Finite Group Databasebeta

← D15×#482 #14431511

Subgroups — D15×#482 #14431511

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#121C211yesmaximal, characteristic
2D15×#117C211yesmaximal, characteristic, complemented
3C3×C5×#482C211yesmaximal, characteristic, complemented
4#11751136C211yesmaximal, characteristic, complemented
5#11751104C211yesmaximal, characteristic, complemented
6#11750986C211yesmaximal, characteristic, complemented
7D15×#107C211yesmaximal, characteristic, complemented
8#11750967C211yesmaximal, characteristic, complemented
9D15×#106C211yesmaximal, characteristic, complemented
10#11750885C211yesmaximal, characteristic, complemented
11#11750880C211yesmaximal, characteristic, complemented
12D15×#102C211yesmaximal, characteristic, complemented
13D15×#102C211yesmaximal, characteristic, complemented
14#11750838C211yesmaximal, characteristic, complemented
15D15×C22⋊C8C211yesmaximal, characteristic, complemented
16D5×#482—31nomaximal, Hall
17C2×D4×D15—21no—
18C2×D4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C3×C5×#117C2211yescharacteristic, complemented
22#91828—21no—
23#91827C2211yescharacteristic
24#91819C2211yescharacteristic
25#91815C2211yescharacteristic, complemented
26C2×C8×D15C2211yescharacteristic
27C2×C8×D15C2211yescharacteristic
28#91784C2211yescharacteristic
29#91781C2211yescharacteristic, complemented
30#91781C2211yescharacteristic, complemented
31C4⋊C4×D15C2211yescharacteristic
32C4⋊C4×D15C2211yescharacteristic
33C4⋊C4×D15C2211yescharacteristic
34#91773—21no—
35C22⋊C4×D15—21no—
36C22⋊C4×D15—21no—
37#91766—21no—
38#91761—21no—
39C42×D15—21no—
40C3×C5×#107C2211yescharacteristic, complemented
41C3×C5×#106C2211yescharacteristic, complemented
42C3×C5×#102C2211yescharacteristic, complemented
43C3×C5×#102C2211yescharacteristic, complemented
44C3×C5×C22⋊C8C2211yescharacteristic, complemented
45#91116C2211yescharacteristic, complemented
46#91116C2211yescharacteristic, complemented
47#91114C2211yescharacteristic, complemented
48#91105C2211yescharacteristic, complemented
49#91105C2211yescharacteristic, complemented
50#91104C2211yescharacteristic, complemented
51#91104C2211yescharacteristic, complemented
52#91102C2211yescharacteristic, complemented
53#91101C2211yescharacteristic, complemented
54#91093C2211yescharacteristic, complemented
55#91093C2211yescharacteristic, complemented
56#91092C2211yescharacteristic, complemented
57#91092C2211yescharacteristic, complemented
58#91091C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60D3×#482—51nomaximal, Hall
61D5×#121—31no—
62D5×#117—31no—
63C5×#482D311yescharacteristic, complemented
64#65324—31no—
65#65292—31no—
66#65174—31no—
67D5×#107—31no—
68#65155—31no—
69D5×#106—31no—
70#65073—31no—
71#65068—31no—
72D5×#102—31no—
73D5×#102—31no—
74#65026—31no—
75D5×C22⋊C8—31no—
76C23×D15—21no—
77C23×D15D411yescharacteristic
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×#1220—21no—
83C2×#1220—21no—
84C22×Dic15D411yescharacteristic
85D4×D15—22no—
86D4×D15—22no—
87D4×D15—44no—
88C2×D60—21no—
89C2×D60C2311yescharacteristic
