Finite Group Databasebeta

← #14458454

Subgroups — #14458454

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
1C3×C5×D42C211yesmaximal, characteristic
2#11756302C211yesmaximal, characteristic, complemented
3#11751319C212yesmaximal, complemented
4C2×#91116C212yesmaximal, complemented
5#11751176C211yesmaximal, characteristic, complemented
6#11751171C211yesmaximal, characteristic, complemented
7#11751142C212yesmaximal, complemented
8#11751135C212yesmaximal, complemented
9C4×#6716C211yesmaximal, characteristic, complemented
10D4×C3⋊#168C211yesmaximal, characteristic, complemented
11#11751109C211yesmaximal, characteristic, complemented
12#10615214—31nomaximal, Hall
13C22×C3×C5×D4—21no—
14C22×C3×C5×D4C2212yes—
15C3×C5×#127C2211yescharacteristic
16C3×C5×#121—21no—
17C3×C5×#121C2212yes—
18C3×C5×#120—22no—
19C3×C4×C5×D4C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21D4×Dic15—21no—
22C2×#6716C2211yescharacteristic
23C2×#6716C2212yescomplemented
24C2×C4⋊Dic15C2212yescomplemented
25#91813C2212yescomplemented
26C22×C3⋊#168C2212yescomplemented
27#91779—21no—
28#91767—22no—
29#91758C2211yescharacteristic, complemented
30C4×Dic30C2211yescharacteristic, complemented
31#91116C2211yescharacteristic
32#91116C2212yes—
33#91116C2212yescomplemented
34#91116C2212yescomplemented
35#91116C2212yescomplemented
36#91114C2212yescomplemented
37#91094C2211yescharacteristic, complemented
38#91092C2212yescomplemented
39#91092C2211yescharacteristic, complemented
40C4⋊(C3⋊#168)C2211yescharacteristic, complemented
41C4×C3⋊#168C2211yescharacteristic, complemented
42#83483—51nomaximal, Hall
43C5×D42D311yescharacteristic
44#65877—31no—
45#65507—32no—
46C2×#3964—32no—
47#65364—31no—
48#65359—31no—
49#65330—32no—
50#65323—32no—
51C4×#687—31no—
52D4×#168—31no—
53#65297—31no—
54C24×C3×C5—22no—
55C2×C3×C5×D4—24no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4—42no—
61C2×C3×C5×D4—44no—
62C2×C3×C5×D4D411yescharacteristic
63C2×C3×C5×D4C2312yes—
64C2×C3×C5×D4C2311yescharacteristic
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5C2312yes—
67C22×Dic15—22no—
68C2×Dic30—21no—
69C2×Dic30C2311yescharacteristic
70C3×C5×C4⋊C4D411yescharacteristic
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C22⋊C4—21no—
73C3×C5×C22⋊C4—22no—
74C3×C5×C22⋊C4D412yes—
75C3×C42×C5C2311yescharacteristic
76#6719—22no—
77#6716—22no—
78#6716—42no—
79C4⋊Dic15—21no—
80C4⋊Dic15—22no—
81C4⋊Dic15C2311yescharacteristic
82C4⋊Dic15C2312yes—
83#6712—21no—
84#6712—22no—
85C4×Dic15—21no—
86C2×C3⋊#168—42no—
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2312yes—
89C2×C3⋊#168C2311yescharacteristic
90C3×D42D511yescharacteristic
91#5543—51no—
92#5218—52no—
93C2×#832—52no—
94#5075—51no—
95#5070—51no—
96#5041—52no—
97#5034—52no—
98C4×#214—51no—
99D4×C3⋊C8—51no—
100#5008—51no—
101C22×C5×D4—21no—
102C22×C5×D4C2×D312yes—
103C5×#127C2×D311yescharacteristic
104C5×#121—21no—
105C5×#121C2×D312yes—
106C5×#120—22no—
107C4×C5×D4C2×D311yescharacteristic
108C4×C5×D4C2×D311yescharacteristic
109D4×Dic5—61no—
110C2×#687—31no—
111C2×#687—32no—
112C2×C4⋊Dic5—32no—
