Finite Group Databasebeta

← #14429830

Subgroups — #14429830

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×D15C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic, complemented
3C5×#5007C211yesmaximal, characteristic, complemented
4C3×#65296C211yesmaximal, characteristic, complemented
5#11749115C212yesmaximal, complemented
6#11748957C212yesmaximal
7#11747438C212yesmaximal, complemented
8#11747180C212yesmaximal, complemented
9#11747000C211yesmaximal, characteristic, complemented
10#11746971C211yesmaximal, characteristic, complemented
11#11746966C211yesmaximal, characteristic, complemented
12D5×#474—31nomaximal, Hall
13C2×D4×D15C2211yescharacteristic
14C22×C4×D15—21no—
15C2×D15⋊Q8—21no—
16C3×C4×C5×D4C2211yescharacteristic
17D4×Dic15C2211yescharacteristic
18C4×#1220—21no—
19#91782C2211yescharacteristic
20C4⋊C4×D15C2211yescharacteristic
21#91770—21no—
22C22⋊C4×D15—21no—
23C4×D60C2211yescharacteristic
24C42×D15C2211yescharacteristic
25C5×#869C2211yescharacteristic, complemented
26C3×#4015C2211yescharacteristic, complemented
27#91470—21no—
28#91470C2212yescomplemented
29#91437—21no—
30#91437C2212yes—
31#91385—21no—
32C2×#6648C2212yes—
33C5×#832C2212yes—
34C5×#807C2212yescomplemented
35C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×#3964C2212yes—
37C3×#3939C2212yescomplemented
38C3×C4⋊#168C2211yescharacteristic, complemented
39#90990C2212yescomplemented
40#90988C2212yescomplemented
41#90983C2212yescomplemented
42#90969C2212yes—
43#90968C2212yes—
44D3×#474—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46C4×D4×D5—31no—
47C5×#474—31no—
48#65376—31no—
49#65296D311yescharacteristic, complemented
50#65179—32no—
51D5×#107—32no—
52#65135—31no—
53D5×C4⋊C8—31no—
54D5×#102—32no—
55#65048—32no—
56C23×D15—21no—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5—21no—
59C2×#1220—21no—
60C22×Dic15—21no—
61D4×D15—22no—
62D4×D15Q814yescomplemented
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×C4×D15—21no—
66C2×C4×D15—21no—
67C2×C4×D15—44no—
68C2×C4×D15D411yescharacteristic
69C2×C4×D15D411yescharacteristic
70C2×C4×D15C2311yescharacteristic
71C2×C5×Dic6—21no—
72C2×C3×Dic10—21no—
73C2×#1204—22no—
74C2×#1200—22no—
75D15⋊Q8—44no—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79#6719—21no—
80#6714—21no—
81#6714—21no—
82C4⋊Dic15C2311yescharacteristic
83#6712—21no—
84C4×Dic15D411yescharacteristic
85C4×Dic15D411yescharacteristic
86C4×Dic15C2311yescharacteristic
87C5×C4⋊Dic3—21no—
88C5×C4⋊Dic3C2312yes—
89C2×C5×C3⋊C8C2312yes—
90C3×C4⋊Dic5—21no—
91C3×C4⋊Dic5C2312yes—
92C2×C3×#168C2312yes—
93#6669—22no—
94#6669—22no—
95#6648—24no—
96D3×C4⋊Q8—51no—
97C4×D3×D4—51no—
98C3×#474—51no—
99#5087—51no—
