Finite Group Databasebeta

← #14458572

Subgroups — #14458572

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×#66051C211yesmaximal, characteristic
2#11752648C211yesmaximal, characteristic, complemented
3#11751176C211yesmaximal, characteristic, complemented
4C5×#5070C211yesmaximal, characteristic, complemented
5#11749046C212yesmaximal, complemented
6#11749045C212yesmaximal, complemented
7#11748952C212yesmaximal, complemented
8D5×#832C212yesmaximal, complemented
9C4×#6657C211yesmaximal, characteristic, complemented
10C3⋊C8×D20C211yesmaximal, characteristic, complemented
11#11746880C211yesmaximal, characteristic, complemented
12#10613308—31nomaximal, Hall
13C2×C3×D4×D5—21no—
14C2×C3×D4×D5C2212yes—
15C3×C5×#127C2211yescharacteristic
16C2×#6716C2212yescomplemented
17C4×Dic30C2211yescharacteristic, complemented
18C5×#869C2211yescharacteristic, complemented
19C3×#4084—21no—
20C3×#4084C2212yes—
21C3×#4083—22no—
22C3×C4×D20C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91434—21no—
25#91421—22no—
26D5×C4⋊Dic3C2212yescomplemented
27#91384—21no—
28#91360C2212yescomplemented
29C2×#6657C2211yescharacteristic
30C2×D5×C3⋊C8C2212yescomplemented
31#91116C2212yescomplemented
32C4⋊(C3⋊#168)C2211yescharacteristic, complemented
33C5×#832C2212yescomplemented
34C5×#832C2212yescomplemented
35C4×C5×C3⋊C8C2211yescharacteristic, complemented
36#90987C2211yescharacteristic, complemented
37#90986C2212yescomplemented
38#90974C2211yescharacteristic, complemented
39#90965C2211yescharacteristic
40#90964C2212yes—
41#90955C2212yescomplemented
42#83483—51nomaximal, Hall
43#66064—31no—
44#66051D311yescharacteristic
45C5×#486—31no—
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×C3×D5—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2312yes—
58C2×Dic30C2311yescharacteristic
59C2×C5×Dic6—21no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—22no—
62C3×D4×D5—24no—
63C3×D4×D5—42no—
64C3×D4×D5—44no—
65C2×C3×D20D411yescharacteristic
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C2×C3×C4×D5C2312yes—
69C2×D5×Dic3—22no—
70C3×C42×C5C2311yescharacteristic
71#6716—42no—
72C4⋊Dic15C2311yescharacteristic
73#6712—21no—
74C4×Dic15—21no—
75C2×C3⋊#168C2312yes—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C22⋊Dic5—22no—
81C3×#685—21no—
82C3×#685D412yes—
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5C2311yescharacteristic
85Dic3⋊Dic5—22no—
86#6668—22no—
87#6665—22no—
88#6657—22no—
89D5×C3⋊C8—42no—
90C3×D42—51no—
91#5543—51no—
92#5218—52no—
93C2×#832—52no—
94#5075—51no—
95#5070D511yescharacteristic, complemented
96#5041—52no—
97#5034—52no—
98C4×#214—51no—
99D4×C3⋊C8—51no—
100#5008—51no—
101C2×D4×D5—21no—
102C2×D4×D5C2×D312yes—
103C5×C4⋊Q8—31no—
104C5×#127C2×D311yescharacteristic
105#4092—62no—
106#4084—21no—
107#4084C2×D312yes—
108#4083—22no—
109C2×#687—32no—
110C2×#677—31no—
111C2×C8×D5—32no—
112#4043—32no—
113#4039—61no—
114D5×C4⋊C4—32no—
115#4036—61no—
116C4×D20C2×D311yescharacteristic
117C4×D20C2×D311yescharacteristic
118C4×Dic10—31no—
119C5×#102—32no—
120C5×#102—32no—
121C4×C5×C8—31no—
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×C3×D5—21no—
133C22×C3×D5—44no—
134C22×C3×D5—44no—
135C22×C3×D5—82no—
136C22×C3×D5C2×D412yes—
137C3×C5×D4—22no—
138C3×C5×D4—22no—
139C3×C5×D4—42no—
140C3×C5×D4—81no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146Dic30—21no—
147Dic30—21no—
148C2×C5×Dic3—22no—
149C5×Dic6—81no—
150C3×C22⋊D5—44no—
151C3×C22⋊D5—44no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5C2×D412yes—
154C3×D20—21no—
155C3×D20SD1614yescomplemented
156C3×D20#4112yes—
157C3×C4×D5—22no—
158C3×C4×D5—22no—
159C3×C4×D5—42no—
160D5×Dic3—82no—
161C3⋊#168—22no—
162C5×C3⋊C8—21no—
163C5×C3⋊C8—21no—
164C22×C3×D4—52no—
165C22×C3×D4—101no—
166C3×#127C2×D511yescharacteristic
167C3×#121—52no—
168C3×#121—101no—
169C3×#120—102no—
170C3×C4×D4—51no—
171C3×C4×D4—51no—
172D4×Dic3—101no—
173C2×#214—52no—
174C2×#214—51no—
175C2×C4⋊Dic3—52no—
176#924—52no—
177C22×C3⋊C8—52no—
178#890—101no—