113#4070—32no—
114C22×#168—32no—
115#4036—61no—
116#4024—62no—
117#4015—31no—
118C4×Dic10—31no—
119#3964—32no—
120#3964—31no—
121#3964—32no—
122#3964—32no—
123#3964—32no—
124C22⋊#168—32no—
125#3942—31no—
126#3940—32no—
127#3940—31no—
128C4⋊#168—31no—
129C4×#168—31no—
130#3295—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5—22no—
133C23×C3×C5—44no—
134C23×C3×C5—44no—
135C23×C3×C5—82no—
136C23×C3×C5C2×D412yes—
137C3×C5×D4—22no—
138C3×C5×D4—21no—
139C3×C5×D4—22no—
140C3×C5×D4—44no—
141C3×C5×D4—44no—
142C3×C5×D4—42no—
143C3×C5×D4—81no—
144C3×C5×D4SD1614yescomplemented
145C3×C5×D4#4112yes—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—42no—
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15—21no—
155C2×Dic15—21no—
156C2×Dic15—22no—
157C2×Dic15—82no—
158Dic30—21no—
159Dic30—21no—
160Dic30—81no—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C3⋊#168—22no—
164C22×C3×D4—21no—
165C22×C3×D4C2×D512yes—
166C3×#127C2×D511yescharacteristic
167C3×#121—21no—
168C3×#121C2×D512yes—
169C3×#120—22no—
170C3×C4×D4C2×D511yescharacteristic
171C3×C4×D4C2×D511yescharacteristic
172D4×Dic3—101no—
173C2×#214—51no—
174C2×#214—52no—
175C2×C4⋊Dic3—52no—
176#924—52no—
177C22×C3⋊C8—52no—
178#890—101no—
179#878—102no—
180#869—51no—
181C4×Dic6—51no—
182#832—51no—
183#832—52no—
184#832—52no—
185#832—52no—
186#832—52no—
187#830—52no—
188#810—51no—
189#808—52no—
190#808—51no—
191C4⋊(C3⋊C8)—51no—
192C4×C3⋊C8—51no—
193C24×C5—22no—
194C2×C5×D4—24no—
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4—42no—
200C2×C5×D4—44no—
201C2×C5×D4#6711yescharacteristic
202C2×C5×D4C22×D312yes—
203C2×C5×D4C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5C22×D312yes—
206C22×Dic5—62no—
207C2×Dic10—31no—
208C2×Dic10—61no—
209C5×C4⋊C4#6711yescharacteristic
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C22⋊C4—21no—
212C5×C22⋊C4—22no—
213C5×C22⋊C4#6712yes—
214C42×C5C22×D311yescharacteristic
215C22⋊Dic5—62no—
216#687—62no—
217#687—122no—
218C4⋊Dic5—31no—
219C4⋊Dic5—32no—
220C4⋊Dic5—61no—
221C4⋊Dic5—62no—
222#683—61no—
223#683—62no—
224C4×Dic5—61no—
225C2×#168—31no—
226C2×#168—31no—
227C2×#168—32no—
228C2×#168—122no—
229#554—151no—
230D42D1511yescharacteristic
231#486—151no—
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—22no—
241C22×C3×C5—22no—
242C22×C3×C5—22no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5—42no—
247C22×C3×C5—42no—
248C22×C3×C5—88no—
249C22×C3×C5C2×SD1614yes—
250C22×C3×C5C22×D411yescharacteristic
251C3×C4×C5—22no—
252C3×C4×C5—21no—
253C3×C4×C5—41no—
254C3×C4×C5C2×SD1612yes—
255C3×C4×C5C2×#4111yescharacteristic
256C3×C4×C5H(5,𝔽2)11yescharacteristic
257Dic15—41no—
258Dic15—42no—
259Dic15—41no—
260C24×C3—22no—
261C2×C3×D4—24no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—42no—
267C2×C3×D4—44no—
268C2×C3×D4C22⋊D511yescharacteristic
269C2×C3×D4C22×D512yes—
270C2×C3×D4C22×D511yescharacteristic
271C22×C3×C4—21no—
272C22×C3×C4C22×D512yes—
273C22×Dic3—102no—
274C2×Dic6—51no—
275C2×Dic6—101no—
276C3×C4⋊C4C22⋊D511yescharacteristic
