Finite Group Databasebeta

← #14458551

Subgroups — #14458551

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×#5730C211yesmaximal, characteristic, complemented
2#11752745C211yesmaximal, characteristic
3#11751185C211yesmaximal, characteristic, complemented
4C3×#65377C211yesmaximal, characteristic, complemented
5#11747483C212yesmaximal, complemented
6D3×#3941C212yesmaximal, complemented
7#11747321C212yesmaximal, complemented
8#11747320C212yesmaximal, complemented
9#11747068C211yesmaximal, characteristic, complemented
10C4×#6660C211yesmaximal, characteristic, complemented
11D12×#168C211yesmaximal, characteristic, complemented
12#10615365—31nomaximal, Hall
13C2×#6777—21no—
14C2×D3×D20C2212yes—
15C3×C5×C4⋊Q8C2211yescharacteristic, complemented
16C4×D60C2211yescharacteristic
17C5×#946—22no—
18C5×#897C2212yescomplemented
19C5×#893—21no—
20C5×D3×C4⋊C4C2212yescomplemented
21C5×#890—21no—
22C4×C5×D12C2211yescharacteristic
23C4×C5×Dic6C2211yescharacteristic, complemented
24C3×#4020C2211yescharacteristic
25#91474—22no—
26#91465—21no—
27#91456C2212yes—
28C2×#6660C2211yescharacteristic
29C2×#6655C2212yescomplemented
30C2×D3×#168C2212yescomplemented
31#91093C2212yes—
32#91092C2212yescomplemented
33C4⋊(C3⋊#168)C2211yescharacteristic, complemented
34C3×#3941C2212yescomplemented
35C3×#3941C2212yescomplemented
36C3×C4×#168C2211yescharacteristic, complemented
37#90985C2211yescharacteristic, complemented
38#90973C2211yescharacteristic, complemented
39#90969C2211yescharacteristic
40#90964C2212yescomplemented
41(C2×D3)⋊#168C2212yescomplemented
42#81577—51nomaximal, Hall
43C5×#554—31no—
44D4×D20—31no—
45#65377D311yescharacteristic, complemented
46#65373—31no—
47#65337—32no—
48#65335—32no—
49#65316—31no—
50C4×#688—31no—
51D4×#168—31no—
52#65257—32no—
53C2×#3941—32no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8—21no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C5×D12D411yescharacteristic
59C2×C4×C5×D3—22no—
60C2×C4×C5×D3C2312yes—
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20C2312yes—
65C2×#1202—22no—
66C2×#1201—22no—
67#6777—44no—
68D3×D20—24no—
69D3×D20—42no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C42×C5C2311yescharacteristic
73#6714—21no—
74C4⋊Dic15C2311yescharacteristic
75C2×C3⋊#168C2312yes—
76C5×(C2×D3)⋊C4—22no—
77C5×(C2×D3)⋊C4D412yes—
78C5×C4⋊Dic3—22no—
79C5×C4⋊Dic3D411yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C5×Dic3⋊C4—21no—
82C5×Dic3⋊C4—22no—
83C4×C5×Dic3—21no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
86#6665—22no—
87#6660—22no—
88#6655—42no—
89D3×#168—42no—
90#5730D511yescharacteristic, complemented
91#5717—51no—
92C3×#486—51no—
93#5084—51no—
94#5075—51no—
95#4778—52no—
96#4777—52no—
97#4776—52no—
98D3×#102—52no—
99C4×#204—51no—
100C8×D12—51no—
101C2×D4×D5—61no—
102C22×D20—32no—
103C5×C4⋊Q8C2×D311yescharacteristic, complemented
104C5×#125—61no—
105C5×C22⋊Q8—32no—
106C5×C22⋊Q8—62no—
107C4×C5×Q8—31no—
108C4×C5×D4—31no—
109C4×C5×D4—61no—
110C2×C5×C4⋊C4—32no—
111C2×#688—32no—
112C2×#688—31no—
113#4076—32no—
114C22×#168—32no—
