Finite Group Databasebeta

← #14458511

Subgroups — #14458511

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×D4×D20C211yesmaximal, characteristic
2#11752657C211yesmaximal, characteristic, complemented
3#11751109C211yesmaximal, characteristic, complemented
4C4×C5×#214C211yesmaximal, characteristic, complemented
5#11749044C212yesmaximal, complemented
6D5×#832C212yesmaximal, complemented
7#11747339C212yesmaximal, complemented
8#11747195C212yesmaximal, complemented
9#11747068C211yesmaximal, characteristic, complemented
10C3⋊C8×D20C211yesmaximal, characteristic, complemented
11#11746890C211yesmaximal, characteristic, complemented
12#10611407—31nomaximal, Hall
13C2×C3×D4×D5C2212yes—
14C22×C3×D20—21no—
15C3×C4×C5×D4C2211yescharacteristic
16#91758C2211yescharacteristic, complemented
17C2×C5×#214C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic, complemented
19C3×#4076—21no—
20C3×#4041C2212yes—
21C3×#4028—22no—
22C3×#4020C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91431—22no—
25Dic3×D20—21no—
26D5×C4⋊Dic3C2212yescomplemented
27#91381—21no—
28#91359C2212yescomplemented
29C2×#6655C2212yescomplemented
30C2×D5×C3⋊C8C2212yescomplemented
31#91116C2212yes—
32#91092C2212yescomplemented
33C4⋊(C3⋊#168)C2211yescharacteristic, complemented
34C5×#832C2211yescharacteristic
35C5×#810C2211yescharacteristic, complemented
36C5×#808C2211yescharacteristic, complemented
37C4×C5×C3⋊C8C2211yescharacteristic, complemented
38#90965C2212yescomplemented
39#90965C2212yescomplemented
40#90964C2212yescomplemented
41#90955C2212yescomplemented
42#83483—51nomaximal, Hall
43#65913—31no—
44D4×D20D311yescharacteristic
45C4×C5×SD16—31no—
46#65458—32no—
47#65316—31no—
48#65297—31no—
49#65152—32no—
50#65096—32no—
51D5×#102—32no—
52#64983—31no—
53C8×D20—31no—
54C23×C3×D5—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×Dic30—21no—
58C2×C5×Dic6C2311yescharacteristic
59C2×C3×C22⋊D5—22no—
60C3×D4×D5—24no—
61C3×D4×D5—42no—
62C2×C3×D20—22no—
63C2×C3×D20—21no—
64C2×C3×D20—21no—
65C2×C3×D20—44no—
66C2×C3×D20D411yescharacteristic
67C2×C3×D20C2312yes—
68C2×C3×C4×D5C2312yes—
69C2×D5×Dic3—22no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75C2×C3⋊#168C2312yes—
76C5×#214—22no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×Dic3⋊C4—21no—
79C4×C5×Dic3—21no—
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C3×#685—22no—
83C3×#685D412yes—
84C3×C4⋊Dic5D411yescharacteristic
85#6669—22no—
86#6668—22no—
87#6665—22no—
88#6655—42no—
89D5×C3⋊C8—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×#214D511yescharacteristic, complemented
99D4×C3⋊C8—51no—
100#5008—51no—
101C2×D4×D5C2×D312yes—
102C22×D20—21no—
103C2×C5×SD16—31no—
104C4×C5×Q8—31no—
105C4×C5×D4C2×D311yescharacteristic
106#4092—32no—
107C2×#688—32no—
108#4076—21no—
109C2×C8×D5—32no—
110#4042—62no—
111#4041C2×D312yes—
112D5×C4⋊C4—32no—
113#4028—22no—
114#4020C2×D311yescharacteristic
115C4×D20—61no—
116C4×D20C2×D311yescharacteristic
117#4016—61no—
118#4015—31no—
119C5×#106—31no—
120C5×#103—31no—
121C5×#102—31no—
122C4×C5×C8—31no—
123#3964—32no—
124#3953—32no—
125#3953—32no—
126#3952—32no—
127#3941—32no—
128#3940—32no—
129C4⋊#168—31no—
130#3295—151noSylow
131C23×C3×C5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—44no—
134C22×C3×D5—44no—
135C22×C3×D5—82no—
136C22×C3×D5C2×D412yes—
137C3×C5×D4—21no—
138C3×C5×D4#4112yes—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—42no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—22no—
145Dic30—81no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C5×Dic6—21no—
149C5×Dic6—21no—
150C3×C22⋊D5—44no—
151C2×C3×Dic5C2×D412yes—
152C3×D20—22no—
153C3×D20—22no—
154C3×D20—44no—
155C3×D20—42no—
156C3×D20—81no—
157C3×D20SD1614yescomplemented
158C3×C4×D5—22no—
159C3×C4×D5—22no—
160D5×Dic3—82no—
161C3⋊#168—22no—
162C5×C3⋊C8—21no—
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—52no—
174C2×#214C2×D511yescharacteristic
