Finite Group Databasebeta

← #14458575

Subgroups — #14458575

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
1C5×#5717C211yesmaximal, characteristic
2#11752660C211yesmaximal, characteristic, complemented
3#11751171C211yesmaximal, characteristic, complemented
4C3×#65364C211yesmaximal, characteristic, complemented
5#11749058C212yesmaximal, complemented
6#11749050C212yesmaximal, complemented
7#11748956C212yesmaximal, complemented
8D3×#3964C212yesmaximal, complemented
9C4×#6656C211yesmaximal, characteristic, complemented
10#11746998C211yesmaximal, characteristic, complemented
11#11746883C211yesmaximal, characteristic, complemented
12#10615214—31nomaximal, Hall
13C2×C5×D3×D4—21no—
14C2×C5×D3×D4C2212yes—
15C3×C5×#127C2211yescharacteristic
16#91758C2211yescharacteristic, complemented
17C5×#938—21no—
18C5×#938C2212yes—
19C5×#937—22no—
20C4×C5×D12C2211yescharacteristic
21C4×C5×D12C2211yescharacteristic
22C2×C3×#687C2212yescomplemented
23C3×C4×Dic10C2211yescharacteristic, complemented
24#91432—22no—
25D3×C4⋊Dic5C2212yescomplemented
26Dic5×D12—21no—
27#91388—21no—
28#91369C2212yescomplemented
29C2×#6656C2211yescharacteristic
30C2×D3×#168C2212yescomplemented
31#91116C2212yescomplemented
32#91116C2212yescomplemented
33C4×C3⋊#168C2211yescharacteristic, complemented
34C3×#3964C2212yescomplemented
35C3×C4⋊#168C2211yescharacteristic, complemented
36#90986C2211yescharacteristic, complemented
37#90985C2212yescomplemented
38#90970C2211yescharacteristic, complemented
39#90967C2212yes—
40#90966C2211yescharacteristic
41(C2×D3)⋊#168C2212yescomplemented
42#80395—51nomaximal, Hall
43C5×D42—31no—
44#65877—31no—
45#65507—32no—
46C2×#3964—32no—
47#65364D311yescharacteristic, complemented
48#65359—31no—
49#65330—32no—
50#65323—32no—
51C4×#687—31no—
52D4×#168—31no—
53#65297—31no—
54C23×C5×D3—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2312yes—
58C2×Dic30—21no—
59C2×C5×#67—22no—
60C2×C5×#67—22no—
61C5×D3×D4—24no—
62C5×D3×D4—42no—
63C5×D3×D4—44no—
64C2×C5×D12D411yescharacteristic
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C2×C4×C5×D3C2312yes—
68C2×C3×Dic10C2311yescharacteristic
69C2×D3×Dic5—22no—
70C3×C42×C5C2311yescharacteristic
71C4⋊Dic15—21no—
72C4⋊Dic15C2312yes—
73C2×C3⋊#168C2311yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75C5×#217—22no—
76C5×(C2×D3)⋊C4—21no—
77C5×(C2×D3)⋊C4D412yes—
78C5×C4⋊Dic3D411yescharacteristic
79C5×C4⋊Dic3C2311yescharacteristic
80C3×#687—42no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—21no—
83C3×C4×Dic5—21no—
84C2×C3×#168C2312yes—
85Dic3⋊Dic5—22no—
86#6669—22no—
87(C2×D3)⋊Dic5—22no—
88#6656—22no—
89D3×#168—42no—
90#5717D511yescharacteristic
91#5579—51no—
92C3×#460—51no—
93#5171—52no—
94#5169—52no—
95#5070—51no—
96C4×#215—51no—
97#4842—51no—
98#4834—51no—
99#4777—52no—
100D3×#102—52no—
101C22×C5×D4—32no—
102C22×C5×D4—61no—
103C5×#127C2×D311yescharacteristic
104C5×#121—32no—
105C5×#121—61no—
106C5×#120—62no—
107C4×C5×D4—31no—
108C4×C5×D4—31no—
109D4×Dic5—61no—
110C2×#687—31no—
111C2×#687C2×D312yescomplemented