115#4041—61no—
116#4028—62no—
117#4020C2×D311yescharacteristic
118C4×D20—31no—
119#3967—31no—
120C22⋊#168—32no—
121#3941—32no—
122#3941—32no—
123#3941—31no—
124#3941C2×D312yescomplemented
125#3941C2×D312yescomplemented
126#3940—32no—
127#3940—31no—
128C4⋊#168—31no—
129C4×#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C22×D15—21no—
132C22×C5×D3C2×D412yes—
133C22×C3×D5—22no—
134C2×D3×D5—44no—
135C2×D3×D5—44no—
136C2×D3×D5—82no—
137C3×C5×Q8—81no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143D60—21no—
144D60#4112yes—
145C4×D15—42no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3C2×D412yes—
149C5×D12SD1614yescomplemented
150C4×C5×D3—22no—
151C4×C5×D3—22no—
152C4×C5×D3—82no—
153C5×Dic6—21no—
154C5×Dic6—21no—
155C3×D20—22no—
156C3×D20—22no—
157C3×D20—42no—
158C3×D20—81no—
159#1202—44no—
160#1201—44no—
161C3⋊#168—22no—
162C3×#168—21no—
163C3×#168—21no—
164C2×D3×D4—52no—
165C2×D3×D4—101no—
166C3×C4⋊Q8C2×D511yescharacteristic, complemented
167C3×#127—51no—
168#946—22no—
169#938—52no—
170#938—101no—
171#937—102no—
172C2×#214—52no—
173C2×#204—51no—
174C2×D3×C8—52no—
175#897C2×D512yescomplemented
176#893—21no—
177D3×C4⋊C4C2×D512yescomplemented
178#890—21no—
179C4×D12—51no—
180C4×D12C2×D511yescharacteristic
181C4×Dic6C2×D511yescharacteristic, complemented
182C3×#102—52no—
183C3×#102—52no—
184C3×C4×C8—51no—
185#832—52no—
186#821—51no—
187(C2×D3)⋊C8—52no—
188#817—51no—
189#816—51no—
190#809—52no—
191#808—52no—
192C4⋊(C3⋊C8)—51no—
193C23×D5—62no—
194C2×C5×Q8—21no—
195C2×C5×Q8—31no—
196C2×C5×D4—31no—
197C22×C4×C5—32no—
198C22×C4×C5—62no—
199C2×C22⋊D5—62no—
200D4×D5—124no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20—31no—
204C2×D20—64no—
205C2×D20—62no—
206C2×D20—122no—
207C2×D20C22×D312yes—
208C2×C4×D5—61no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—31no—
212C5×C4⋊C4—62no—
213C5×C4⋊C4—62no—
214C5×C4⋊C4—61no—
215C5×C4⋊C4C22×D312yes—
216C5×C22⋊C4—32no—
217C5×C22⋊C4—62no—
218C42×C5—61no—
219C42×C5C22×D311yescharacteristic
220#688—62no—
221#688—122no—
222#685—62no—
223#685—61no—
224C4⋊Dic5—31no—
225C2×#168—32no—
226C2×#168—122no—
227C2×#168C22×D311yescharacteristic
228C2×#168C22×D311yescharacteristic
229#554—31no—
230D42—151no—
231#486—51no—
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×C5C22×D411yescharacteristic
241C2×D15—22no—
242C2×D15—41no—
243C2×D15—41no—
244C2×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3C2×SD1614yes—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—42no—
250D3×D5—88no—
251C3×C4×C5—21no—
252C3×C4×C5—42no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—41no—
257C5×Dic3—22no—
258C5×Dic3—41no—
259C5×Dic3—41no—
260C23×D3—102no—
261C2×C3×Q8—21no—
262C2×C3×D4—52no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×#67—102no—
266C2×#67—102no—
267D3×D4—104no—
268D3×D4—202no—
269D3×D4—204no—
270C2×D12—51no—
271C2×D12C22⋊D511yescharacteristic
272C2×C4×D3—22no—
273C2×C4×D3—101no—
274C2×C4×D3C22×D512yes—
275C2×Dic6C22×D511yescharacteristic
276C2×C3×C8—51no—
277C2×C3×C8—51no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4C22×D512yes—