175C2×C4⋊Dic3—52no—
176#924—52no—
177C22×C3⋊C8—52no—
178#890—101no—
179#878—102no—
180#869—51no—
181C4×Dic6C2×D511yescharacteristic, complemented
182#832—52no—
183#832—52no—
184#832—52no—
185#832—52no—
186#832C2×D511yescharacteristic
187#830—52no—
188#810C2×D511yescharacteristic, complemented
189#808—52no—
190#808C2×D511yescharacteristic, complemented
191C4⋊(C3⋊C8)—51no—
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—22no—
194C2×C5×Q8—31no—
195C2×C5×D4C22×D311yescharacteristic
196C22×C4×C5—21no—
197C2×C22⋊D5—22no—
198D4×D5—24no—
199D4×D5—42no—
200C2×D20—22no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20—44no—
204C2×D20#6711yescharacteristic
205C2×D20C22×D312yes—
206C2×C4×D5—62no—
207C2×C4×D5C22×D312yes—
208C2×Dic10—61no—
209C5×SD16—62no—
210C2×C5×C8—31no—
211C2×C5×C8—31no—
212C5×C4⋊C4—31no—
213C5×C4⋊C4—61no—
214C5×C4⋊C4C22×D311yescharacteristic
215C5×C22⋊C4—21no—
216C42×C5—61no—
217C42×C5C22×D311yescharacteristic
218#688—122no—
219#685—22no—
220#685—62no—
221#685#6712yes—
222C4⋊Dic5—32no—
223C4⋊Dic5—61no—
224C4⋊Dic5#6711yescharacteristic
225#683—62no—
226#683—62no—
227C2×#168—32no—
228C8×D5—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—31no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—41no—
243C22×C3×C5C22×D411yescharacteristic
244C2×C3×D5—22no—
245C2×C3×D5—22no—
246C2×C3×D5—42no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—88no—
250C2×C3×D5C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—42no—
257C3×Dic5—22no—
258C5×Dic3—41no—
259C5×Dic3—41no—
260C24×C3—102no—
261C2×C3×D4—51no—
262C2×C3×D4—52no—
263C2×C3×D4—102no—
264C2×C3×D4—102no—
265C2×C3×D4—104no—
266C2×C3×D4—101no—
267C2×C3×D4—101no—
268C2×C3×D4—204no—
269C2×C3×D4—202no—
270C2×C3×D4C22×D511yescharacteristic
271C22×C3×C4—21no—
272C22×C3×C4—52no—
273C22×Dic3—102no—
274C2×Dic6—101no—
275C2×Dic6C22×D511yescharacteristic
276C3×C4⋊C4—51no—
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C22⋊C4—21no—
279C3×C22⋊C4—52no—
280C3×C22⋊C4—102no—
281C3×C42C22×D511yescharacteristic
282#217—102no—
283#214—22no—
284#214—202no—
285C4⋊Dic3—52no—
286C4⋊Dic3—102no—
287C4⋊Dic3—101no—
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—102no—
291C4×Dic3—21no—
292C2×C3⋊C8—52no—
293C2×C3⋊C8—202no—
294C2×C3⋊C8C22×D511yescharacteristic
295C2×C3⋊C8C22×D511yescharacteristic
296C23×C5—21no—
297C22×D5—22no—
298C22×D5—44no—
299C22×D5—44no—
300C22×D5—82no—
301C22×D5C2×#6712yes—
302C5×Q8—61no—
303C5×Q8—61no—
304C5×D4—21no—
305C5×D4#23712yes—
306C2×C4×C5—21no—
307C2×C4×C5—42no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5C2×#6711yescharacteristic
311C2×C4×C5C2×#6711yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C22⋊D5—44no—
314C2×Dic5—62no—
315C2×Dic5C2×#6712yes—
316D20—22no—
317D20—22no—
318D20—44no—
319D20—42no—
320D20—81no—
321D20#21414yescomplemented
322C4×D5—22no—
323C4×D5—22no—
324C4×D5—242no—
325Dic10—241no—
326C5×C8—61no—
327C5×C8—61no—
328#168—62no—
329C22×D4—52no—
330C22×D4—101no—
331C2×SD16—31no—
332C2×SD16—152no—
333C22×C8—152no—
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—31no—
343C4×D4—51no—
344C4×D4—301no—
345C4×D4D3×D511yescharacteristic
346C2×C4⋊C4—152no—
347#106—31no—
348#106—152no—
349C4⋊C8—151no—
350#103—31no—
351#102—31no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—31no—
358C2×C3×C5—42no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362C3×D5—24no—
363C3×D5—82no—
364C23×C3—21no—
365C23×C3—52no—
366C23×C3—102no—
367C23×C3—204no—
368C23×C3—204no—
369C23×C3—402no—
370C3×D4—21no—
371C3×D4—54no—
372C3×D4—102no—
373C3×D4—102no—
374C3×D4—204no—
375C3×D4—204no—
376C3×D4—202no—
377C3×D4—401no—
378C3×D4#70912yes—
379C2×C3×C4—21no—
380C2×C3×C4—42no—
381C2×C3×C4—52no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—102no—
390C2×Dic3—402no—
391Dic6—21no—
392Dic6—21no—
393Dic6—401no—
394C3⋊C8—21no—
395C3⋊C8—21no—
396C3⋊C8—102no—