112C2×C4⋊Dic5—32no—
113#4070—32no—
114C22×#168—32no—
115#4036—61no—
116#4024—62no—
117#4015—31no—
118C4×Dic10C2×D311yescharacteristic, complemented
119#3964—32no—
120#3964—32no—
121#3964—31no—
122#3964—32no—
123#3964C2×D312yescomplemented
124C22⋊#168—32no—
125#3942—31no—
126#3940—31no—
127#3940—32no—
128C4⋊#168C2×D311yescharacteristic, complemented
129C4×#168—31no—
130#3295—151noSylow
131C23×C3×C5—22no—
132C22×C5×D3—21no—
133C22×C5×D3—44no—
134C22×C5×D3—44no—
135C22×C5×D3—82no—
136C22×C5×D3C2×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—22no—
145Dic30—81no—
146C5×#67—44no—
147C5×#67—44no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3C2×D412yes—
150C5×D12—21no—
151C5×D12SD1614yescomplemented
152C5×D12#4112yes—
153C4×C5×D3—22no—
154C4×C5×D3—22no—
155C4×C5×D3—42no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C3×Dic10—21no—
159C3×Dic10—21no—
160D3×Dic5—82no—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C3×#168—22no—
164C2×D3×D4—21no—
165C2×D3×D4C2×D512yes—
166C2×C3×SD16—52no—
167C3×#127C2×D511yescharacteristic
168C3×C4×Q8—51no—
169#946—52no—
170C2×#215—51no—
171#938—21no—
172#938C2×D512yes—
173#937—22no—
174C2×D3×C8—52no—
175#896—102no—
176D3×C4⋊C4—52no—
177C4×D12—101no—
178C4×D12C2×D511yescharacteristic
179C4×D12C2×D511yescharacteristic
180#870—101no—
181#869—51no—
182C3×C4⋊C8—51no—
183C3×#102—52no—
184#835—51no—
185#832—52no—
186#832—52no—
187#821—52no—
188(C2×D3)⋊C8—52no—
189#817—52no—
190#809—51no—
191#808—51no—
192C4×C3⋊C8—51no—
193C24×C5—62no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—31no—
197C2×C5×D4—31no—
198C2×C5×D4—62no—
199C2×C5×D4—64no—
200C2×C5×D4—62no—
201C2×C5×D4—122no—
202C2×C5×D4—124no—
203C2×C5×D4C22×D312yes—
204C22×C4×C5—32no—
205C22×C4×C5—61no—
206C22×Dic5—62no—
207C2×Dic10—61no—
208C2×Dic10C22×D311yescharacteristic
209C5×C4⋊C4—31no—
210C5×C4⋊C4—31no—
211C5×C22⋊C4—32no—
212C5×C22⋊C4—62no—
213C5×C22⋊C4—61no—
214C42×C5C22×D311yescharacteristic
215C22⋊Dic5—62no—
216#687—42no—
217#687—62no—
218C4⋊Dic5—32no—
219C4⋊Dic5—62no—
220C4⋊Dic5—61no—
221C4⋊Dic5C22×D311yescharacteristic
222#683—21no—
223#683—62no—
224C4×Dic5—21no—
225C2×#168—31no—
226C2×#168—31no—
227C2×#168—122no—
228C2×#168C22×D312yes—
229#554—151no—
230D42—31no—
231#486—151no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—51no—
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×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—41no—
249C2×C5×D3—88no—
250C2×C5×D3C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5C2×SD1612yes—
253C3×C4×C5C2×#4111yescharacteristic
254C3×C4×C5H(5,𝔽2)11yescharacteristic
255Dic15—42no—
256C3×Dic5—41no—
257C3×Dic5—41no—
258C5×Dic3—22no—
259C5×Dic3—41no—
260C23×D3—22no—
261C2×C3×Q8—51no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4C22×D512yes—
265C2×#67—22no—
266C2×#67—22no—
267D3×D4—24no—
268D3×D4—42no—
269D3×D4—44no—
270C2×D12C22⋊D511yescharacteristic
271C2×D12C22×D511yescharacteristic
272C2×C4×D3—21no—
273C2×C4×D3—102no—
274C2×C4×D3C22×D512yes—
275C2×Dic6—101no—
276C3×SD16—202no—
277C2×C3×C8—52no—