100#5007D511yescharacteristic, complemented
101#4890—52no—
102D3×#107—52no—
103#4846—51no—
104D3×C4⋊C8—51no—
105D3×#102—52no—
106#4759—52no—
107C2×Q8×D5—61no—
108C2×D4×D5—31no—
109C22×C4×D5—61no—
110C5×C4⋊Q8—31no—
111C4×C5×D4C2×D311yescharacteristic
112#4090—61no—
113D4×Dic5—31no—
114C4×C22⋊D5—61no—
115C2×C8×D5—32no—
116#4039—31no—
117D5×C4⋊C4—31no—
118D5×C4⋊C4—32no—
119D5×C4⋊C4—61no—
120#4034—32no—
121#4034—61no—
122#4027—61no—
123D5×C22⋊C4—61no—
124C4×D20—31no—
125C42×D5—31no—
126#4015C2×D311yescharacteristic, complemented
127C5×#107—32no—
128C5×C4⋊C8—31no—
129C5×#102—32no—
130#3964C2×D312yes—
131#3953—32no—
132#3950—32no—
133#3946—32no—
134#3941—32no—
135#3939—32no—
136#3939C2×D312yescomplemented
137C4⋊#168C2×D311yescharacteristic, complemented
138C2×#474—151noSylow
139C23×C3×C5—21no—
140C22×D15—21no—
141C22×D15—24no—
142C22×D15—42no—
143C22×D15—42no—
144C22×D15C2×D411yescharacteristic
145C3×C5×D4—21no—
146C3×C5×D4C2×Q812yescomplemented
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—42no—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2411yescharacteristic
152#1220—24no—
153C2×Dic15—21no—
154C2×Dic15—42no—
155C2×Dic15C2×D411yescharacteristic
156C2×Dic15C2×D411yescharacteristic
157C2×Dic15C2×D411yescharacteristic
158D60—21no—
159D60C2×Q812yescomplemented
160C4×D15—22no—
161C4×D15—42no—
162C4×D15—42no—
163C4×D15—42no—
164C4×D15D814yes—
165C4×D15C2×Q812yes—
166C4×D15#4112yes—
167C2×C5×Dic3—22no—
168C5×Dic6—42no—
169C2×C3×Dic5—22no—
170C3×Dic10—42no—
171#1204—44no—
172#1200—44no—
173C3×#168—22no—
174C5×C3⋊C8—22no—
175C2×D3×Q8—101no—
176C2×D3×D4—51no—
177C22×C4×D3—101no—
178C3×C4⋊Q8—51no—
179C3×C4×D4C2×D511yescharacteristic
180#944—101no—
181D4×Dic3—51no—
182C4×#67—101no—
183C2×D3×C8—52no—
184#893—51no—
185D3×C4⋊C4—51no—
186D3×C4⋊C4—52no—
187D3×C4⋊C4—101no—
188#888—52no—
189#888—101no—
190#67⋊C4—101no—
191D3×C22⋊C4—101no—
192C4×D12—51no—
193C42×D3—51no—
194#869C2×D511yescharacteristic, complemented
195C3×#107—52no—
196C3×C4⋊C8—51no—
197C3×#102—52no—
198#832C2×D512yes—
199#821—52no—
200#818—52no—
201Dic3⋊C8—52no—
202#809—52no—
203#807—52no—
204#807C2×D512yescomplemented
205C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
206C23×D5—61no—
207C2×C5×Q8—61no—
208C2×C5×D4C22×D311yescharacteristic
209C22×C4×C5—21no—
210C2×C22⋊D5—61no—
211C22×Dic5—61no—
212Q8×D5—124no—
213D4×D5—34no—
214D4×D5—62no—
215C2×D20—31no—
216C2×C4×D5—31no—
217C2×C4×D5—31no—
218C2×C4×D5—31no—
219C2×C4×D5—62no—
220C2×C4×D5—61no—
221C2×C4×D5—61no—
222C2×C4×D5—61no—
223C2×C4×D5—124no—
224C2×Dic10—21no—
225C2×Dic10—62no—
226C2×C5×C8—32no—
227C5×C4⋊C4—32no—
228C5×C4⋊C4—61no—
229C5×C4⋊C4C22×D311yescharacteristic
230C5×C22⋊C4—21no—