179#878—102no—
180#869C2×D511yescharacteristic, complemented
181C4×Dic6—51no—
182#832—52no—
183#832—52no—
184#832—51no—
185#832C2×D512yescomplemented
186#832C2×D512yescomplemented
187#830—52no—
188#810—51no—
189#808—52no—
190#808—51no—
191C4⋊(C3⋊C8)—51no—
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—22no—
194C2×C5×Q8—61no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4C22×D312yes—
198C2×C22⋊D5—22no—
199C2×C22⋊D5—22no—
200D4×D5—24no—
201D4×D5—42no—
202D4×D5—44no—
203C2×D20#6711yescharacteristic
204C2×D20C22×D311yescharacteristic
205C2×C4×D5—21no—
206C2×C4×D5—62no—
207C2×C4×D5C22×D312yes—
208C2×Dic10—31no—
209C2×C5×C8—31no—
210C2×C5×C8—31no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—61no—
213C42×C5C22×D311yescharacteristic
214C22⋊Dic5—22no—
215#687—122no—
216#685—21no—
217#685—62no—
218#685#6712yes—
219C4⋊Dic5—31no—
220C4⋊Dic5—62no—
221C4⋊Dic5#6711yescharacteristic
222C4⋊Dic5C22×D311yescharacteristic
223#683—61no—
224#683—62no—
225C4×Dic5—61no—
226C2×#168—32no—
227#677—62no—
228C8×D5—122no—
229#554—151no—
230D42—51no—
231#486—31no—
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×C3×D5—22no—
245C2×C3×D5—22no—
246C2×C3×D5—22no—
247C2×C3×D5—41no—
248C2×C3×D5—41no—
249C2×C3×D5—88no—
250C2×C3×D5C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5C2×SD1612yes—
253C3×C4×C5C2×#4111yescharacteristic
254C3×C4×C5H(5,𝔽2)11yescharacteristic
255Dic15—41no—
256Dic15—41no—
257C3×Dic5—22no—
258C3×Dic5—41no—
259C5×Dic3—42no—
260C24×C3—102no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—51no—
264C2×C3×D4—51no—
265C2×C3×D4—102no—
266C2×C3×D4—104no—
267C2×C3×D4—102no—
268C2×C3×D4—202no—
269C2×C3×D4—204no—
270C2×C3×D4C22×D512yes—
271C22×C3×C4—52no—
272C22×C3×C4—101no—
273C22×Dic3—102no—
274C2×Dic6—21no—
275C2×Dic6—51no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—51no—
278C3×C22⋊C4—52no—
279C3×C22⋊C4—102no—
280C3×C22⋊C4—101no—
281C3×C42C22×D511yescharacteristic
282#217—102no—
283#214—102no—
284#214—202no—
285C4⋊Dic3—21no—
286C4⋊Dic3—51no—
287C4⋊Dic3—102no—
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—102no—
290Dic3⋊C4—101no—
291C4×Dic3—101no—
292C2×C3⋊C8—52no—
293C2×C3⋊C8—202no—
294C2×C3⋊C8C22×D511yescharacteristic
295C2×C3⋊C8C22×D511yescharacteristic
296C23×C5—22no—
297C22×D5—21no—
298C22×D5—44no—
299C22×D5—44no—
300C22×D5—82no—
301C22×D5C2×#6712yes—
302C5×Q8—241no—
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—42no—
306C5×D4—81no—
307C2×C4×C5—62no—
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C2×#6711yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—44no—
312C22⋊D5—44no—
313C2×Dic5—21no—
314C2×Dic5—61no—
315C2×Dic5—61no—
316C2×Dic5C2×#6712yes—
317D20—21no—
318D20#21414yescomplemented
319D20#23712yes—
320C4×D5—22no—
321C4×D5—22no—
322C4×D5—42no—
323C4×D5—242no—
324Dic10—61no—
325Dic10—61no—
326C5×C8—61no—
327C5×C8—61no—
328#168—62no—
329C22×D4—52no—
330C22×D4—101no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8—31no—
335#127D3×D511yescharacteristic
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—51no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—152no—
348#106—151no—
349C4⋊C8—151no—
350#103—151no—
351#102—32no—
352#102—32no—
353#102—152no—
354#102—151no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—31no—
358C2×C3×C5—82no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362C3×D5—24no—
363C3×D5—42no—
364C23×C3—22no—
365C23×C3—52no—
366C23×C3—101no—
367C23×C3—204no—
368C23×C3—204no—
369C23×C3—402no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—42no—
373C3×D4—52no—
374C3×D4—54no—
375C3×D4—81no—
376C3×D4—101no—
377C3×D4—204no—
378C3×D4—204no—
379C2×C3×C4—52no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—101no—
383C2×C3×C4—202no—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387C2×Dic3—22no—
388C2×Dic3—101no—
389C2×Dic3—101no—
390C2×Dic3—402no—
391Dic6—81no—
392Dic6—101no—
393Dic6—101no—
394C3⋊C8—21no—
395C3⋊C8—21no—
396C3⋊C8—102no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5C22×#6711yescharacteristic