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C22⋊C4—21no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4C22⋊D512yes—
281C3×C42C22×D511yescharacteristic
282#217—102no—
283#214—102no—
284#214—202no—
285C4⋊Dic3—51no—
286C4⋊Dic3—52no—
287C4⋊Dic3—101no—
288C4⋊Dic3—102no—
289Dic3⋊C4—101no—
290Dic3⋊C4—102no—
291C4×Dic3—101no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294C2×C3⋊C8—52no—
295C2×C3⋊C8—202no—
296C23×C5—21no—
297C23×C5—22no—
298C23×C5—44no—
299C23×C5—44no—
300C23×C5—82no—
301C23×C5C2×#6712yes—
302C5×D4—22no—
303C5×D4—21no—
304C5×D4—22no—
305C5×D4—44no—
306C5×D4—44no—
307C5×D4—42no—
308C5×D4—81no—
309C5×D4#21414yescomplemented
310C5×D4#23712yes—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—42no—
315C2×C4×C5C2×#6712yes—
316C2×C4×C5C2×#6711yescharacteristic
317C2×C4×C5C2×#6711yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C2×Dic5—61no—
320C2×Dic5—61no—
321C2×Dic5—62no—
322C2×Dic5—242no—
323Dic10—61no—
324Dic10—61no—
325Dic10—241no—
326#168—61no—
327#168—61no—
328#168—62no—
329C22×D4—21no—
330C22×D4C2×D1512yes—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8—151no—
335#127C2×D1511yescharacteristic
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—21no—
340#121C2×D1512yes—
341#120—22no—
342C4×Q8—151no—
343C4×D4—301no—
344C4×D4C2×D1511yescharacteristic
345C4×D4C2×D1511yescharacteristic
346C2×C4⋊C4—152no—
347#106—151no—
348#106—152no—
349C4⋊C8—151no—
350#103—151no—
351#102—151no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—151no—
358C2×C3×C5—24no—
359C2×C3×C5—42no—
360C2×C3×C5—82no—
361C2×C3×C5#54611yescharacteristic
362C2×C3×C5C22×SD1611yescharacteristic
363C2×C3×C5#57611yescharacteristic
364C23×C3—21no—
365C23×C3—22no—
366C23×C3—44no—
367C23×C3—44no—
368C23×C3—82no—
369C23×C3C2×C22⋊D512yes—
370C3×D4—22no—
371C3×D4—21no—
372C3×D4—22no—
373C3×D4—44no—
374C3×D4—44no—
375C3×D4—42no—
376C3×D4—81no—
377C3×D4#68714yescomplemented
378C3×D4#71112yes—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—42no—
383C2×C3×C4C2×C22⋊D512yes—
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C2×C22⋊D511yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387C2×Dic3—101no—
388C2×Dic3—101no—
389C2×Dic3—102no—
390C2×Dic3—402no—
391Dic6—101no—
392Dic6—101no—
393Dic6—401no—
394C3⋊C8—101no—
395C3⋊C8—101no—
396C3⋊C8—102no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—22no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—42no—
403C22×C5—42no—
404C22×C5—42no—
405C22×C5—88no—
406C22×C5C2×#21414yes—
407C22×C5C22×#6711yescharacteristic
408C4×C5—22no—
409C4×C5—21no—
410C4×C5—41no—
411C4×C5C2×#21412yes—
412C4×C5C2×#23711yescharacteristic
413C4×C5#100411yescharacteristic
414Dic5—121no—
415Dic5—122no—
416Dic5—121no—
417C24—22no—
418C2×Q8—151no—
419C2×Q8—301no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—44no—
427C2×D4#122011yescharacteristic
428C2×D4C22×D1512yes—
429C2×D4C22×D1511yescharacteristic
430C22×C4—21no—
431C22×C4—302no—
432C22×C4C22×D1512yes—
433SD16—302no—
434SD16—602no—
435C2×C8—151no—
436C2×C8—151no—
437C2×C8—152no—
438C2×C8—602no—
439C4⋊C4—151no—
440C4⋊C4—152no—
441C4⋊C4—302no—
442C4⋊C4—301no—
