Finite Group Databasebeta

← #14458562

Subgroups — #14458562

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×#5579C211yesmaximal, characteristic, complemented
2D12×D20C211yesmaximal, characteristic
3#11751128C211yesmaximal, characteristic, complemented
4C3×C4×#688C211yesmaximal, characteristic, complemented
5#11749398C212yesmaximal, complemented
6#11749280C212yesmaximal, complemented
7D3×#3941C212yesmaximal, complemented
8#11747173C212yesmaximal, complemented
9D12×#168C211yesmaximal, characteristic, complemented
10#11746912C211yesmaximal, characteristic, complemented
11#11746880C211yesmaximal, characteristic, complemented
12#10615365—31nomaximal, Hall
13C2×D3×D20C2212yes—
14C2×D5×D12—21no—
15C3×C4×C5×Q8C2211yescharacteristic, complemented
16C2×#6717C2212yescomplemented
17#91763C2211yescharacteristic
18C5×#946C2212yescomplemented
19C5×#896—22no—
20C5×D3×C4⋊C4C2212yescomplemented
21C4×C5×D12—21no—
22C4×C5×D12C2211yescharacteristic
23C5×#870—21no—
24C5×#869C2211yescharacteristic, complemented
25C2×C3×#688C2211yescharacteristic
26C3×C4×D20C2211yescharacteristic
27#91476—22no—
28#91460C2212yes—
29#91450—21no—
30C2×D3×#168C2212yescomplemented
31#91093C2212yescomplemented
32C4⋊(C3⋊#168)C2211yescharacteristic, complemented
33C3×#3967C2211yescharacteristic, complemented
34C3×#3941C2211yescharacteristic
35C3×#3940C2211yescharacteristic, complemented
36C3×C4×#168C2211yescharacteristic, complemented
37#90986C2212yescomplemented
38#90969C2212yescomplemented
39#90969C2212yescomplemented
40#90964C2212yes—
41(C2×D3)⋊#168C2212yescomplemented
42#79676—51nomaximal, Hall
43C5×#554—31no—
44D4×D20—31no—
45#65377—31no—
46#65373—31no—
47#65337—32no—
48#65335—32no—
49#65316—31no—
50C4×#688D311yescharacteristic, complemented
51D4×#168—31no—
52#65257—32no—
53C2×#3941—32no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×D60—21no—
57C2×D60—21no—
58C2×D60C2312yes—
59C2×C5×D12D411yescharacteristic
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3C2312yes—
62C2×C5×Dic6—21no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×#1203—22no—
66C2×#1202—22no—
67D3×D20—24no—
68D3×D20—42no—
69D5×D12—44no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C42×C5—21no—
73C3×C42×C5C2311yescharacteristic
74#6717—42no—
75C2×C3⋊#168C2312yes—
76C5×(C2×D3)⋊C4—22no—
77C5×(C2×D3)⋊C4D412yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3D411yescharacteristic
80C5×C4⋊Dic3C2312yes—
81C5×Dic3⋊C4—22no—
82C5×Dic3⋊C4—22no—
83C3×#688—22no—
84C3×#685—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88#6667—22no—
89D3×#168—42no—
90#5579D511yescharacteristic, complemented
91D4×D12—51no—
92C3×C4×SD16—51no—
93#5169—52no—
94#5027—51no—
95#5008—51no—
96#4863—52no—
97#4807—52no—
98D3×#102—52no—
99#4694—51no—
100C8×D12—51no—
101C2×D4×D5—61no—
102C22×D20—32no—
103C5×C4⋊Q8—31no—
104C5×#125—61no—
105C5×C22⋊Q8—32no—
106C5×C22⋊Q8—62no—
107C4×C5×Q8C2×D311yescharacteristic, complemented
108C4×C5×D4—31no—
109C4×C5×D4—61no—
110C2×C5×C4⋊C4—32no—
111C2×#688—32no—
112C2×#688C2×D311yescharacteristic
113#4076—32no—
114C22×#168—32no—
115#4041—61no—
116#4028—62no—
117#4020—31no—