231C42×C5C22×D311yescharacteristic
232C22⋊Dic5—61no—
233#685—61no—
234#685—61no—
235C4⋊Dic5—21no—
236C4⋊Dic5—31no—
237C4⋊Dic5C22×D312yes—
238#683—62no—
239#683—62no—
240#683—61no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C2×#168C22×D312yes—
245C8×D5—64no—
246C2×C4⋊Q8—151no—
247C2×C4×D4—151no—
248#474—31no—
249#474—51no—
250#474—152no—
251#474—151no—
252#474—151no—
253#474—152no—
254C2×#107—152no—
255C2×C4⋊C8—151no—
256C2×#102—152no—
257C22×C3×C5—22no—
258C22×C3×C5—41no—
259C22×C3×C5—41no—
260C22×C3×C5C22×D411yescharacteristic
261C2×D15—22no—
262C2×D15—41no—
263C2×D15—41no—
264C2×D15—48no—
265C2×D15C22⋊Q812yes—
266C2×D15C2×D812yes—
267C2×D15#13712yes—
268C3×C4×C5—21no—
269C3×C4×C5—41no—
270C3×C4×C5C2×D812yes—
271C3×C4×C5C22×Q811yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—21no—
274Dic15—41no—
275Dic15C22⋊Q812yes—
276Dic15C2×D812yes—
277C3×Dic5—42no—
278C5×Dic3—42no—
279C23×D3—101no—
280C2×C3×Q8—101no—
281C2×C3×D4C22×D511yescharacteristic
282C22×C3×C4—21no—
283C2×#67—101no—
284C22×Dic3—101no—
285D3×Q8—204no—
286D3×D4—54no—
287D3×D4—102no—
288C2×D12—51no—
289C2×C4×D3—51no—
290C2×C4×D3—51no—
291C2×C4×D3—51no—
292C2×C4×D3—102no—
293C2×C4×D3—101no—
294C2×C4×D3—101no—
295C2×C4×D3—101no—
296C2×C4×D3—204no—
297C2×Dic6—21no—
298C2×Dic6—102no—
299C2×C3×C8—52no—
300C3×C4⋊C4—52no—
301C3×C4⋊C4—101no—
302C3×C4⋊C4C22×D511yescharacteristic
303C3×C22⋊C4—21no—
304C3×C42C22×D511yescharacteristic
305#217—101no—
306(C2×D3)⋊C4—101no—
307(C2×D3)⋊C4—101no—
308C4⋊Dic3—21no—
309C4⋊Dic3—51no—
310C4⋊Dic3C22×D512yes—
311Dic3⋊C4—102no—
312Dic3⋊C4—102no—
313Dic3⋊C4—101no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—51no—
317C2×C3⋊C8C22×D512yes—
318D3×C8—104no—
319C23×C5—21no—
320C22×D5—31no—
321C22×D5—64no—
322C22×D5—61no—
323C22×D5—122no—
324C22×D5—122no—
325C5×Q8—122no—
326C5×D4—21no—
327C5×D4D3×Q812yescomplemented
328C2×C4×C5—21no—
329C2×C4×C5—42no—
330C2×C4×C5—62no—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5C23×D311yescharacteristic
334C22⋊D5—64no—
335C2×Dic5—22no—
336C2×Dic5—31no—
337C2×Dic5—31no—
338C2×Dic5—31no—
339C2×Dic5—61no—
340C2×Dic5—122no—
341D20—32no—
342D20—61no—
343C4×D5—34no—
344C4×D5—32no—
345C4×D5—32no—
346C4×D5—62no—
347C4×D5—122no—
348C4×D5—124no—
349C4×D5—122no—
350C4×D5—122no—
351Dic10—42no—
352Dic10—124no—
353C5×C8—62no—
354#168—22no—
355C22×Q8—301no—
356C22×D4—151no—
357C23×C4—301no—
358C22×C8—152no—
359C4⋊Q8—31no—
360C4⋊Q8—51no—
361C4⋊Q8—152no—
362C4⋊Q8—301no—
363C4⋊Q8—301no—
364C4×D4—151no—
365C4×D4—151no—
366C4×D4—151no—
367C4×D4—301no—
368C4×D4—301no—
369C4×D4D3×D511yescharacteristic
370C2×C4⋊C4—152no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—301no—