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15—21no—
93C2×C4×D15—21no—
94C2×C4×D15—21no—
95C2×C4×D15D411yescharacteristic
96C2×C4×D15D411yescharacteristic
97C2×C4×D15C2311yescharacteristic
98C2×C4×D15C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4—21no—
106C3×C42×C5—21no—
107#6719—21no—
108#6719—21no—
109#6714—21no—
110#6714—21no—
111#6714—21no—
112#6714—21no—
113C4⋊Dic15C2311yescharacteristic
114C4⋊Dic15C2311yescharacteristic
115C4⋊Dic15C2311yescharacteristic
116#6712—21no—
117#6712—21no—
118#6712—21no—
119C4×Dic15—21no—
120C4×Dic15—21no—
121C4×Dic15—21no—
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C8×D15—22no—
125C8×D15—22no—
126D3×#121—51no—
127D3×#117—51no—
128C3×#482D511yescharacteristic, complemented
129#5035—51no—
130#5003—51no—
131#4885—51no—
132D3×#107—51no—
133#4866—51no—
134D3×#106—51no—
135#4784—51no—
136#4779—51no—
137D3×#102—51no—
138D3×#102—51no—
139#4737—51no—
140D3×C22⋊C8—51no—
141C2×D4×D5—31no—
142C2×D4×D5—61no—
143C22×C4×D5—31no—
144C5×#121C2×D311yescharacteristic
145C5×#117C2×D311yescharacteristic, complemented
146#4085—61no—
147#4084—31no—
148#4076—31no—
149#4072—31no—
150C2×C8×D5—31no—
151C2×C8×D5—31no—
152#4041—31no—
153#4038—31no—
154#4038—31no—
155D5×C4⋊C4—31no—
156D5×C4⋊C4—31no—
157D5×C4⋊C4—31no—
158#4030—61no—
159D5×C22⋊C4—61no—
160D5×C22⋊C4—61no—
161#4023—61no—
162#4018—61no—
163C42×D5—61no—
164C5×#107C2×D311yescharacteristic, complemented
165C5×#106C2×D311yescharacteristic, complemented
166C5×#102C2×D311yescharacteristic, complemented
167C5×#102C2×D311yescharacteristic, complemented
168C5×C22⋊C8C2×D311yescharacteristic, complemented
169#3964—31no—
170#3964—31no—
171C22⋊#168—31no—
172#3953—31no—
173#3953—31no—
174#3952—31no—
175#3952—31no—
176#3950—31no—
177#3949—31no—
178#3941—31no—
179#3941—31no—
180#3940—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C2×#482—151noSylow
185C23×C3×C5—21no—
186C23×C3×C5C2×D411yescharacteristic
187C22×D15—22no—
188C22×D15—22no—
189C22×D15—22no—
190C22×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—42no—
194C22×D15C2×D411yescharacteristic
195C22×D15C2×D411yescharacteristic
196C3×C5×D4—21no—
197C3×C5×D4—21no—
198C3×C5×D4—42no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2411yescharacteristic
206#1220—42no—
207#1220—42no—
208#1220—42no—
209C2×Dic15—22no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15C2×D411yescharacteristic
214C2×Dic15C2×D411yescharacteristic
215D60—21no—
216D60—21no—
217D60—42no—
218C4×D15—22no—
219C4×D15—21no—
220C4×D15—21no—
221C4×D15—22no—
222C4×D15—42no—
223C4×D15—42no—
224C4×D15—42no—
225C4×D15#4112yes—
226C4×D15#4112yes—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3⋊#168—21no—
230C3⋊#168—21no—
231C2×D3×D4—51no—
232C2×D3×D4—101no—
233C22×C4×D3—51no—
234C3×#121C2×D511yescharacteristic
235C3×#117C2×D511yescharacteristic, complemented
236#939—101no—
237#938—51no—
238#930—51no—
239#926—51no—
240C2×D3×C8—51no—
241C2×D3×C8—51no—
242#895—51no—
243#892—51no—
244#892—51no—
245D3×C4⋊C4—51no—
246D3×C4⋊C4—51no—
247D3×C4⋊C4—51no—
248#884—101no—