118C4×D20C2×D311yescharacteristic
119#3967C2×D311yescharacteristic, complemented
120C22⋊#168—32no—
121#3941—32no—
122#3941—32no—
123#3941—32no—
124#3941—32no—
125#3941C2×D311yescharacteristic
126#3940—32no—
127#3940C2×D311yescharacteristic, complemented
128C4⋊#168—31no—
129C4×#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C22×D15—22no—
132C22×C5×D3C2×D412yes—
133C22×C3×D5—21no—
134C2×D3×D5—44no—
135C2×D3×D5—44no—
136C2×D3×D5—82no—
137C3×C5×Q8—21no—
138C3×C5×Q8—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144D60—22no—
145D60—22no—
146D60—42no—
147D60—81no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C2×D412yes—
150C5×D12SD1614yescomplemented
151C4×C5×D3—22no—
152C4×C5×D3—22no—
153C4×C5×D3—82no—
154C5×Dic6—81no—
155C2×C3×Dic5—21no—
156C3×D20—21no—
157C3×D20#4112yes—
158C3×C4×D5—42no—
159#1203—44no—
160#1202—44no—
161C3⋊#168—22no—
162C3×#168—21no—
163C3×#168—21no—
164C2×D3×D4—52no—
165C22×D12—101no—
166C2×C3×SD16—51no—
167C3×C4×Q8C2×D511yescharacteristic, complemented
168C3×C4×D4—51no—
169#946C2×D512yescomplemented
170C2×#215—52no—
171#930—101no—
172C2×D3×C8—52no—
173#896—22no—
174#895—52no—
175D3×C4⋊C4C2×D512yescomplemented
176#882—102no—
177#874—51no—
178C4×D12—21no—
179C4×D12C2×D511yescharacteristic
180#870—21no—
181#869C2×D511yescharacteristic, complemented
182C3×#106—51no—
183C3×#103—51no—
184C3×#102—51no—
185C3×C4×C8—51no—
186#832—52no—
187#821—52no—
188#821—52no—
189(C2×D3)⋊C8—52no—
190#809—52no—
191#808—52no—
192C4⋊(C3⋊C8)—51no—
193C23×D5—62no—
194C2×C5×Q8—61no—
195C2×C5×Q8C22×D311yescharacteristic
196C2×C5×D4—31no—
197C22×C4×C5—32no—
198C22×C4×C5—62no—
199C2×C22⋊D5—62no—
200D4×D5—124no—
201C2×D20—32no—
202C2×D20—64no—
203C2×D20—62no—
204C2×D20—61no—
205C2×D20—61no—
206C2×D20—122no—
207C2×D20C22×D311yescharacteristic
208C2×C4×D5—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—62no—
213C5×C4⋊C4—62no—
214C5×C4⋊C4—61no—
215C5×C4⋊C4C22×D311yescharacteristic
216C5×C22⋊C4—32no—
217C5×C22⋊C4—62no—
218C42×C5—21no—
219C42×C5C22×D311yescharacteristic
220#688—22no—
221#688—122no—
222#685—21no—
223#685—62no—
224C4⋊Dic5C22×D311yescharacteristic
225C2×#168—32no—
226C2×#168—122no—
227C2×#168C22×D311yescharacteristic
228C2×#168C22×D311yescharacteristic
229#554—31no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—51no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5C22×D411yescharacteristic
241C2×D15—42no—
242C2×D15—42no—
243C2×D15—42no—
244C2×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3C2×SD1614yes—
247C2×C3×D5—22no—
248C2×C3×D5—41no—
249C2×C3×D5—41no—
250D3×D5—88no—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5—41no—
254C3×C4×C5C2×SD1612yes—
255C3×C4×C5C2×#4111yescharacteristic
256C3×C4×C5H(5,𝔽2)11yescharacteristic
257C3×Dic5—41no—
258C5×Dic3—22no—
259C5×Dic3—42no—
260C23×D3—102no—
261C2×C3×Q8C22×D511yescharacteristic
262C2×C3×D4—51no—
263C22×C3×C4—101no—
264C2×#67—102no—
265D3×D4—104no—
266D3×D4—202no—
267C2×D12—52no—
268C2×D12—102no—
269C2×D12—101no—
270C2×D12—101no—
271C2×D12—204no—
272C2×D12C22⋊D511yescharacteristic
273C2×C4×D3—22no—
274C2×C4×D3C22×D512yes—
275C2×Dic6—21no—
276C3×SD16—102no—