278C3×C4⋊C4—51no—
279C3×C4⋊C4—101no—
280C3×C42—101no—
281C3×C42C22×D511yescharacteristic
282#217—22no—
283#215—102no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—102no—
286(C2×D3)⋊C4C22⋊D512yes—
287C4⋊Dic3—52no—
288C4⋊Dic3—101no—
289C4⋊Dic3C22⋊D511yescharacteristic
290C4⋊Dic3C22×D511yescharacteristic
291Dic3⋊C4—102no—
292Dic3⋊C4—102no—
293C2×C3⋊C8—51no—
294C2×C3⋊C8—51no—
295D3×C8—202no—
296C23×C5—22no—
297C23×C5—32no—
298C23×C5—61no—
299C23×C5—124no—
300C23×C5—124no—
301C23×C5—242no—
302C5×D4—22no—
303C5×D4—22no—
304C5×D4—34no—
305C5×D4—32no—
306C5×D4—42no—
307C5×D4—61no—
308C5×D4—81no—
309C5×D4—124no—
310C5×D4—124no—
311C2×C4×C5—32no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—61no—
315C2×C4×C5—122no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—62no—
322C2×Dic5—242no—
323Dic10—21no—
324Dic10—21no—
325Dic10—241no—
326#168—22no—
327#168—61no—
328#168—61no—
329C22×D4—32no—
330C22×D4—61no—
331C2×SD16—52no—
332C2×SD16—151no—
333C22×C8—152no—
334C4⋊Q8—151no—
335#127D3×D511yescharacteristic
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—32no—
340#121—61no—
341#120—62no—
342C4×Q8—51no—
343C4×D4—31no—
344C4×D4—31no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—151no—
348#106—152no—
349C4⋊C8—51no—
350#103—151no—
351#102—52no—
352#102—151no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—151no—
358C2×C3×C5—82no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362C5×D3—24no—
363C5×D3—42no—
364C23×C3—22no—
365C22×D3—21no—
366C22×D3—44no—
367C22×D3—44no—
368C22×D3—82no—
369C22×D3C2×C22⋊D512yes—
370C3×Q8—101no—
371C3×Q8—101no—
372C3×D4—22no—
373C3×D4—22no—
374C3×D4—42no—
375C3×D4—81no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C2×C22⋊D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—44no—
382#67—44no—
383C2×Dic3—21no—
384C2×Dic3—102no—
385C2×Dic3C2×C22⋊D512yes—
386D12—21no—
387D12#68714yescomplemented
388D12#71112yes—
389C4×D3—22no—
390C4×D3—22no—
391C4×D3—42no—
392C4×D3—402no—
393Dic6—401no—
394C3×C8—102no—
395C3⋊C8—101no—
396C3⋊C8—101no—
397C22×C5—34no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5—42no—
401C22×C5—62no—
402C22×C5—62no—
403C22×C5—62no—
404C22×C5—121no—
405C22×C5—121no—
406C22×C5—248no—
407C22×C5C2×D3×D411yescharacteristic
408C4×C5—21no—
409C4×C5—62no—
410C4×C5—121no—
411C4×C5D3×SD1612yes—
412C4×C5#100411yescharacteristic
413C4×C5D3×#4111yescharacteristic
414Dic5—41no—
415Dic5—41no—
416Dic5—122no—
417C24—62no—
418C2×Q8—51no—
419C2×Q8—301no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—31no—
423C2×D4—31no—
424C2×D4—62no—
425C2×D4—64no—
426C2×D4—62no—
427C2×D4—122no—
428C2×D4—124no—
429C2×D4C2×D3×D512yes—
430C22×C4—32no—
431C22×C4—61no—
432C22×C4—302no—
433SD16—202no—
434SD16—302no—
435C2×C8—52no—
436C2×C8—151no—
437C2×C8—151no—
438C2×C8—602no—
439C4⋊C4—31no—
440C4⋊C4—31no—
441C4⋊C4—51no—
442C4⋊C4—101no—
443C4⋊C4—152no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—301no—
447C22⋊C4—32no—
448C22⋊C4—62no—
449C22⋊C4—61no—
450C22⋊C4—302no—