249D3×C22⋊C4—101no—
250D3×C22⋊C4—101no—
251#877—101no—
252#872—101no—
253C42×D3—101no—
254C3×#107C2×D511yescharacteristic, complemented
255C3×#106C2×D511yescharacteristic, complemented
256C3×#102C2×D511yescharacteristic, complemented
257C3×#102C2×D511yescharacteristic, complemented
258C3×C22⋊C8C2×D511yescharacteristic, complemented
259#832—51no—
260#832—51no—
261#830—51no—
262#821—51no—
263#821—51no—
264(C2×D3)⋊C8—51no—
265(C2×D3)⋊C8—51no—
266#818—51no—
267#817—51no—
268#809—51no—
269#809—51no—
270#808—51no—
271#808—51no—
272#807—51no—
273#807—51no—
274C23×D5—31no—
275C23×D5—61no—
276C2×C5×D4—21no—
277C2×C5×D4C22×D311yescharacteristic
278C22×C4×C5C22×D311yescharacteristic
279C2×C22⋊D5—61no—
280C2×C22⋊D5—61no—
281C2×C22⋊D5—61no—
282C22×Dic5—31no—
283D4×D5—62no—
284D4×D5—62no—
285D4×D5—124no—
286C2×D20—31no—
287C2×D20—61no—
288C2×C4×D5—31no—
289C2×C4×D5—31no—
290C2×C4×D5—31no—
291C2×C4×D5—31no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C5×C8C22×D311yescharacteristic
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C42×C5—21no—
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307#685—61no—
308#685—61no—
309#685—61no—
310#685—61no—
311C4⋊Dic5—31no—
312C4⋊Dic5—31no—
313C4⋊Dic5—31no—
314#683—61no—
315#683—61no—
316#683—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C8×D5—62no—
323C8×D5—62no—
324C2×#121—151no—
325C2×#117—151no—
326#482—151no—
327#482—151no—
328#482—151no—
329#482—151no—
330#482—151no—
331#482—151no—
332#482—151no—
333#482D1511yescharacteristic, direct product factor
334C2×#107—151no—
335C2×#106—151no—
336C2×#102—151no—
337C2×#102—151no—
338C2×C22⋊C8—151no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5—41no—
345C22×C3×C5C22×D411yescharacteristic
346C2×D15—21no—
347C2×D15—21no—
348C2×D15—21no—
349C2×D15—44no—
350C2×D15—41no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—84no—
354C2×D15#12312yes—
355C2×D15#13512yes—
356C2×D15AGL(1,ℤ/8)12yes—
357C3×C4×C5—21no—
358C3×C4×C5—41no—
359C3×C4×C5—41no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5C2×#4111yescharacteristic
363Dic15—21no—
364Dic15—41no—
365Dic15—41no—
366Dic15—41no—
367Dic15#12312yes—
368C23×D3—51no—
369C23×D3—101no—
370C2×C3×D4—21no—
371C2×C3×D4C22×D511yescharacteristic
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—101no—
374C2×#67—101no—
375C2×#67—101no—
376C22×Dic3—51no—
377D3×D4—102no—
378D3×D4—102no—
379D3×D4—204no—
380C2×D12—51no—
381C2×D12—101no—
382C2×C4×D3—51no—
383C2×C4×D3—51no—
384C2×C4×D3—51no—
385C2×C4×D3—51no—
386C2×C4×D3—102no—
387C2×C4×D3—102no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C2×C4×D3—101no—
391C2×C3×C8C22×D511yescharacteristic
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4C22×D511yescharacteristic
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C42—21no—
399#217—101no—
400#217—101no—
401(C2×D3)⋊C4—101no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405C4⋊Dic3—51no—
406C4⋊Dic3—51no—
407C4⋊Dic3—51no—
408Dic3⋊C4—101no—
409Dic3⋊C4—101no—
410Dic3⋊C4—101no—
411C4×Dic3—101no—
412C4×Dic3—101no—
413C4×Dic3—101no—