277C2×C3×C8—51no—
278C2×C3×C8—51no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C22⋊C4—101no—
283C3×C42—21no—
284C3×C42C22×D511yescharacteristic
285#215—202no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4C22⋊D512yes—
289C4⋊Dic3—21no—
290C4⋊Dic3C22⋊D511yescharacteristic
291C4⋊Dic3C22×D512yes—
292Dic3⋊C4—22no—
293Dic3⋊C4—22no—
294C2×C3⋊C8—52no—
295D3×C8—202no—
296C23×C5—32no—
297C22×D5—21no—
298C22×D5—62no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—21no—
303C5×Q8—21no—
304C5×Q8—241no—
305C5×D4—34no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—32no—
309C2×C4×C5—62no—
310C2×C4×C5—62no—
311C2×C4×C5—62no—
312C2×C4×C5—242no—
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—124no—
317C2×Dic5—21no—
318D20—21no—
319D20—62no—
320D20—62no—
321D20—124no—
322D20—122no—
323D20—241no—
324D20#23512yes—
325C4×D5—42no—
326#168—21no—
327#168—21no—
328#168—62no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—51no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8—31no—
335#127—151no—
336#125—61no—
337C22⋊Q8—32no—
338C22⋊Q8—62no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8D3×D511yescharacteristic, complemented
343C4×D4—31no—
344C4×D4—51no—
345C4×D4—61no—
346C2×C4⋊C4—32no—
347#106—51no—
348#106—152no—
349C4⋊C8—151no—
350#103—51no—
351#102—51no—
352#102—152no—
353#102—152no—
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—82no—
362C3×D5—42no—
363C5×D3—24no—
364C23×C3—101no—
365C22×D3—102no—
366C22×D3—204no—
367C22×D3—204no—
368C22×D3—402no—
369C22×D3C2×C22⋊D512yes—
370C3×Q8—21no—
371C3×Q8—21no—
372C3×D4—52no—
373C3×D4—101no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—101no—
377C2×C3×C4—202no—
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C2×C22⋊D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—204no—
382C2×Dic3—22no—
383C2×Dic3C2×C22⋊D512yes—
384D12—102no—
385D12—102no—
386D12—204no—
387D12—202no—
388D12—401no—
389D12#68814yescomplemented
390C4×D3—22no—
391C4×D3—22no—
392C4×D3—82no—
393Dic6—81no—
394C3×C8—101no—
395C3×C8—101no—
396C3⋊C8—102no—
397C22×C5—34no—
398C22×C5—62no—
399C22×C5—62no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—22no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—122no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—62no—
412C4×C5—122no—
413C4×C5D3×SD1612yes—
414C4×C5C2×#23511yescharacteristic
415C4×C5#100911yescharacteristic
416Dic5—41no—
417C24—302no—
418C2×Q8—61no—
419C2×Q8C2×D3×D511yescharacteristic
420C2×D4—31no—
421C2×D4—51no—
422C2×D4—152no—
423C2×D4—302no—
424C2×D4—304no—
425C2×D4—302no—
426C2×D4—301no—
427C2×D4—301no—
428C2×D4—602no—
429C2×D4—604no—
430C22×C4—32no—
431C22×C4—62no—
432C22×C4—101no—
433SD16—102no—
434SD16—602no—
435C2×C8—51no—
436C2×C8—51no—
437C2×C8—152no—
438C2×C8—602no—
439C4⋊C4—21no—
440C4⋊C4—31no—
441C4⋊C4—32no—
442C4⋊C4—51no—
443C4⋊C4—62no—
444C4⋊C4—62no—
445C4⋊C4—61no—
446C4⋊C4C2×D3×D511yescharacteristic
447C22⋊C4—32no—
448C22⋊C4—62no—
449C22⋊C4—101no—
450C22⋊C4—302no—
451C42—21no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—102no—
455C22×C3—201no—
456C22×C3—201no—
457C22×C3C22×C22⋊D511yescharacteristic
