Finite Group Databasebeta

← #14458349

Subgroups — #14458349

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D4×D12C211yesmaximal, characteristic, complemented
2#11752549C211yesmaximal, characteristic, complemented
3C4×#6715C211yesmaximal, characteristic, complemented
4C3×#65296C211yesmaximal, characteristic, complemented
5#11749033C212yesmaximal, complemented
6D3×#3964C212yesmaximal, complemented
7#11747446C212yesmaximal, complemented
8#11747196C212yesmaximal, complemented
9#11747045C211yesmaximal, characteristic, complemented
10#11746998C211yesmaximal, characteristic, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10615213—31nomaximal, Hall
13C2×C5×D3×D4C2212yes—
14C22×C5×D12—21no—
15C2×#6768—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×#6715C2211yescharacteristic
18C4×D60C2211yescharacteristic, complemented
19C5×#930—21no—
20C5×#895C2212yes—
21C5×#882—22no—
22C5×#874C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C3×#4015C2211yescharacteristic, complemented
25#91460C2212yescomplemented
26#91427—22no—
27D3×C4⋊Dic5C2212yescomplemented
28#91390—21no—
29C2×#6654C2212yescomplemented
30C2×D3×#168C2212yescomplemented
31#91116C2211yescharacteristic
32#91093C2211yescharacteristic, complemented
33#91091C2211yescharacteristic, complemented
34C4×C3⋊#168C2211yescharacteristic, complemented
35C3×#3964C2212yes—
36C3×#3939C2212yescomplemented
37C3×C4⋊#168C2211yescharacteristic, complemented
38#90967C2212yescomplemented
39#90966C2212yescomplemented
40#90966C2212yescomplemented
41(C2×D3)⋊#168C2212yescomplemented
42#80980—51nomaximal, Hall
43C5×D42—31no—
44#65889—31no—
45#65506—32no—
46C2×#3964—32no—
47#65361—31no—
48#65359—31no—
49#65327—32no—
50#65322—32no—
51C4×#686—31no—
52D4×#168—31no—
53#65296D311yescharacteristic, complemented
54C23×C5×D3—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×C5×#67—22no—
60C5×D3×D4—24no—
61C5×D3×D4—42no—
62C2×C5×D12—22no—
63C2×C5×D12—21no—
64C2×C5×D12—21no—
65C2×C5×D12—44no—
66C2×C5×D12D411yescharacteristic
67C2×C5×D12C2312yes—
68C2×C4×C5×D3C2312yes—
69C2×C3×Dic10—21no—
70C2×#1203—22no—
71C2×D3×Dic5—22no—
72#6768—44no—
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76#6715—22no—
77#6714—21no—
78C4⋊Dic15C2311yescharacteristic
79C2×C3⋊#168C2311yescharacteristic
80C2×C3⋊#168C2311yescharacteristic
81C5×(C2×D3)⋊C4—22no—
82C5×(C2×D3)⋊C4D412yes—
83C5×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86C2×C3×#168C2312yes—
87Dic3⋊Dic5—22no—
88#6667—22no—
89#6654—42no—
90D3×#168—42no—
91#5726—51no—
92D4×D12D511yescharacteristic, complemented
93C3×#474—51no—
94#5088—51no—
95C4×#213—51no—
96#4883—52no—
97#4882—52no—
98#4843—51no—
99#4834—51no—
100#4773—52no—
101D3×#102—52no—
102C22×C5×D4—32no—
103C22×C5×D4—61no—
104C2×#711—61no—
105C5×#127—31no—
106C5×#121—32no—
107C5×#121—61no—
108C5×#120—62no—
109C4×C5×D4—31no—
110C4×C5×D4C2×D311yescharacteristic
111C2×#686—31no—
112C2×#686—32no—
113#4076—32no—
114C2×C4⋊Dic5—32no—
115C22×#168—32no—
116#4043—61no—
117#4032—62no—
118C4×D20—31no—
119#4015C2×D311yescharacteristic, complemented
120#3964—31no—
121#3964—32no—
122#3964—32no—
123#3964—32no—
124#3964C2×D312yes—
125C22⋊#168—32no—
126#3941—31no—
127#3939—31no—