414C2×C3⋊C8—51no—
415C2×C3⋊C8—51no—
416D3×C8—102no—
417D3×C8—102no—
418C23×C5—21no—
419C23×C5D3×D411yescharacteristic
420C22×D5—31no—
421C22×D5—31no—
422C22×D5—62no—
423C22×D5—62no—
424C22×D5—62no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—122no—
429C5×D4—21no—
430C5×D4—21no—
431C5×D4—42no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5D3×D411yescharacteristic
438C2×C4×C5C23×D311yescharacteristic
439C22⋊D5—122no—
440C22⋊D5—122no—
441C22⋊D5—122no—
442C2×Dic5—31no—
443C2×Dic5—31no—
444C2×Dic5—62no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448D20—61no—
449D20—61no—
450D20—122no—
451C4×D5—32no—
452C4×D5—32no—
453C4×D5—62no—
454C4×D5—62no—
455C4×D5—61no—
456C4×D5—61no—
457C4×D5—122no—
458C4×D5—122no—
459C4×D5—122no—
460C5×C8—21no—
461C5×C8—21no—
462#168—61no—
463#168—61no—
464C22×D4—151no—
465C22×D4—301no—
466C23×C4—151no—
467C22×C8—151no—
468C22×C8—151no—
469#121—151no—
470#121—151no—
471#121—151no—
472#121—301no—
473#121—301no—
474#121C2×D1511yescharacteristic
475#117—151no—
476#117—151no—
477#117—151no—
478#117—301no—
479#117—301no—
480#117C2×D1511yescharacteristic, complemented
481C2×C4⋊C4—151no—
482C2×C4⋊C4—151no—
483C2×C4⋊C4—151no—
484C2×C22⋊C4—301no—
485C2×C22⋊C4—301no—
486C2×C42—301no—
487#107—151no—
488#107—151no—
489#107—151no—
490#107C2×D1511yescharacteristic, complemented
491#106—151no—
492#106—151no—
493#106—151no—
494#106C2×D1511yescharacteristic, complemented
495#102—151no—
496#102—151no—
497#102—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102C2×D1511yescharacteristic, complemented
502#102C2×D1511yescharacteristic, complemented
503C22⋊C8—151no—
504C22⋊C8—151no—
505C22⋊C8—151no—
506C22⋊C8C2×D1511yescharacteristic, complemented
507C2×C3×C5—41no—
508C2×C3×C5—81no—
509C2×C3×C5C2×#12311yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
512D15—41no—
513D15—81no—
514D15#48214yesdirect product factor
515C23×C3—21no—
516C23×C3D4×D511yescharacteristic
517C22×D3—51no—
518C22×D3—51no—
519C22×D3—102no—
520C22×D3—102no—
521C22×D3—102no—
522C22×D3—101no—
523C22×D3—202no—
524C22×D3—202no—
525C22×D3—202no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—42no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4D4×D511yescharacteristic
535C2×C3×C4C23×D511yescharacteristic
536#67—202no—
537#67—202no—
538#67—202no—
539C2×Dic3—51no—
540C2×Dic3—51no—
541C2×Dic3—102no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544C2×Dic3—101no—
545D12—101no—
546D12—101no—
547D12—202no—
548C4×D3—52no—
549C4×D3—52no—
550C4×D3—102no—
551C4×D3—102no—
552C4×D3—101no—
553C4×D3—101no—
554C4×D3—202no—
555C4×D3—202no—
556C4×D3—202no—
557C3×C8—21no—
558C3×C8—21no—
559C3⋊C8—101no—
560C3⋊C8—101no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5C2×D3×D411yescharacteristic
568C2×D5—32no—
569C2×D5—32no—
570C2×D5—32no—
571C2×D5—61no—
572C2×D5—61no—
573C2×D5—61no—
574C2×D5—124no—
575C2×D5—121no—
576C2×D5—121no—
577C2×D5—121no—
578C2×D5—244no—
579C4×C5—21no—
580C4×C5—41no—
581C4×C5—41no—
582C4×C5—41no—
583C4×C5D3×#4111yescharacteristic
584C4×C5D3×#4111yescharacteristic
