Finite Group Databasebeta

← D15×#479 #14430119

Subgroups — D15×#479 #14430119

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#125C211yesmaximal, characteristic
2C4×Q8×D15C211yesmaximal, characteristic
3C3×C5×#479C211yesmaximal, characteristic, complemented
4#11751164C211yesmaximal, characteristic, complemented
5#11751123C211yesmaximal, characteristic, complemented
6D15×#107C211yesmaximal, characteristic
7#11750978C211yesmaximal, characteristic, complemented
8D15×#106C211yesmaximal, characteristic
9#11750958C211yesmaximal, characteristic, complemented
10D15×C4⋊C8C211yesmaximal, characteristic
11#11750930C211yesmaximal, characteristic, complemented
12D15×#103C211yesmaximal, characteristic
13D15×#103C211yesmaximal, characteristic
14#11750900C211yesmaximal, characteristic, complemented
15#11750897C211yesmaximal, characteristic, complemented
16D5×#479—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22C2×C8×D15C2211yescharacteristic
23C4⋊C4×D15—21no—
24C4⋊C4×D15—21no—
25C4⋊C4×D15—21no—
26C4⋊C4×D15C2211yescharacteristic
27C4⋊C4×D15C2211yescharacteristic
28C4⋊C4×D15C2211yescharacteristic
29#91779C2211yescharacteristic
30#91779C2211yescharacteristic
31#91778—21no—
32#91778—21no—
33#91776—21no—
34#91776C2211yescharacteristic
35C42×D15—21no—
36C42×D15C2211yescharacteristic
37#91759C2211yescharacteristic
38C4×Dic30—21no—
39C4×Dic30C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic
41C3×C5×#106C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45#91119C2211yescharacteristic
46#91119C2211yescharacteristic
47#91102C2211yescharacteristic
48#91101C2211yescharacteristic
49#91100C2211yescharacteristic
50#91100C2211yescharacteristic
51#91098C2211yescharacteristic
52#91098C2211yescharacteristic
53#91094C2211yescharacteristic
54#91094C2211yescharacteristic
55#91092C2211yescharacteristic
56#91092C2211yescharacteristic
57#91091C2211yescharacteristic
58#91091C2211yescharacteristic
59C4⋊(C3⋊#168)C2211yescharacteristic
60D3×#479—51nomaximal, Hall
61D5×#125—31no—
62C4×Q8×D5—31no—
63C5×#479D311yescharacteristic, complemented
64#65352—31no—
65#65311—31no—
66D5×#107—31no—
67#65166—31no—
68D5×#106—31no—
69#65146—31no—
70D5×C4⋊C8—31no—
71#65118—31no—
72D5×#103—31no—
73D5×#103—31no—
74#65088—31no—
75#65085—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77Q8×D15—22no—
78Q8×D15Q814yes—
79C2×C4×D15—21no—
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C4×D15—21no—
83C2×C4×D15D411yescharacteristic
84C2×C4×D15D411yescharacteristic
85C2×C4×D15C2311yescharacteristic
86C2×Dic30—21no—
87C2×Dic30C2311yescharacteristic
88C2×C3×C5×C8C2311yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C42×C5—21no—
97C3×C42×C5C2311yescharacteristic
98C4⋊Dic15—21no—
99C4⋊Dic15—21no—
100C4⋊Dic15—21no—
101C4⋊Dic15C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105#6712—21no—
106#6712—21no—
107#6712—21no—
108#6712—21no—
109#6712—21no—
110#6712—21no—
111#6712—21no—
112#6712—21no—
113C4×Dic15—21no—
114C4×Dic15—21no—
115C4×Dic15—21no—
116C4×Dic15D411yescharacteristic
117C4×Dic15D411yescharacteristic
118C4×Dic15C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C2×C3⋊#168C2311yescharacteristic
121C8×D15—22no—
122C8×D15—22no—
123D3×#125—51no—
124C4×D3×Q8—51no—
125C3×#479D511yescharacteristic, complemented
126#5063—51no—
127#5022—51no—
128D3×#107—51no—
129#4877—51no—
130D3×#106—51no—
131#4857—51no—
132D3×C4⋊C8—51no—
133#4829—51no—
134D3×#103—51no—
135D3×#103—51no—
136#4799—51no—
137#4796—51no—