128#3939C2×D312yescomplemented
129C4⋊#168C2×D311yescharacteristic, complemented
130C4×#168—31no—
131#3294—151noSylow
132C23×C3×C5—21no—
133C22×D15—21no—
134C22×C5×D3—22no—
135C22×C5×D3—44no—
136C22×C5×D3—44no—
137C22×C5×D3—82no—
138C22×C5×D3C2×D412yes—
139C3×C5×D4—21no—
140C3×C5×D4#4112yescomplemented
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—21no—
147D60—21no—
148D60—21no—
149C4×D15—42no—
150C5×#67—44no—
151C2×C5×Dic3C2×D412yes—
152C5×D12—22no—
153C5×D12—22no—
154C5×D12—44no—
155C5×D12—42no—
156C5×D12—81no—
157C5×D12D814yescomplemented
158C4×C5×D3—22no—
159C4×C5×D3—22no—
160C2×C3×Dic5—22no—
161C3×Dic10—42no—
162#1203—44no—
163D3×Dic5—44no—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3×#168—22no—
167C2×#239—101no—
168C2×D3×D4C2×D512yes—
169C22×D12—21no—
170C3×C4⋊Q8—51no—
171C3×C4×D4C2×D511yescharacteristic
172#946—101no—
173C2×#213—51no—
174#930—21no—
175C2×D24—52no—
176C2×D3×C8—52no—
177#895—52no—
178#895C2×D512yes—
179#894—102no—
180D3×C4⋊C4—52no—
181#882—22no—
182#874C2×D511yescharacteristic
183C4×D12—51no—
184C4×D12C2×D511yescharacteristic
185C3×#107—52no—
186C3×C4⋊C8—51no—
187C3×#102—52no—
188#832—51no—
189#821—52no—
190(C2×D3)⋊C8—52no—
191#809—52no—
192#809—52no—
193#809—51no—
194#807—51no—
195C4×C3⋊C8—51no—
196C24×C5—62no—
197C2×C5×D4—31no—
198C2×C5×D4—32no—
199C2×C5×D4—62no—
200C2×C5×D4—62no—
201C2×C5×D4—64no—
202C2×C5×D4—61no—
203C2×C5×D4—61no—
204C2×C5×D4—124no—
205C2×C5×D4—122no—
206C2×C5×D4C22×D311yescharacteristic
207C22×C4×C5—21no—
208C22×C4×C5—32no—
209C2×C22⋊D5—62no—
210C22×Dic5—62no—
211#711—124no—
212C2×D20—31no—
213C2×C4×D5—61no—
214C2×Dic10—21no—
215C5×C4⋊C4—31no—
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C22⋊C4—21no—
218C5×C22⋊C4—32no—
219C5×C22⋊C4—62no—
220C42×C5C22×D311yescharacteristic
221#686—62no—
222#686—122no—
223#685—62no—
224#685—61no—
225C4⋊Dic5—21no—
226C4⋊Dic5—31no—
227C4⋊Dic5—62no—
228C4⋊Dic5C22×D312yes—
229C2×#168—31no—
230C2×#168—31no—
231C2×#168—122no—
232C2×#168C22×D312yes—
233#547—151no—
234D42—31no—
235#486—151no—
236#480—152no—
237#474—51no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—151no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C2×C5×D3—22no—
252C2×C5×D3—22no—
253C2×C5×D3—42no—
254C2×C5×D3—42no—
255C2×C5×D3—42no—
256C2×C5×D3—88no—
257C2×C5×D3C2×D814yes—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5C2×D812yes—
261C3×C4×C5C2×#4111yescharacteristic
262C3×C4×C5H(5,𝔽2)11yescharacteristic
263Dic15—41no—
264C3×Dic5—42no—
265C5×Dic3—22no—
266C23×D3—22no—
267C2×C3×Q8—101no—
268C2×C3×D4C22×D511yescharacteristic
269C22×C3×C4—21no—
270C2×#67—22no—
271#239—204no—
272D3×D4—24no—
273D3×D4—42no—
274C2×D12—22no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—44no—
278C2×D12—51no—
279C2×D12—102no—
280C2×D12C22⋊D511yescharacteristic
281C2×D12C22×D512yes—
282C2×C4×D3—102no—
283C2×C4×D3—101no—
284C2×C4×D3C22×D512yes—
285C2×C3×C8—52no—
286C3×C4⋊C4—52no—
287C3×C4⋊C4—101no—
288C3×C4⋊C4C22×D511yescharacteristic
289C3×C22⋊C4—21no—
290C3×C42C22×D511yescharacteristic
291#213—102no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—101no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4C22⋊D512yes—
296C4⋊Dic3—51no—
297C4⋊Dic3C22⋊D511yescharacteristic
