Finite Group Databasebeta

← #14458517

Subgroups — #14458517

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#11756302C211yesmaximal, characteristic, complemented
2C3×D4×D20C211yesmaximal, characteristic
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748539C212yesmaximal, complemented
5#11748530C212yesmaximal, complemented
6#11748375C212yesmaximal, complemented
7C2×#90965C212yesmaximal, complemented
8#11747083C211yesmaximal, characteristic, complemented
9C4×#6657C211yesmaximal, characteristic, complemented
10#11746890C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10611170—31nomaximal, Hall
13C2×C3×D4×D5—21no—
14C22×C3×D20C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16D4×Dic15—21no—
17C2×C4⋊Dic15C2212yescomplemented
18#91813C2212yescomplemented
19#91779—21no—
20#91767—22no—
21#91758C2211yescharacteristic, complemented
22C4×Dic30C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2212yescomplemented
24C3×#4076C2212yes—
25C3×#4041—21no—
26C3×#4028—22no—
27C3×#4020C2211yescharacteristic
28C3×C4×D20C2211yescharacteristic
29C2×#6657C2211yescharacteristic
30C2×#6657C2212yescomplemented
31C5×#830C2212yescomplemented
32C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
33C4×C5×C3⋊C8C2211yescharacteristic, complemented
34#90987C2211yescharacteristic, complemented
35#90987C2212yescomplemented
36#90974C2211yescharacteristic, complemented
37#90965C2211yescharacteristic
38#90965C2212yes—
39#90965C2212yescomplemented
40#90965C2212yescomplemented
41#90965C2212yescomplemented
42#83483—51nomaximal, Hall
43D4×D20D311yescharacteristic
44#65877—31no—
45C5×C8×D4—31no—
46#65403—32no—
47C2×#3953—32no—
48#65137—31no—
49#65131—31no—
50#65024—32no—
51#65020—32no—
52#64983—31no—
53C4×#677—31no—
54C23×C3×D5—22no—
55C2×C3×C5×D4D411yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×Dic15—22no—
58C2×Dic30—21no—
59C2×Dic30C2311yescharacteristic
60C2×C3×C22⋊D5—22no—
61C3×D4×D5—44no—
62C2×C3×D20—24no—
63C2×C3×D20—22no—
64C2×C3×D20—21no—
65C2×C3×D20—21no—
66C2×C3×D20—42no—
67C2×C3×D20C2312yes—
68C2×C3×D20C2311yescharacteristic
69C2×C3×C4×D5—21no—
70C3×C5×C4⋊C4D411yescharacteristic
71C3×C5×C22⋊C4D412yes—
72C3×C42×C5C2311yescharacteristic
73#6719—22no—
74C4⋊Dic15—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15C2311yescharacteristic
77C4⋊Dic15C2312yes—
78#6712—21no—
79#6712—22no—
80C4×Dic15—21no—
81C2×C5×C3⋊C8—42no—
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2312yes—
84C2×C5×C3⋊C8C2311yescharacteristic
85C3×#685—21no—
86C3×#685—22no—
87C3×C4⋊Dic5C2311yescharacteristic
88#6657—22no—
89#6657—42no—
90C3×D42—51no—
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⋊C8D511yescharacteristic, complemented
100#5008—51no—
101C2×D4×D5—21no—
102C22×D20C2×D312yes—
103C22×C5×C8—32no—
104C4×C5×D4C2×D311yescharacteristic
105D4×Dic5—61no—
106#4076C2×D312yes—
107C2×C4⋊Dic5—32no—
108#4070—32no—
109C2×#677—31no—
110C2×#677—32no—
111#4041—21no—
112#4036—61no—
113#4028—22no—
114#4024—62no—
115#4020C2×D311yescharacteristic
116C4×D20C2×D311yescharacteristic