451C42—101no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3C22×C22⋊D511yescharacteristic
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—22no—
461C2×D3—41no—
462C2×D3—41no—
463C2×D3—88no—
464C2×D3C2×#68714yes—
465C3×C4—21no—
466C3×C4—201no—
467C3×C4—201no—
468C3×C4C2×#68712yes—
469C3×C4C2×#71111yescharacteristic
470C3×C4#414411yescharacteristic
471Dic3—22no—
472Dic3—41no—
473Dic3—202no—
474C2×C5—64no—
475C2×C5—82no—
476C2×C5—122no—
477C2×C5#561211yescharacteristic
478C2×C5C2×D3×SD1611yescharacteristic
479C2×C5#577411yescharacteristic
480C23—22no—
481C23—32no—
482C23—61no—
483C23—124no—
484C23—124no—
485C23—242no—
486Q8—101no—
487Q8—101no—
488Q8—1201no—
489D4—22no—
490D4—22no—
491D4—34no—
492D4—32no—
493D4—42no—
494D4—61no—
495D4—81no—
496D4—124no—
497D4—124no—
498C2×C4—32no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—61no—
502C2×C4—101no—
503C2×C4—101no—
504C2×C4—122no—
505C2×C4—302no—
506C2×C4—1202no—
507C2×C4D3×C22⋊D511yescharacteristic
508C2×C4D3×C22⋊D511yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—102no—
511C8—301no—
512C8—301no—
513C2×C3—82no—
514C2×C3C22×#68711yescharacteristic
515C2×C3#6614011yescharacteristic
516C2×C3#6616911yescharacteristic
517D3—24no—
518D3—42no—
519C5#8039511yescharacteristic, complemented, Sylow
520C22—34no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—62no—
525C22—62no—
526C22—62no—
527C22—121no—
528C22—121no—
529C22—248no—
530C22C2×D3×C22⋊D511yescharacteristic
531C4—21no—
532C4—62no—
533C4—121no—
534C4—201no—
535C4—201no—
536C4—602no—
537C4D3×#68712yes—
538C4D3×#71111yescharacteristic
539C4#9202511yescharacteristic
540C3#1061521411yescharacteristic, complemented, Sylow
541C2—64no—
542C2—82no—
543C2—122no—
544C2#1175469811yescharacteristic
545C2C2×D3×#68711yescharacteristic
546C2#1175494611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC5×#5717C2
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. #11752660C2semidirect
3. #11751171C2semidirect
4. C3×#65364C2semidirect
5. #11749058C2semidirect
6. #11749050C2semidirect
7. #11748956C2semidirect
8. D3×#3964C2semidirect
9. C4×#6656C2semidirect
10. #11746998C2semidirect
11. #11746883C2semidirect
16. #91758C22semidirect
22. C2×C3×#687C22semidirect
23. C3×C4×Dic10C22semidirect
25. D3×C4⋊Dic5C22semidirect
28. #91369C22semidirect
30. C2×D3×#168C22semidirect
31. #91116C22semidirect
32. #91116C22semidirect
33. C4×C3⋊#168C22semidirect
34. C3×#3964C22semidirect
35. C3×C4⋊#168C22semidirect
36. #90986C22semidirect
37. #90985C22semidirect
38. #90970C22semidirect
41. (C2×D3)⋊#168C22semidirect
47. #65364D3semidirect
111. C2×#687C2×D3semidirect
118. C4×Dic10C2×D3semidirect
123. #3964C2×D3semidirect
128. C4⋊#168C2×D3semidirect
151. C5×D12SD16semidirect
387. D12#687semidirect
453. C3×C5#3295semidirect
519. C5#80395semidirect
540. C3#10615214semidirect

Maximal subgroups

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

subgroupindex
C5×#57172
#117526602
#117511712
C3×#653642
#117490582
#117490502
#117489562
D3×#39642
C4×#66562
#117469982
#117468832
#106152143
#803955