298Dic3⋊C4—102no—
299C2×C3⋊C8—51no—
300C2×C3⋊C8—51no—
301D24—202no—
302D3×C8—202no—
303C23×C5—21no—
304C23×C5—32no—
305C23×C5—62no—
306C23×C5—124no—
307C23×C5—124no—
308C23×C5—242no—
309C22×D5—61no—
310C5×D4—21no—
311C5×D4—34no—
312C5×D4—62no—
313C5×D4—62no—
314C5×D4—124no—
315C5×D4—124no—
316C5×D4—122no—
317C5×D4—241no—
318C5×D4#23912yescomplemented
319C2×C4×C5—21no—
320C2×C4×C5—32no—
321C2×C4×C5—42no—
322C2×C4×C5—62no—
323C2×C4×C5—62no—
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5D3×D411yescharacteristic
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—124no—
328C2×Dic5—22no—
329C2×Dic5—61no—
330C2×Dic5—124no—
331D20—61no—
332D20—61no—
333C4×D5—122no—
334Dic10—42no—
335#168—22no—
336#168—61no—
337#168—61no—
338C2×#41—301no—
339C22×D4—32no—
340C22×D4—61no—
341C2×D8—152no—
342C2×D8—151no—
343C22×C8—152no—
344C4⋊Q8—51no—
345#127—31no—
346#123—302no—
347C22⋊Q8—301no—
348#121—32no—
349#121—61no—
350#121—152no—
351#120—62no—
352C4×D4—31no—
353C4×D4—151no—
354C4×D4D3×D511yescharacteristic
355C2×C4⋊C4—152no—
356#107—52no—
357#107—151no—
358C4⋊C8—51no—
359#102—52no—
360#102—152no—
361#102—152no—
362#102—152no—
363#102—151no—
364#102—151no—
365C22⋊C8—152no—
366C4×C8—151no—
367C2×C3×C5—42no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—81no—
372C5×D3—24no—
373C5×D3—82no—
374C23×C3—21no—
375C22×D3—22no—
376C22×D3—44no—
377C22×D3—44no—
378C22×D3—82no—
379C22×D3—101no—
380C22×D3C2×C22⋊D512yes—
381C3×Q8—202no—
382C3×D4—21no—
383C3×D4#71112yescomplemented
384C2×C3×C4—21no—
385C2×C3×C4—42no—
386C2×C3×C4—102no—
387C2×C3×C4C2×C22⋊D511yescharacteristic
388C2×C3×C4C2×C22⋊D511yescharacteristic
389C2×C3×C4C23×D511yescharacteristic
390#67—44no—
391C2×Dic3—101no—
392C2×Dic3C2×C22⋊D512yes—
393D12—22no—
394D12—22no—
395D12—44no—
396D12—42no—
397D12—81no—
398D12—101no—
399D12—101no—
400D12—204no—
401D12#68614yescomplemented
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—204no—
405C4×D3—202no—
406C3×C8—102no—
407C3⋊C8—101no—
408C3⋊C8—101no—
409C22×C5—22no—
410C22×C5—34no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—62no—
414C22×C5—62no—
415C22×C5—122no—
416C22×C5—122no—
417C22×C5—122no—
418C22×C5—248no—
419C22×C5C2×D3×D411yescharacteristic
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—121no—
423C4×C5—21no—
424C4×C5—41no—
425C4×C5—62no—
426C4×C5D3×D812yes—
427C4×C5C2×#23911yescharacteristic
428C4×C5#100911yescharacteristic
429Dic5—42no—
430Dic5—121no—
431C24—62no—
432#41—604no—
433C2×Q8—101no—
434C2×D4—31no—
435C2×D4—32no—
436C2×D4—62no—
437C2×D4—62no—
438C2×D4—64no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—124no—
442C2×D4—122no—
443C2×D4—151no—
444C2×D4—302no—
445C2×D4C2×D3×D511yescharacteristic
446C22×C4—21no—
447C22×C4—32no—
448C22×C4—302no—
449C22×C4—301no—
450D8—302no—
451D8—602no—
452C2×C8—52no—
453C2×C8—151no—
454C2×C8—151no—
455C2×C8—602no—
456C4⋊C4—31no—
457C4⋊C4—52no—
458C4⋊C4—101no—
459C4⋊C4—151no—
460C4⋊C4—302no—
461C4⋊C4C2×D3×D511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—32no—
464C22⋊C4—62no—
465C22⋊C4—302no—
466C22⋊C4—301no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3C22×C22⋊D511yescharacteristic
473C2×D3—22no—
474C2×D3—22no—