138C2×Q8×D5—31no—
139C5×#125C2×D311yescharacteristic
140C4×C5×Q8C2×D311yescharacteristic
141Q8×Dic5—31no—
142C2×C8×D5—31no—
143C2×C8×D5—31no—
144D5×C4⋊C4—31no—
145D5×C4⋊C4—31no—
146D5×C4⋊C4—31no—
147D5×C4⋊C4—61no—
148D5×C4⋊C4—61no—
149D5×C4⋊C4—61no—
150#4036—31no—
151#4036—31no—
152#4035—61no—
153#4035—61no—
154#4033—31no—
155#4033—61no—
156C42×D5—31no—
157C42×D5—61no—
158#4016—31no—
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#107C2×D311yescharacteristic
162C5×#106C2×D311yescharacteristic
163C5×C4⋊C8C2×D311yescharacteristic
164C5×#103C2×D311yescharacteristic
165C5×#103C2×D311yescharacteristic
166#3967—31no—
167#3967—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181C2×#479—151noSylow
182C22×D15C2×D411yescharacteristic
183C3×C5×Q8—21no—
184C3×C5×Q8C2×Q812yes—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2411yescharacteristic
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15C2×D411yescharacteristic
197C2×Dic15C2×D411yescharacteristic
198C2×Dic15C2×D411yescharacteristic
199C4×D15—24no—
200C4×D15—22no—
201C4×D15—22no—
202C4×D15—42no—
203C4×D15—42no—
204C4×D15—42no—
205C4×D15C2×Q812yes—
206C4×D15#4112yes—
207Dic30—21no—
208Dic30—24no—
209Dic30C2×Q812yes—
210C3×C5×C8—21no—
211C3×C5×C8—21no—
212C3⋊#168—21no—
213C3⋊#168—21no—
214C2×D3×Q8—51no—
215C3×#125C2×D511yescharacteristic
216C3×C4×Q8C2×D511yescharacteristic
217Q8×Dic3—51no—
218C2×D3×C8—51no—
219C2×D3×C8—51no—
220D3×C4⋊C4—51no—
221D3×C4⋊C4—51no—
222D3×C4⋊C4—51no—
223D3×C4⋊C4—101no—
224D3×C4⋊C4—101no—
225D3×C4⋊C4—101no—
226#890—51no—
227#890—51no—
228#889—101no—
229#889—101no—
230#887—51no—
231#887—101no—
232C42×D3—51no—
233C42×D3—101no—
234#870—51no—
235C4×Dic6—51no—
236C4×Dic6—101no—
237C3×#107C2×D511yescharacteristic
238C3×#106C2×D511yescharacteristic
239C3×C4⋊C8C2×D511yescharacteristic
240C3×#103C2×D511yescharacteristic
241C3×#103C2×D511yescharacteristic
242#835—51no—
243#835—51no—
244#818—51no—
245#817—51no—
246#816—51no—
247#816—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250#810—51no—
251#810—51no—
252#808—51no—
253#808—51no—
254#807—51no—
255#807—51no—
256C4⋊(C3⋊C8)—51no—
257C2×C5×Q8C22×D311yescharacteristic
258Q8×D5—34no—
259Q8×D5—62no—
260C2×C4×D5—31no—
261C2×C4×D5—31no—
262C2×C4×D5—31no—
263C2×C4×D5—61no—
264C2×C4×D5—61no—
265C2×C4×D5—61no—
266C2×C4×D5—61no—
267C2×Dic10—31no—
268C2×Dic10—61no—
269C2×C5×C8C22×D311yescharacteristic
270C2×C5×C8C22×D311yescharacteristic
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4C22×D311yescharacteristic
275C5×C4⋊C4C22×D311yescharacteristic
276C5×C4⋊C4C22×D311yescharacteristic
277C42×C5—21no—
278C42×C5C22×D311yescharacteristic
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—31no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284C4⋊Dic5—61no—
285#683—61no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294C4×Dic5—31no—
295C4×Dic5—31no—
296C4×Dic5—31no—
297C4×Dic5—61no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C2×#168—31no—
301C2×#168—31no—
302C8×D5—62no—
303C8×D5—62no—
304C2×#125—151no—
305C2×C4×Q8—151no—
306#479—151no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#479—151no—
312#479—151no—
313#479D1511yescharacteristic, direct product factor
314C2×#107—151no—
315C2×#106—151no—
316C2×C4⋊C8—151no—
317C2×#103—151no—
318C2×#103—151no—
319C22×C3×C5C22×D411yescharacteristic
320C2×D15C22⋊Q812yes—
321C2×D15#13512yes—
322C2×D15#13712yes—
323C3×C4×C5—22no—
324C3×C4×C5—21no—
325C3×C4×C5—21no—
326C3×C4×C5—41no—