280C3×C42C22×D511yescharacteristic
281#217—102no—
282#214—202no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—101no—
285(C2×D3)⋊C4C22⋊D512yes—
286C4⋊Dic3—22no—
287C4⋊Dic3—51no—
288C4⋊Dic3C22⋊D511yescharacteristic
289C4⋊Dic3C22×D511yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—22no—
292C4×Dic3—21no—
293C2×C3⋊C8—52no—
294#204—102no—
295D3×C8—202no—
296C23×C5—32no—
297C22×D5—22no—
298C22×D5—61no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—61no—
303C5×Q8—61no—
304C5×Q8—81no—
305C5×D4—34no—
306C2×C4×C5—22no—
307C2×C4×C5—32no—
308C2×C4×C5—62no—
309C2×C4×C5—62no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5—242no—
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—124no—
317C2×Dic5—61no—
318D20—22no—
319D20—22no—
320D20—32no—
321D20—42no—
322D20—61no—
323D20—81no—
324D20—124no—
325C4×D5—122no—
326#168—21no—
327#168—21no—
328#168—62no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8D3×D511yescharacteristic, complemented
335#127—51no—
336#125—61no—
337C22⋊Q8—32no—
338C22⋊Q8—62no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—31no—
343C4×D4—31no—
344C4×D4—61no—
345C4×D4—151no—
346C2×C4⋊C4—32no—
347#106—151no—
348#106—152no—
349C4⋊C8—151no—
350#103—151no—
351#102—52no—
352#102—52no—
353#102—151no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—51no—
358C2×C3×C5#54611yescharacteristic
359C2×C3×C5C22×SD1611yescharacteristic
360C2×C3×C5#57611yescharacteristic
361D15—42no—
362C3×D5—82no—
363C5×D3—24no—
364C23×C3—102no—
365C22×D3—101no—
366C22×D3—204no—
367C22×D3—204no—
368C22×D3—402no—
369C22×D3C2×C22⋊D512yes—
370C3×Q8—81no—
371C3×D4—102no—
372C3×D4—102no—
373C3×D4—202no—
374C3×D4—401no—
375C2×C3×C4—22no—
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—204no—
380#67—204no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—101no—
384C2×Dic3C2×C22⋊D512yes—
385D12—52no—
386D12—101no—
387D12#68814yescomplemented
388C4×D3—22no—
389C4×D3—22no—
390C4×D3—82no—
391C4×D3—202no—
392Dic6—21no—
393Dic6—21no—
394C3×C8—101no—
395C3×C8—101no—
396C3⋊C8—102no—
397C22×C5—34no—
398C22×C5—62no—
399C22×C5—62no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—42no—
410C4×C5—62no—
411C4×C5—121no—
412C4×C5—121no—
413C4×C5D3×SD1612yes—
414C4×C5D3×#4111yescharacteristic
415C4×C5#100911yescharacteristic
416Dic5—121no—
417C24—302no—
418C2×Q8—21no—
419C2×Q8—31no—
420C2×D4—31no—
421C2×D4—52no—
422C2×D4—101no—
423C2×D4—101no—
424C2×D4—151no—
425C2×D4—302no—
426C2×D4—304no—
427C2×D4—302no—
428C2×D4—602no—
429C2×D4—604no—
430C22×C4—32no—
431C22×C4—62no—
432C22×C4—301no—
433SD16—302no—
434SD16—602no—
435C2×C8—51no—
436C2×C8—51no—
437C2×C8—152no—
438C2×C8—602no—
439C4⋊C4—21no—
440C4⋊C4—31no—
441C4⋊C4—31no—
442C4⋊C4—62no—
443C4⋊C4—62no—
444C4⋊C4—61no—
445C4⋊C4—151no—
446C4⋊C4C2×D3×D512yes—
447C22⋊C4—32no—
448C22⋊C4—62no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—61no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—202no—
455C22×C3—202no—
456C22×C3—202no—
457C22×C3C22×C22⋊D511yescharacteristic