117#4015—31no—
118C4×Dic10—31no—
119C5×C4⋊C8—31no—
120C5×C22⋊C8—32no—
121C4×C5×C8—31no—
122#3953—32no—
123#3953—32no—
124#3953—32no—
125#3953—31no—
126#3953—32no—
127#3949—31no—
128#3949—32no—
129#3948—31no—
130#3295—151noSylow
131C23×C3×C5C2×D412yes—
132C22×C3×D5—21no—
133C22×C3×D5—22no—
134C22×C3×D5—44no—
135C22×C3×D5—44no—
136C22×C3×D5—82no—
137C3×C5×D4SD1614yescomplemented
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15—82no—
148Dic30—21no—
149Dic30—21no—
150Dic30—81no—
151C3×C22⋊D5—44no—
152C2×C3×Dic5—21no—
153C3×D20—22no—
154C3×D20—21no—
155C3×D20—22no—
156C3×D20—44no—
157C3×D20—42no—
158C3×D20—81no—
159C3×D20#4112yes—
160C3×C4×D5—42no—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—22no—
163C5×C3⋊C8—21no—
164C22×C3×D4—52no—
165C22×C3×D4—101no—
166C3×#127—51no—
167C3×#121—52no—
168C3×#121—101no—
169C3×#120—102no—
170C3×C4×D4—51no—
171C3×C4×D4C2×D511yescharacteristic
172D4×Dic3—101no—
173C2×#214—51no—
174C2×#214—52no—
175C2×C4⋊Dic3—52no—
176#924—52no—
177C22×C3⋊C8C2×D512yescomplemented
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#830C2×D512yescomplemented
188#810—51no—
189#808—52no—
190#808—51no—
191C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—22no—
194C2×C5×D4#6711yescharacteristic
195C22×C4×C5C22×D312yes—
196C2×C22⋊D5—22no—
197C22×Dic5—62no—
198D4×D5—44no—
199C2×D20—24no—
200C2×D20—22no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20—42no—
204C2×D20C22×D312yes—
205C2×D20C22×D311yescharacteristic
206C2×C4×D5—21no—
207C2×Dic10—31no—
208C2×Dic10—61no—
209C2×C5×C8—31no—
210C2×C5×C8—32no—
211C2×C5×C8—31no—
212C2×C5×C8—122no—
213C5×C4⋊C4#6711yescharacteristic
214C5×C22⋊C4#6712yes—
215C42×C5C22×D311yescharacteristic
216C22⋊Dic5—62no—
217#685—21no—
218#685—22no—
219C4⋊Dic5—31no—
220C4⋊Dic5—32no—
221C4⋊Dic5—61no—
222C4⋊Dic5—62no—
223C4⋊Dic5C22×D311yescharacteristic
224#683—61no—
225#683—62no—
226C4×Dic5—61no—
227#677—62no—
228#677—122no—
229#554—151no—
230D42—51no—
231#486—151no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—31no—
239C2×#102—152no—
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5C2×SD1614yes—
243C22×C3×C5C22×D411yescharacteristic
244C2×C3×D5—22no—
245C2×C3×D5—41no—
246C2×C3×D5—41no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—42no—
250C2×C3×D5—88no—
251C3×C4×C5—22no—
252C3×C4×C5—21no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—41no—
257Dic15—42no—
258Dic15—41no—
259C3×Dic5—41no—
260C24×C3—102no—
261C2×C3×D4—51no—
262C2×C3×D4—52no—
263C2×C3×D4—104no—
264C2×C3×D4—102no—
265C2×C3×D4—102no—
266C2×C3×D4—101no—
267C2×C3×D4—101no—
268C2×C3×D4—202no—
269C2×C3×D4—204no—
270C2×C3×D4D2011yescharacteristic
271C22×C3×C4—101no—
272C22×C3×C4C22×D512yes—
273C22×Dic3—102no—
274C2×Dic6—51no—
275C2×Dic6—101no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4D2011yescharacteristic
278C3×C22⋊C4—101no—
279C3×C22⋊C4—102no—
280C3×C22⋊C4D2012yes—
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—42no—
293C2×C3⋊C8C22×D511yescharacteristic
294C2×C3⋊C8C22×D511yescharacteristic