443C4⋊C4—301no—
444C4⋊C4—302no—
445C4⋊C4#122011yescharacteristic
446C4⋊C4C22×D1511yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—22no—
449C22⋊C4—302no—
450C22⋊C4#122012yes—
451C42—301no—
452C42C22×D1511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—88no—
463C22×C3C2×#68714yes—
464C22×C3C22×C22⋊D511yescharacteristic
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—41no—
468C3×C4C2×#68712yes—
469C3×C4C2×#71111yescharacteristic
470C3×C4#414411yescharacteristic
471Dic3—201no—
472Dic3—202no—
473Dic3—201no—
474C2×C5—24no—
475C2×C5—42no—
476C2×C5—82no—
477C2×C5C22×#21411yescharacteristic
478C2×C5#580611yescharacteristic
479C2×C5#583511yescharacteristic
480C23—21no—
481C23—22no—
482C23—44no—
483C23—44no—
484C23—82no—
485C23C2×#122012yes—
486Q8—301no—
487Q8—301no—
488Q8—1201no—
489D4—22no—
490D4—21no—
491D4—22no—
492D4—44no—
493D4—44no—
494D4—42no—
495D4—81no—
496D4#671614yescomplemented
497D4#681912yes—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—42no—
502C2×C4—301no—
503C2×C4—301no—
504C2×C4—302no—
505C2×C4—1202no—
506C2×C4C2×#122011yescharacteristic
507C2×C4C2×#122012yes—
508C2×C4C2×#122011yescharacteristic
509C2×C4C23×D1511yescharacteristic
510C8—301no—
511C8—301no—
512C8—302no—
513C2×C3—24no—
514C2×C3—42no—
515C2×C3—82no—
516C2×C3C22×#68711yescharacteristic
517C2×C3#6614011yescharacteristic
518C2×C3#6616911yescharacteristic
519C5#8348311yescharacteristic, complemented, Sylow
520C22—22no—
521C22—22no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—88no—
529C22C2×#671614yes—
530C22C22×#122011yescharacteristic
531C4—22no—
532C4—21no—
533C4—41no—
534C4—601no—
535C4—601no—
536C4—602no—
537C4C2×#671612yes—
538C4C2×#681911yescharacteristic
539C4#9209511yescharacteristic
540C3#1061521411yescharacteristic, complemented, Sylow
541C2—24no—
542C2—42no—
543C2—82no—
544C2C22×#671611yescharacteristic
545C2#1175656511yescharacteristic
546C2#1175659411yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC3×C5×D42C2
socleC22×C3×C5C22×D4
hypercenterD42D15
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
2. #11756302C2semidirect
3. #11751319C2semidirect
4. C2×#91116C2semidirect
5. #11751176C2semidirect
6. #11751171C2semidirect
7. #11751142C2semidirect
8. #11751135C2semidirect
9. C4×#6716C2semidirect
10. D4×C3⋊#168C2semidirect
11. #11751109C2semidirect
23. C2×#6716C22semidirect
24. C2×C4⋊Dic15C22semidirect
25. #91813C22semidirect
26. C22×C3⋊#168C22semidirect
29. #91758C22semidirect
30. C4×Dic30C22semidirect
33. #91116C22semidirect
34. #91116C22semidirect
35. #91116C22semidirect
36. #91114C22semidirect
37. #91094C22semidirect
38. #91092C22semidirect
39. #91092C22semidirect
40. C4⋊(C3⋊#168)C22semidirect
41. C4×C3⋊#168C22semidirect
144. C3×C5×D4SD16semidirect
309. C5×D4#214semidirect
377. C3×D4#687semidirect
453. C3×C5#3295semidirect
496. D4#6716semidirect
519. C5#83483semidirect
540. C3#10615214semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D422
#117563022
#117513192
C2×#911162
#117511762
#117511712
#117511422
#117511352
C4×#67162
D4×C3⋊#1682
#117511092
#106152143
#834835