373C2×C22⋊C4—301no—
374C2×C42—151no—
375#107—32no—
376#107—52no—
377#107—152no—
378#107—152no—
379C4⋊C8—31no—
380C4⋊C8—51no—
381C4⋊C8—152no—
382#102—32no—
383#102—52no—
384#102—152no—
385#102—152no—
386C2×C3×C5—42no—
387C2×C3×C5C2×C22⋊Q811yescharacteristic
388C2×C3×C5C22×D811yescharacteristic
389C2×C3×C5C2×#13711yescharacteristic
390D15—42no—
391D15#47414yescomplemented
392C23×C3—21no—
393C22×D3—51no—
394C22×D3—104no—
395C22×D3—101no—
396C22×D3—202no—
397C22×D3—202no—
398C3×Q8—202no—
399C3×D4—21no—
400C3×D4Q8×D512yescomplemented
401C2×C3×C4—21no—
402C2×C3×C4—42no—
403C2×C3×C4—102no—
404C2×C3×C4D4×D511yescharacteristic
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407#67—104no—
408C2×Dic3—22no—
409C2×Dic3—51no—
410C2×Dic3—51no—
411C2×Dic3—51no—
412C2×Dic3—101no—
413C2×Dic3—202no—
414D12—52no—
415D12—101no—
416C4×D3—52no—
417C4×D3—52no—
418C4×D3—54no—
419C4×D3—102no—
420C4×D3—204no—
421C4×D3—202no—
422C4×D3—202no—
423C4×D3—202no—
424Dic6—42no—
425Dic6—204no—
426C3×C8—102no—
427C3⋊C8—22no—
428C22×C5—22no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5C2×D3×D411yescharacteristic
432C2×D5—32no—
433C2×D5—32no—
434C2×D5—32no—
435C2×D5—62no—
436C2×D5—128no—
437C2×D5—121no—
438C2×D5—121no—
439C4×C5—21no—
440C4×C5—41no—
441C4×C5—122no—
442C4×C5D3×D812yes—
443C4×C5C2×D3×Q811yescharacteristic
444C4×C5D3×#4111yescharacteristic
445Dic5—32no—
446Dic5—32no—
447Dic5—42no—
448Dic5—61no—
449Dic5—121no—
450C24—301no—
451C2×Q8—61no—
452C2×Q8—101no—
453C2×Q8—302no—
454C2×Q8—604no—
455C2×D4—154no—
456C2×D4—151no—
457C2×D4—302no—
458C2×D4—301no—
459C2×D4C2×D3×D511yescharacteristic
460C22×C4—21no—
461C22×C4—151no—
462C22×C4—151no—
463C22×C4—151no—
464C22×C4—301no—
465C22×C4—301no—
466C22×C4—302no—
467C22×C4—301no—
468C22×C4—301no—
469C22×C4—604no—
470C2×C8—32no—
471C2×C8—52no—
472C2×C8—304no—
473C4⋊C4—32no—
474C4⋊C4—52no—
475C4⋊C4—61no—
476C4⋊C4—101no—
477C4⋊C4—151no—
478C4⋊C4—301no—
479C4⋊C4—302no—
480C4⋊C4—302no—
481C4⋊C4C2×D3×D511yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C22⋊C4—301no—
486C42—151no—
487C42—151no—
488C42—151no—
489C42C2×D3×D511yescharacteristic
490C3×C5C2×#47411yescharacteristic, complemented, Hall
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3C2×D4×D511yescharacteristic
495C2×D3—52no—
496C2×D3—52no—
497C2×D3—52no—
498C2×D3—102no—
499C2×D3—208no—
500C2×D3—201no—
501C2×D3—201no—
502C3×C4—21no—
503C3×C4—41no—
504C3×C4—202no—
505C3×C4D5×D812yes—
506C3×C4C2×Q8×D511yescharacteristic
507C3×C4D5×#4111yescharacteristic
508Dic3—42no—
509Dic3—52no—
510Dic3—52no—
511Dic3—101no—
512Dic3—201no—
513C2×C5—42no—
514C2×C5D3×C22⋊Q811yescharacteristic
515C2×C5C2×D3×D811yescharacteristic
516C2×C5D3×#13711yescharacteristic