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—202no—
461C2×D3—202no—
462C2×D3—202no—
463C2×D3—408no—
464C2×D3C2×#68814yes—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—201no—
469C3×C4C2×#68812yes—
470C3×C4D5×#4111yescharacteristic
471C3×C4#414911yescharacteristic
472Dic3—22no—
473Dic3—42no—
474C2×C5—64no—
475C2×C5#555011yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#576911yescharacteristic
478D5—42no—
479D5—242no—
480C23—32no—
481C23—101no—
482C23—302no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—21no—
487Q8—21no—
488Q8—241no—
489D4—34no—
490D4—52no—
491D4—101no—
492D4—302no—
493D4—302no—
494D4—604no—
495D4—604no—
496D4—602no—
497D4—1201no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—32no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—101no—
505C2×C4—202no—
506C2×C4—242no—
507C2×C4D3×C22⋊D511yescharacteristic
508C2×C4D3×C22⋊D511yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—101no—
511C8—101no—
512C8—302no—
513C2×C3—202no—
514C2×C3C22×#68811yescharacteristic
515C2×C3#6616311yescharacteristic
516C2×C3#6616911yescharacteristic
517D3—24no—
518D3—402no—
519C5#7967611yescharacteristic, complemented, Sylow
520C22—34no—
521C22—62no—
522C22—62no—
523C22—102no—
524C22—201no—
525C22—201no—
526C22—602no—
527C22—602no—
528C22—602no—
529C22—1208no—
530C22C2×D3×C22⋊D511yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—62no—
535C4—122no—
536C4—201no—
537C4D3×#68812yes—
538C4D5×#23511yescharacteristic
539C4#9201911yescharacteristic
540C3#1061536511yescharacteristic, complemented, Sylow
541C2—64no—
542C2—202no—
543C2—1202no—
544C2#1175465111yescharacteristic
545C2C2×D3×#68811yescharacteristic
546C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalD12×D20C2
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×#5579C2semidirect
3. #11751128C2semidirect
4. C3×C4×#688C2semidirect
5. #11749398C2semidirect
6. #11749280C2semidirect
7. D3×#3941C2semidirect
8. #11747173C2semidirect
9. D12×#168C2semidirect
10. #11746912C2semidirect
11. #11746880C2semidirect
15. C3×C4×C5×Q8C22semidirect
16. C2×#6717C22semidirect
18. C5×#946C22semidirect
20. C5×D3×C4⋊C4C22semidirect
24. C5×#869C22semidirect
30. C2×D3×#168C22semidirect
31. #91093C22semidirect
32. C4⋊(C3⋊#168)C22semidirect
33. C3×#3967C22semidirect
35. C3×#3940C22semidirect
36. C3×C4×#168C22semidirect
37. #90986C22semidirect
38. #90969C22semidirect
39. #90969C22semidirect
41. (C2×D3)⋊#168C22semidirect
50. C4×#688D3semidirect
90. #5579D5semidirect
107. C4×C5×Q8C2×D3semidirect
119. #3967C2×D3semidirect
127. #3940C2×D3semidirect
129. C4×#168C2×D3semidirect
150. C5×D12SD16semidirect
167. C3×C4×Q8C2×D5semidirect
169. #946C2×D5semidirect
175. D3×C4⋊C4C2×D5semidirect
181. #869C2×D5semidirect
342. C4×Q8D3×D5semidirect
389. D12#688semidirect
453. C3×C5#3295semidirect
519. C5#79676semidirect
540. C3#10615365semidirect

Maximal subgroups

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

subgroupindex
C5×#55792
D12×D202
#117511282
C3×C4×#6882
#117493982
#117492802
D3×#39412
#117471732
D12×#1682
#117469122
#117468802
#106153653
#796765