475C2×D3—42no—
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—88no—
479C2×D3—201no—
480C2×D3—201no—
481C2×D3—201no—
482C2×D3C2×#68614yes—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—202no—
486C3×C4C2×#68612yes—
487C3×C4C2×#71111yescharacteristic
488C3×C4#414411yescharacteristic
489Dic3—22no—
490Dic3—201no—
491C2×C5—42no—
492C2×C5—64no—
493C2×C5—242no—
494C2×C5#563011yescharacteristic
495C2×C5C2×D3×D811yescharacteristic
496C2×C5#577811yescharacteristic
497D5—241no—
498C23—21no—
499C23—32no—
500C23—62no—
501C23—124no—
502C23—124no—
503C23—242no—
504C23—301no—
505Q8—202no—
506D4—21no—
507D4—34no—
508D4—62no—
509D4—62no—
510D4—124no—
511D4—124no—
512D4—122no—
513D4—241no—
514D4—301no—
515D4—301no—
516D4—604no—
517D4#676812yescomplemented
518C2×C4—21no—
519C2×C4—32no—
520C2×C4—42no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—102no—
524C2×C4—301no—
525C2×C4—604no—
526C2×C4—602no—
527C2×C4D3×C22⋊D511yescharacteristic
528C2×C4D3×C22⋊D511yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—102no—
531C8—301no—
532C8—301no—
533C2×C3—42no—
534C2×C3C22×#68611yescharacteristic
535C2×C3#6614011yescharacteristic
536C2×C3#6617011yescharacteristic
537D3—24no—
538D3—82no—
539D3—401no—
540C5#8098011yescharacteristic, complemented, Sylow
541C22—22no—
542C22—34no—
543C22—41no—
544C22—41no—
545C22—62no—
546C22—62no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—248no—
551C22—601no—
552C22—601no—
553C22—601no—
554C22C2×D3×C22⋊D511yescharacteristic
555C4—21no—
556C4—41no—
557C4—62no—
558C4—202no—
559C4—601no—
560C4D3×#68612yes—
561C4C2×#676811yescharacteristic
562C4#9201811yescharacteristic
563C3#1061521311yescharacteristic, complemented, Sylow
564C2—42no—
565C2—64no—
566C2—242no—
567C2—1201no—
568C2#1175434911yescharacteristic
569C2C2×D3×#68611yescharacteristic
570C2#1175534011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3294
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
1. C5×D4×D12C2semidirect
2. #11752549C2semidirect
3. C4×#6715C2semidirect
4. C3×#65296C2semidirect
5. #11749033C2semidirect
6. D3×#3964C2semidirect
7. #11747446C2semidirect
8. #11747196C2semidirect
9. #11747045C2semidirect
10. #11746998C2semidirect
11. #11746901C2semidirect
18. C4×D60C22semidirect
24. C3×#4015C22semidirect
25. #91460C22semidirect
27. D3×C4⋊Dic5C22semidirect
29. C2×#6654C22semidirect
30. C2×D3×#168C22semidirect
32. #91093C22semidirect
33. #91091C22semidirect
34. C4×C3⋊#168C22semidirect
36. C3×#3939C22semidirect
37. C3×C4⋊#168C22semidirect
38. #90967C22semidirect
39. #90966C22semidirect
40. #90966C22semidirect
41. (C2×D3)⋊#168C22semidirect
53. #65296D3semidirect
92. D4×D12D5semidirect
119. #4015C2×D3semidirect
128. #3939C2×D3semidirect
129. C4⋊#168C2×D3semidirect
140. C3×C5×D4#41semidirect
157. C5×D12D8semidirect
318. C5×D4#239semidirect
383. C3×D4#711semidirect
401. D12#686semidirect
468. C3×C5#3294semidirect
517. D4#6768semidirect
540. C5#80980semidirect
563. C3#10615213semidirect

Maximal subgroups

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

subgroupindex
C5×D4×D122
#117525492
C4×#67152
C3×#652962
#117490332
D3×#39642
#117474462
#117471962
#117470452
#117469982
#117469012
#106152133
#809805