D1511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#486C2
socleC22×C3×C5C22×D4
prime radical#11756476C2
hypercenter#486D15
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
3. C3×C5×#486C2semidirect
4. #11751185C2semidirect
5. #11751176C2semidirect
6. #11750879C2semidirect
7. #11750878C2semidirect
8. #11750877C2semidirect
9. D15×#102C2semidirect
10. C4×#6706C2semidirect
11. C8×D60C2semidirect
15. C3×C5×C4⋊Q8C22semidirect
21. C2×#6716C22semidirect
23. C2×C8×D15C22semidirect
24. #91786C22semidirect
26. C4⋊C4×D15C22semidirect
30. C4×Dic30C22semidirect
31. C3×C5×#102C22semidirect
32. C3×C5×#102C22semidirect
33. C3×C4×C5×C8C22semidirect
34. #91116C22semidirect
36. #91104C22semidirect
37. #91101C22semidirect
38. #91100C22semidirect
40. #91092C22semidirect
41. C4⋊(C3⋊#168)C22semidirect
45. C5×#486D3semidirect
92. C3×#486D5semidirect
103. C5×C4⋊Q8C2×D3semidirect
119. C5×#102C2×D3semidirect
120. C5×#102C2×D3semidirect
121. C4×C5×C8C2×D3semidirect
153. D60SD16semidirect
166. C3×C4⋊Q8C2×D5semidirect
182. C3×#102C2×D5semidirect
183. C3×#102C2×D5semidirect
184. C3×C4×C8C2×D5semidirect
231. #486D15semidirect
334. C4⋊Q8C2×D15semidirect
354. #102C2×D15semidirect
355. #102C2×D15semidirect
357. C4×C8C2×D15semidirect
453. C3×C5#3295semidirect
519. C5#81577semidirect
540. C3#10613308semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117564762
C3×C5×#4862
#117511852
#117511762
#117508792
#117508782
#117508772
D15×#1022
C4×#67062
C8×D602
#106133083
#815775