517D5—34no—
518D5—122no—
519C23—21no—
520C23—151no—
521C23—304no—
522C23—301no—
523C23—602no—
524C23—602no—
525Q8—122no—
526Q8—202no—
527Q8—604no—
528D4—21no—
529D4—152no—
530D4—304no—
531D4—301no—
532D4D15⋊Q812yescomplemented
533C2×C4—21no—
534C2×C4—42no—
535C2×C4—62no—
536C2×C4—102no—
537C2×C4—151no—
538C2×C4—151no—
539C2×C4—154no—
540C2×C4—152no—
541C2×C4—152no—
542C2×C4—151no—
543C2×C4—302no—
544C2×C4—301no—
545C2×C4—602no—
546C2×C4—602no—
547C2×C4—604no—
548C2×C4—602no—
549C2×C4—602no—
550C2×C4#679011yescharacteristic
551C2×C4#679011yescharacteristic
552C2×C4C22×D3×D511yescharacteristic
553C8—62no—
554C8—102no—
555C2×C3—42no—
556C2×C3D5×C22⋊Q811yescharacteristic
557C2×C3C2×D5×D811yescharacteristic
558C2×C3D5×#13711yescharacteristic
559D3—54no—
560D3—202no—
561C5D3×#47411yescharacteristic, complemented, Sylow
562C22—22no—
563C22—41no—
564C22—41no—
565C22—152no—
566C22—152no—
567C22—152no—
568C22—302no—
569C22—608no—
570C22—601no—
571C22—601no—
572C22C2×#679011yescharacteristic
573C4—21no—
574C4—41no—
575C4—122no—
576C4—152no—
577C4—152no—
578C4—202no—
579C4—301no—
580C4—601no—
581C4#9148112yes—
582C4C2×D15⋊Q811yescharacteristic
583C4#9201611yescharacteristic
584C3D5×#47411yescharacteristic, complemented, Sylow
585C2—42no—
586C2—154no—
587C2—602no—
588C2#1175438311yescharacteristic
589C2C2×#9148111yescharacteristic
590C2#1175534211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×D4×D15C22
hypercenterC4×D4D3×D5
hypocenterC3×C5C2×#474
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
2. #11752562C2semidirect
3. C5×#5007C2semidirect
4. C3×#65296C2semidirect
5. #11749115C2semidirect
7. #11747438C2semidirect
8. #11747180C2semidirect
9. #11747000C2semidirect
10. #11746971C2semidirect
11. #11746966C2semidirect
25. C5×#869C22semidirect
26. C3×#4015C22semidirect
28. #91470C22semidirect
34. C5×#807C22semidirect
35. C5×C4⋊(C3⋊C8)C22semidirect
37. C3×#3939C22semidirect
38. C3×C4⋊#168C22semidirect
39. #90990C22semidirect
40. #90988C22semidirect
41. #90983C22semidirect
49. #65296D3semidirect
62. D4×D15Q8semidirect
100. #5007D5semidirect
126. #4015C2×D3semidirect
136. #3939C2×D3semidirect
137. C4⋊#168C2×D3semidirect
146. C3×C5×D4C2×Q8semidirect
159. D60C2×Q8semidirect
194. #869C2×D5semidirect
204. #807C2×D5semidirect
205. C4⋊(C3⋊C8)C2×D5semidirect
327. C5×D4D3×Q8semidirect
391. D15#474semidirect
400. C3×D4Q8×D5semidirect
490. C3×C5C2×#474semidirect
532. D4D15⋊Q8semidirect
561. C5D3×#474semidirect
584. C3D5×#474semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D152
#117525622
C5×#50072
C3×#652962
#117491152
#117489572
#117474382
#117471802
#117470002
#117469712
#117469662
D5×#4743
D3×#4745