327C3×C4×C5—41no—
328C3×C4×C5—41no—
329C3×C4×C5C22×Q811yescharacteristic
330C3×C4×C5C2×#4111yescharacteristic
331Dic15—22no—
332Dic15—21no—
333Dic15—21no—
334Dic15—41no—
335Dic15—41no—
336Dic15—41no—
337Dic15C22⋊Q812yes—
338C2×C3×Q8C22×D511yescharacteristic
339D3×Q8—54no—
340D3×Q8—102no—
341C2×C4×D3—51no—
342C2×C4×D3—51no—
343C2×C4×D3—51no—
344C2×C4×D3—101no—
345C2×C4×D3—101no—
346C2×C4×D3—101no—
347C2×C4×D3—101no—
348C2×Dic6—51no—
349C2×Dic6—101no—
350C2×C3×C8C22×D511yescharacteristic
351C2×C3×C8C22×D511yescharacteristic
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4C22×D511yescharacteristic
356C3×C4⋊C4C22×D511yescharacteristic
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C42—21no—
359C3×C42C22×D511yescharacteristic
360C4⋊Dic3—51no—
361C4⋊Dic3—51no—
362C4⋊Dic3—51no—
363C4⋊Dic3—101no—
364C4⋊Dic3—101no—
365C4⋊Dic3—101no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375C4×Dic3—51no—
376C4×Dic3—51no—
377C4×Dic3—51no—
378C4×Dic3—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C2×C3⋊C8—51no—
382C2×C3⋊C8—51no—
383D3×C8—102no—
384D3×C8—102no—
385C22×D5—31no—
386C5×Q8—21no—
387C5×Q8D3×Q812yes—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5D3×D411yescharacteristic
393C2×C4×C5D3×D411yescharacteristic
394C2×C4×C5C23×D311yescharacteristic
395C2×Dic5—31no—
396C2×Dic5—31no—
397C2×Dic5—31no—
398C2×Dic5—61no—
399C2×Dic5—61no—
400C2×Dic5—61no—
401C2×Dic5—61no—
402C4×D5—32no—
403C4×D5—32no—
404C4×D5—62no—
405C4×D5—62no—
406C4×D5—64no—
407C4×D5—122no—
408C4×D5—122no—
409C4×D5—122no—
410Dic10—32no—
411Dic10—64no—
412Dic10—61no—
413C5×C8—21no—
414C5×C8—21no—
415#168—61no—
416#168—61no—
417C22×Q8—151no—
418C22×C8—151no—
419C22×C8—151no—
420#125—151no—
421#125—151no—
422#125—151no—
423#125—301no—
424#125—301no—
425#125C2×D1511yescharacteristic
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—301no—
430C4×Q8—301no—
431C4×Q8C2×D1511yescharacteristic
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—301no—
436C2×C4⋊C4—301no—
437C2×C4⋊C4—301no—
438C2×C42—151no—
439C2×C42—301no—
440#107—151no—
441#107—151no—
442#107—151no—
443#107C2×D1511yescharacteristic
444#106—151no—
445#106—151no—
446#106—151no—
447#106C2×D1511yescharacteristic
448C4⋊C8—151no—
449C4⋊C8—151no—
450C4⋊C8—151no—
451C4⋊C8C2×D1511yescharacteristic
452#103—151no—
453#103—151no—
454#103—151no—
455#103—151no—
456#103—151no—
457#103—151no—
458#103C2×D1511yescharacteristic
459#103C2×D1511yescharacteristic
460C2×C3×C5C2×C22⋊Q811yescharacteristic
461C2×C3×C5C2×#13511yescharacteristic
462C2×C3×C5C2×#13711yescharacteristic
463D15#47914yesdirect product factor
464C22×D3—51no—
465C3×Q8—21no—
466C3×Q8Q8×D512yes—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4D4×D511yescharacteristic
472C2×C3×C4D4×D511yescharacteristic
473C2×C3×C4C23×D511yescharacteristic
474C2×Dic3—51no—
475C2×Dic3—51no—
476C2×Dic3—51no—
477C2×Dic3—101no—
478C2×Dic3—101no—
479C2×Dic3—101no—
480C2×Dic3—101no—
481C4×D3—52no—
482C4×D3—52no—
483C4×D3—102no—
484C4×D3—102no—
485C4×D3—104no—
486C4×D3—202no—
487C4×D3—202no—
488C4×D3—202no—
489Dic6—52no—
490Dic6—104no—
491Dic6—101no—
492C3×C8—21no—
493C3×C8—21no—
494C3⋊C8—101no—
495C3⋊C8—101no—
496C22×C5C2×D3×D411yescharacteristic
497C2×D5—32no—
498C2×D5—32no—
499C2×D5—32no—
500C4×C5—21no—
501C4×C5—21no—
502C4×C5—22no—
503C4×C5—41no—
504C4×C5—41no—
505C4×C5—41no—
506C4×C5C2×D3×Q811yescharacteristic
507C4×C5D3×#4111yescharacteristic
508Dic5—32no—
509Dic5—61no—
510Dic5—61no—
511Dic5—62no—