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—102no—
461C2×D3—201no—
462C2×D3—201no—
463C2×D3—408no—
464C2×D3C2×#68814yes—
465C3×C4—21no—
466C3×C4—42no—
467C3×C4C2×#68812yes—
468C3×C4D5×#4111yescharacteristic
469C3×C4#414911yescharacteristic
470Dic3—22no—
471Dic3—41no—
472Dic3—41no—
473Dic3—201no—
474C2×C5—64no—
475C2×C5#567611yescharacteristic
476C2×C5#575711yescharacteristic
477C2×C5C2×D3×SD1611yescharacteristic
478D5—82no—
479D5—122no—
480C23—32no—
481C23—102no—
482C23—301no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—61no—
487Q8—61no—
488Q8—81no—
489D4—34no—
490D4—102no—
491D4—102no—
492D4—152no—
493D4—202no—
494D4—301no—
495D4—401no—
496D4—604no—
497D4—604no—
498C2×C4—22no—
499C2×C4—32no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—242no—
505C2×C4—301no—
506C2×C4—602no—
507C2×C4D3×C22⋊D511yescharacteristic
508C2×C4D3×C22⋊D511yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—101no—
511C8—101no—
512C8—302no—
513C2×C3—402no—
514C2×C3C22×#68811yescharacteristic
515C2×C3#6616311yescharacteristic
516C2×C3#6616911yescharacteristic
517D3—24no—
518D3—202no—
519C5#8157711yescharacteristic, complemented, Sylow
520C22—34no—
521C22—62no—
522C22—62no—
523C22—202no—
524C22—202no—
525C22—202no—
526C22—302no—
527C22—601no—
528C22—601no—
529C22—1208no—
530C22C2×D3×C22⋊D511yescharacteristic
531C4—21no—
532C4—42no—
533C4—62no—
534C4—121no—
535C4—121no—
536C4—601no—
537C4D3×#68812yes—
538C4#9203411yescharacteristic
539C4#9203511yescharacteristic
540C3#1061536511yescharacteristic, complemented, Sylow
541C2—64no—
542C2—402no—
543C2—602no—
544C2#1175469711yescharacteristic
545C2C2×D3×#68811yescharacteristic
546C2#1175528011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752745C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5730C2semidirect
3. #11751185C2semidirect
4. C3×#65377C2semidirect
5. #11747483C2semidirect
6. D3×#3941C2semidirect
7. #11747321C2semidirect
8. #11747320C2semidirect
9. #11747068C2semidirect
10. C4×#6660C2semidirect
11. D12×#168C2semidirect
15. C3×C5×C4⋊Q8C22semidirect
18. C5×#897C22semidirect
20. C5×D3×C4⋊C4C22semidirect
23. C4×C5×Dic6C22semidirect
29. C2×#6655C22semidirect
30. C2×D3×#168C22semidirect
32. #91092C22semidirect
33. C4⋊(C3⋊#168)C22semidirect
34. C3×#3941C22semidirect
35. C3×#3941C22semidirect
36. C3×C4×#168C22semidirect
37. #90985C22semidirect
38. #90973C22semidirect
40. #90964C22semidirect
41. (C2×D3)⋊#168C22semidirect
45. #65377D3semidirect
90. #5730D5semidirect
103. C5×C4⋊Q8C2×D3semidirect
124. #3941C2×D3semidirect
125. #3941C2×D3semidirect
129. C4×#168C2×D3semidirect
149. C5×D12SD16semidirect
166. C3×C4⋊Q8C2×D5semidirect
175. #897C2×D5semidirect
177. D3×C4⋊C4C2×D5semidirect
181. C4×Dic6C2×D5semidirect
334. C4⋊Q8D3×D5semidirect
387. D12#688semidirect
453. C3×C5#3295semidirect
519. C5#81577semidirect
540. C3#10615365semidirect

Maximal subgroups

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

subgroupindex
C5×#57302
#117527452
#117511852
C3×#653772
#117474832
D3×#39412
#117473212
#117473202
#117470682
C4×#66602
D12×#1682
#106153653
#815775