295C2×C3⋊C8C22×D512yes—
296C23×C5C2×#6712yes—
297C22×D5—21no—
298C22×D5—22no—
299C22×D5—44no—
300C22×D5—44no—
301C22×D5—82no—
302C5×D4#21414yescomplemented
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5C2×#6712yes—
306C2×C4×C5C2×#6711yescharacteristic
307C2×C4×C5C2×#6711yescharacteristic
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—44no—
310C2×Dic5—21no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—62no—
314C2×Dic5—242no—
315D20—22no—
316D20—21no—
317D20—22no—
318D20—44no—
319D20—42no—
320D20—81no—
321D20#23712yes—
322C4×D5—42no—
323Dic10—61no—
324Dic10—61no—
325Dic10—241no—
326C5×C8—61no—
327C5×C8—62no—
328C5×C8—61no—
329C22×D4—52no—
330C22×D4—101no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—32no—
334C4⋊Q8—151no—
335#127—51no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—52no—
340#121—101no—
341#120—102no—
342C4×Q8—151no—
343C4×D4—51no—
344C4×D4—301no—
345C4×D4D3×D511yescharacteristic
346C2×C4⋊C4—152no—
347#106—151no—
348#106—152no—
349C4⋊C8—31no—
350#103—151no—
351#102—151no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—32no—
357C4×C8—31no—
358C2×C3×C5—24no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362C3×D5—42no—
363C3×D5—82no—
364C23×C3—101no—
365C23×C3—102no—
366C23×C3—204no—
367C23×C3—204no—
368C23×C3—402no—
369C23×C3C2×D2012yes—
370C3×D4—52no—
371C3×D4—101no—
372C3×D4—102no—
373C3×D4—102no—
374C3×D4—204no—
375C3×D4—204no—
376C3×D4—202no—
377C3×D4—401no—
378C3×D4#67714yescomplemented
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—101no—
382C2×C3×C4—202no—
383C2×C3×C4C2×D2012yes—
384C2×C3×C4C2×D2011yescharacteristic
385C2×C3×C4C2×D2011yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387C2×Dic3—101no—
388C2×Dic3—101no—
389C2×Dic3—102no—
390C2×Dic3—402no—
391Dic6—101no—
392Dic6—101no—
393Dic6—401no—
394C3⋊C8—21no—
395C3⋊C8—22no—
396C3⋊C8—21no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5C2×#21414yes—
400C22×C5C22×#6711yescharacteristic
401C2×D5—22no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—42no—
405C2×D5—42no—
406C2×D5—42no—
407C2×D5—88no—
408C4×C5—22no—
409C4×C5—21no—
410C4×C5C2×#21412yes—
411C4×C5C2×#23711yescharacteristic
412C4×C5#100411yescharacteristic
413Dic5—41no—
414Dic5—121no—
415Dic5—122no—
416Dic5—121no—
417C24—102no—
418C2×Q8—151no—
419C2×Q8—301no—
420C2×D4—51no—
421C2×D4—52no—
422C2×D4—104no—
423C2×D4—102no—
424C2×D4—102no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—202no—
428C2×D4—204no—
429C2×D4#120211yescharacteristic
430C22×C4—101no—
431C22×C4—302no—
432C22×C4C2×D3×D512yes—
433SD16—302no—
434SD16—602no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—32no—
438C2×C8—122no—
439C4⋊C4—51no—
440C4⋊C4—151no—
441C4⋊C4—152no—
442C4⋊C4—302no—
443C4⋊C4—301no—
444C4⋊C4—301no—
445C4⋊C4—302no—
446C4⋊C4#120211yescharacteristic
447C22⋊C4—101no—
448C22⋊C4—102no—
449C22⋊C4—302no—
450C22⋊C4#120212yes—
451C42—301no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—102no—
457C22×C3—201no—
458C22×C3—201no—
459C22×C3—202no—
460C22×C3—202no—
461C22×C3—202no—