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—22no—
404C2×D5—41no—
405C2×D5—41no—
406C2×D5—88no—
407C2×D5C2×#21414yes—
408C4×C5—21no—
409C4×C5—122no—
410C4×C5C2×#21412yes—
411C4×C5C2×#23711yescharacteristic
412C4×C5#100411yescharacteristic
413Dic5—22no—
414Dic5—41no—
415Dic5—121no—
416Dic5—121no—
417C24—102no—
418C2×Q8—61no—
419C2×Q8—151no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—51no—
423C2×D4—51no—
424C2×D4—102no—
425C2×D4—104no—
426C2×D4—102no—
427C2×D4—202no—
428C2×D4—204no—
429C2×D4C2×D3×D512yes—
430C22×C4—52no—
431C22×C4—101no—
432C22×C4—302no—
433SD16—302no—
434SD16—602no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—152no—
438C2×C8—602no—
439C4⋊C4—32no—
440C4⋊C4—51no—
441C4⋊C4—51no—
442C4⋊C4—61no—
443C4⋊C4—151no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—301no—
447C22⋊C4—52no—
448C22⋊C4—102no—
449C22⋊C4—101no—
450C22⋊C4—302no—
451C42—301no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—54no—
458C22×C3—102no—
459C22×C3—102no—
460C22×C3—102no—
461C22×C3—201no—
462C22×C3—201no—
463C22×C3—408no—
464C22×C3C2×D4×D511yescharacteristic
465C3×C4—21no—
466C3×C4—102no—
467C3×C4—201no—
468C3×C4D5×SD1612yes—
469C3×C4D5×#4111yescharacteristic
470C3×C4#414911yescharacteristic
471Dic3—42no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—82no—
475C2×C5C22×#21411yescharacteristic
476C2×C5#580611yescharacteristic
477C2×C5#583511yescharacteristic
478D5—24no—
479D5—42no—
480C23—22no—
481C23—52no—
482C23—101no—
483C23—204no—
484C23—204no—
485C23—402no—
486Q8—241no—
487Q8—301no—
488Q8—301no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—54no—
493D4—52no—
494D4—81no—
495D4—101no—
496D4—204no—
497D4—204no—
498C2×C4—52no—
499C2×C4—62no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4—101no—
503C2×C4—202no—
504C2×C4—301no—
505C2×C4—301no—
506C2×C4—1202no—
507C2×C4D5×#6711yescharacteristic
508C2×C4D5×#6711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—302no—
513C2×C3—82no—
514C2×C3—104no—
515C2×C3—202no—
516C2×C3#6601011yescharacteristic
517C2×C3#6609111yescharacteristic
518C2×C3C2×D5×SD1611yescharacteristic
519C5#8348311yescharacteristic, complemented, Sylow
520C22—42no—
521C22—42no—
522C22—42no—
523C22—54no—
524C22—102no—
525C22—102no—
526C22—102no—
527C22—201no—
528C22—201no—
529C22—408no—
530C22C2×D5×#6711yescharacteristic
531C4—21no—
532C4—102no—
533C4—122no—
534C4—201no—
535C4—601no—
536C4—601no—
537C4D5×#21412yes—
538C4D5×#23711yescharacteristic
539C4#9202611yescharacteristic
540C3#1061330811yescharacteristic, complemented, Sylow
541C2—82no—
542C2—104no—
543C2—202no—
544C2#1175469111yescharacteristic
545C2C2×D5×#21411yescharacteristic
546C2#1175493111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC3×#66051C2
hypercenter#127D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11752648C2semidirect
3. #11751176C2semidirect
4. C5×#5070C2semidirect
5. #11749046C2semidirect
6. #11749045C2semidirect
7. #11748952C2semidirect
8. D5×#832C2semidirect
9. C4×#6657C2semidirect
10. C3⋊C8×D20C2semidirect
11. #11746880C2semidirect
16. C2×#6716C22semidirect
17. C4×Dic30C22semidirect
18. C5×#869C22semidirect
26. D5×C4⋊Dic3C22semidirect
28. #91360C22semidirect
30. C2×D5×C3⋊C8C22semidirect
31. #91116C22semidirect
32. C4⋊(C3⋊#168)C22semidirect
33. C5×#832C22semidirect
34. C5×#832C22semidirect
35. C4×C5×C3⋊C8C22semidirect
36. #90987C22semidirect
37. #90986C22semidirect
38. #90974C22semidirect
41. #90955C22semidirect
95. #5070D5semidirect
155. C3×D20SD16semidirect
180. #869C2×D5semidirect
185. #832C2×D5semidirect
186. #832C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
318. D20#214semidirect
453. C3×C5#3295semidirect
519. C5#83483semidirect
540. C3#10613308semidirect

Maximal subgroups

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

subgroupindex
C3×#660512
#117526482
#117511762
C5×#50702
#117490462
#117490452
#117489522
D5×#8322
C4×#66572
C3⋊C8×D202
#117468802
#106133083
#834835