512Dic5—121no—
513Dic5—121no—
514Dic5—121no—
515C2×Q8—154no—
516C2×Q8—151no—
517C2×Q8—301no—
518C2×Q8—302no—
519C2×Q8C22×D1511yescharacteristic
520C22×C4—151no—
521C22×C4—151no—
522C22×C4—151no—
523C22×C4—301no—
524C22×C4—301no—
525C22×C4—301no—
526C22×C4—301no—
527C2×C8—151no—
528C2×C8—151no—
529C2×C8—302no—
530C2×C8—302no—
531C2×C8C22×D1511yescharacteristic
532C2×C8C22×D1511yescharacteristic
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—151no—
537C4⋊C4—151no—
538C4⋊C4—151no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4—301no—
542C4⋊C4—301no—
543C4⋊C4—301no—
544C4⋊C4—301no—
545C4⋊C4—301no—
546C4⋊C4—301no—
547C4⋊C4—301no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4C22×D1511yescharacteristic
552C4⋊C4C22×D1511yescharacteristic
553C4⋊C4C22×D1511yescharacteristic
554C42—21no—
555C42—151no—
556C42—151no—
557C42—151no—
558C42—301no—
559C42—301no—
560C42—301no—
561C42C22×D1511yescharacteristic
562C3×C5C2×#47911yescharacteristic, complemented, Hall
563C22×C3C2×D4×D511yescharacteristic
564C2×D3—52no—
565C2×D3—52no—
566C2×D3—52no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—22no—
570C3×C4—41no—
571C3×C4—41no—
572C3×C4—41no—
573C3×C4C2×Q8×D511yescharacteristic
574C3×C4D5×#4111yescharacteristic
575Dic3—52no—
576Dic3—101no—
577Dic3—101no—
578Dic3—102no—
579Dic3—201no—
580Dic3—201no—
581Dic3—201no—
582C2×C5D3×C22⋊Q811yescharacteristic
583C2×C5D3×#13511yescharacteristic
584C2×C5D3×#13711yescharacteristic
585D5—34no—
586C23—151no—
587Q8—21no—
588Q8—152no—
589Q8—304no—
590Q8—301no—
591Q8Q8×D1512yes—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—151no—
597C2×C4—152no—
598C2×C4—152no—
599C2×C4—151no—
600C2×C4—151no—
601C2×C4—302no—
602C2×C4—302no—
603C2×C4—304no—
604C2×C4—301no—
605C2×C4—301no—
606C2×C4—301no—
607C2×C4—301no—
608C2×C4—602no—
609C2×C4—602no—
610C2×C4—602no—
611C2×C4D4×D1511yescharacteristic
612C2×C4D4×D1511yescharacteristic
613C2×C4C23×D1511yescharacteristic
614C8—21no—
615C8—21no—
616C8—301no—
617C8—301no—
618C2×C3D5×C22⋊Q811yescharacteristic
619C2×C3D5×#13511yescharacteristic
620C2×C3D5×#13711yescharacteristic
621D3—54no—
622C5D3×#47911yescharacteristic, complemented, Sylow
623C22—152no—
624C22—152no—
625C22—152no—
626C22C2×D4×D1511yescharacteristic
627C4—22no—
628C4—21no—
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—152no—
634C4—302no—
635C4—301no—
636C4—301no—
637C4—601no—
638C4—601no—
639C4—601no—
640C4C2×Q8×D1511yescharacteristic
641C4#41×D1511yescharacteristic
642C3D5×#47911yescharacteristic, complemented, Sylow
643C2—154no—
644C2D15×C22⋊Q811yescharacteristic
645C2D15×#13511yescharacteristic
646C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#479C2
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#479D15
hypocenterC3×C5C2×#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C3×C5×#479C2semidirect
4. #11751164C2semidirect
5. #11751123C2semidirect
7. #11750978C2semidirect
9. #11750958C2semidirect
11. #11750930C2semidirect
14. #11750900C2semidirect
15. #11750897C2semidirect
63. C5×#479D3semidirect
125. C3×#479D5semidirect
313. #479D15direct (N × H)
463. D15#479direct (N × H)
562. C3×C5C2×#479semidirect
622. C5D3×#479semidirect
642. C3D5×#479semidirect

Maximal subgroups

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

subgroupindex
D15×#1252
C4×Q8×D152
C3×C5×#4792
#117511642
#117511232
D15×#1072
#117509782
D15×#1062
#117509582
D15×C4⋊C82
#117509302
D15×#1032
#117509002
#117508972
D5×#4793
D3×#4795