462C22×C3—408no—
463C22×C3C2×#67714yes—
464C22×C3C22×D2011yescharacteristic
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—201no—
468C3×C4C2×#67712yes—
469C3×C4#414411yescharacteristic
470C3×C4D5×#4111yescharacteristic
471Dic3—202no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—24no—
475C2×C5C22×#21411yescharacteristic
476C2×C5#580611yescharacteristic
477C2×C5#583511yescharacteristic
478D5—42no—
479D5—82no—
480C23—101no—
481C23—102no—
482C23—204no—
483C23—204no—
484C23—402no—
485C23C2×#120212yes—
486Q8—301no—
487Q8—301no—
488Q8—1201no—
489D4—52no—
490D4—102no—
491D4—101no—
492D4—102no—
493D4—204no—
494D4—204no—
495D4—202no—
496D4—401no—
497D4#665714yescomplemented
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—101no—
501C2×C4—202no—
502C2×C4—301no—
503C2×C4—301no—
504C2×C4—302no—
505C2×C4—1202no—
506C2×C4C2×#120211yescharacteristic
507C2×C4C2×#120212yes—
508C2×C4C2×#120211yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—62no—
513C2×C3—24no—
514C2×C3—202no—
515C2×C3—402no—
516C2×C3#6588811yescharacteristic
517C2×C3C22×#67711yescharacteristic
518C2×C3#6608611yescharacteristic
519C5#8348311yescharacteristic, complemented, Sylow
520C22—22no—
521C22—22no—
522C22—102no—
523C22—201no—
524C22—201no—
525C22—202no—
526C22—202no—
527C22—202no—
528C22—408no—
529C22C2×#665714yes—
530C22C22×#120211yescharacteristic
531C4—21no—
532C4—22no—
533C4—201no—
534C4—601no—
535C4—602no—
536C4—601no—
537C4C2×#665712yes—
538C4D5×#23711yescharacteristic
539C4#9202511yescharacteristic
540C3#1061117011yescharacteristic, complemented, Sylow
541C2—24no—
542C2—202no—
543C2—402no—
544C2C22×#665711yescharacteristic
545C2#1175496311yescharacteristic
546C2#1175531111yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×D4×D20C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756302C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748539C2semidirect
5. #11748530C2semidirect
6. #11748375C2semidirect
7. C2×#90965C2semidirect
8. #11747083C2semidirect
9. C4×#6657C2semidirect
10. #11746890C2semidirect
11. #11746881C2semidirect
17. C2×C4⋊Dic15C22semidirect
18. #91813C22semidirect
21. #91758C22semidirect
22. C4×Dic30C22semidirect
23. C22×C5×C3⋊C8C22semidirect
30. C2×#6657C22semidirect
31. C5×#830C22semidirect
32. C5×C4⋊(C3⋊C8)C22semidirect
33. C4×C5×C3⋊C8C22semidirect
34. #90987C22semidirect
35. #90987C22semidirect
36. #90974C22semidirect
39. #90965C22semidirect
40. #90965C22semidirect
41. #90965C22semidirect
99. D4×C3⋊C8D5semidirect
137. C3×C5×D4SD16semidirect
177. C22×C3⋊C8C2×D5semidirect
187. #830C2×D5semidirect
191. C4⋊(C3⋊C8)C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
302. C5×D4#214semidirect
378. C3×D4#677semidirect
453. C3×C5#3295semidirect
497. D4#6657semidirect
519. C5#83483semidirect
540. C3#10611170semidirect

Maximal subgroups

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

subgroupindex
#117563022
C3×D4×D202
C5×D4×C3⋊C82
#117485392
#117485302
#117483752
C2×#909652
#117470832
C4×#66572
#117468902
#117468812
#106111703
#834835