397C22×C5—22no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C22×#6711yescharacteristic
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—42no—
404C2×D5—42no—
405C2×D5—42no—
406C2×D5—88no—
407C2×D5C2×#21414yes—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—121no—
411C4×C5—121no—
412C4×C5C2×#21412yes—
413C4×C5C2×#23711yescharacteristic
414C4×C5#100411yescharacteristic
415Dic5—22no—
416Dic5—122no—
417C24—102no—
418C2×Q8—31no—
419C2×Q8—301no—
420C2×D4—51no—
421C2×D4—52no—
422C2×D4—102no—
423C2×D4—102no—
424C2×D4—104no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—204no—
428C2×D4—202no—
429C2×D4C2×D3×D511yescharacteristic
430C22×C4—21no—
431C22×C4—52no—
432C22×C4—302no—
433SD16—62no—
434SD16—602no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—152no—
438C2×C8—602no—
439C4⋊C4—31no—
440C4⋊C4—51no—
441C4⋊C4—61no—
442C4⋊C4—152no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C2×D3×D511yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—52no—
449C22⋊C4—102no—
450C22⋊C4—302no—
451C42—61no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—54no—
458C22×C3—102no—
459C22×C3—102no—
460C22×C3—202no—
461C22×C3—202no—
462C22×C3—202no—
463C22×C3—408no—
464C22×C3C2×D4×D511yescharacteristic
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—102no—
468C3×C4D5×SD1612yes—
469C3×C4C2×#70911yescharacteristic
470C3×C4#414911yescharacteristic
471Dic3—41no—
472Dic3—41no—
473Dic3—202no—
474C2×C5—42no—
475C2×C5C22×#21411yescharacteristic
476C2×C5#580611yescharacteristic
477C2×C5#583511yescharacteristic
478D5—24no—
479D5—82no—
480C23—21no—
481C23—52no—
482C23—102no—
483C23—204no—
484C23—204no—
485C23—402no—
486Q8—61no—
487Q8—61no—
488Q8—1201no—
489D4—21no—
490D4—54no—
491D4—102no—
492D4—102no—
493D4—204no—
494D4—204no—
495D4—202no—
496D4—401no—
497D4#676512yes—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—52no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—102no—
504C2×C4—102no—
505C2×C4—302no—
506C2×C4—1202no—
507C2×C4D5×#6711yescharacteristic
508C2×C4D5×#6711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—302no—
513C2×C3—42no—
514C2×C3—104no—
515C2×C3—402no—
516C2×C3#6588411yescharacteristic
517C2×C3C2×D5×SD1611yescharacteristic
518C2×C3#6610311yescharacteristic
519C5#8348311yescharacteristic, complemented, Sylow
520C22—22no—
521C22—41no—
522C22—41no—
523C22—54no—
524C22—102no—
525C22—102no—
526C22—202no—
527C22—202no—
528C22—202no—
529C22—408no—
530C22C2×D5×#6711yescharacteristic
531C4—21no—
532C4—41no—
533C4—102no—
534C4—121no—
535C4—121no—
536C4—602no—
537C4D5×#21412yes—
538C4C2×#676511yescharacteristic
539C4#9201711yescharacteristic
540C3#1061140711yescharacteristic, complemented, Sylow
541C2—42no—
542C2—104no—
543C2—402no—
544C2#1175430511yescharacteristic
545C2C2×D5×#21411yescharacteristic
546C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752657C2semidirect
3. #11751109C2semidirect
4. C4×C5×#214C2semidirect
5. #11749044C2semidirect
6. D5×#832C2semidirect
7. #11747339C2semidirect
8. #11747195C2semidirect
9. #11747068C2semidirect
10. C3⋊C8×D20C2semidirect
11. #11746890C2semidirect
16. #91758C22semidirect
18. C4×C5×Dic6C22semidirect
26. D5×C4⋊Dic3C22semidirect
28. #91359C22semidirect
29. C2×#6655C22semidirect
30. C2×D5×C3⋊C8C22semidirect
32. #91092C22semidirect
33. C4⋊(C3⋊#168)C22semidirect
35. C5×#810C22semidirect
36. C5×#808C22semidirect
37. C4×C5×C3⋊C8C22semidirect
38. #90965C22semidirect
39. #90965C22semidirect
40. #90964C22semidirect
41. #90955C22semidirect
98. C4×#214D5semidirect
157. C3×D20SD16semidirect
181. C4×Dic6C2×D5semidirect
188. #810C2×D5semidirect
190. #808C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
321. D20#214semidirect
453. C3×C5#3295semidirect
519. C5#83483semidirect
540. C3#10611407semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D202
#117526572
#117511092
C4×C5×#2142
#117490442
D5×#8322
#117473392
#117471952
#117470682
C3⋊C8×D202
#117468902
#106114073
#834835