585Dic5—32no—
586Dic5—61no—
587Dic5—121no—
588Dic5—121no—
589Dic5—121no—
590C24—151no—
591C24—301no—
592C2×D4—21no—
593C2×D4—151no—
594C2×D4—301no—
595C2×D4—302no—
596C2×D4—302no—
597C2×D4—301no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—604no—
601C2×D4C22×D1511yescharacteristic
602C22×C4—151no—
603C22×C4—151no—
604C22×C4—151no—
605C22×C4—151no—
606C22×C4—151no—
607C22×C4—302no—
608C22×C4—302no—
609C22×C4—301no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4C22×D1511yescharacteristic
613C2×C8—151no—
614C2×C8—151no—
615C2×C8—302no—
616C2×C8—302no—
617C2×C8C22×D1511yescharacteristic
618C2×C8C22×D1511yescharacteristic
619C4⋊C4—151no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4C22×D1511yescharacteristic
626C4⋊C4C22×D1511yescharacteristic
627C4⋊C4C22×D1511yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C42—21no—
637C42—301no—
638C42—301no—
639C42—301no—
640C3×C5C2×#48211yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3C2×D4×D511yescharacteristic
648C2×D3—52no—
649C2×D3—52no—
650C2×D3—52no—
651C2×D3—101no—
652C2×D3—101no—
653C2×D3—101no—
654C2×D3—204no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—201no—
658C2×D3—404no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4D5×#4111yescharacteristic
664C3×C4D5×#4111yescharacteristic
665Dic3—52no—
666Dic3—101no—
667Dic3—201no—
668Dic3—201no—
669Dic3—201no—
670C2×C5—41no—
671C2×C5—81no—
672C2×C5D3×#12311yescharacteristic
673C2×C5D3×#13511yescharacteristic
674C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
675D5—34no—
676D5—121no—
677D5—241no—
678C23—21no—
679C23—151no—
680C23—151no—
681C23—302no—
682C23—302no—
683C23—302no—
684C23—301no—
685C23—602no—
686C23—602no—
687C23—602no—
688C23D4×D1511yescharacteristic
689D4—21no—
690D4—21no—
691D4—42no—
692D4—301no—
693D4—301no—
694D4—602no—
695D4—602no—
696D4—602no—
697D4—602no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—151no—
704C2×C4—152no—
705C2×C4—152no—
706C2×C4—151no—
707C2×C4—302no—
708C2×C4—302no—
709C2×C4—302no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—301no—
714C2×C4—301no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4D4×D1511yescharacteristic
719C2×C4C23×D1511yescharacteristic
720C8—21no—
721C8—21no—
722C8—301no—
723C8—301no—
724C2×C3—41no—
725C2×C3—81no—
726C2×C3D5×#12311yescharacteristic
727C2×C3D5×#13511yescharacteristic
728C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
729D3—54no—
730D3—201no—
731D3—401no—
732C5D3×#48211yescharacteristic, complemented, Sylow
733C22—21no—
734C22—21no—
735C22—21no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—152no—
740C22—152no—
741C22—152no—
742C22—301no—
743C22—301no—
744C22—301no—
745C22—604no—
746C22—601no—
747C22—601no—
748C22—601no—
749C22—1204no—
750C22C2×D4×D1511yescharacteristic
751C4—21no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—152no—
756C4—301no—
757C4—601no—
758C4—601no—
759C4—601no—
760C4#41×D1511yescharacteristic
761C4#41×D1511yescharacteristic
762C3D5×#48211yescharacteristic, complemented, Sylow
763C2—41no—
764C2—81no—
765C2—154no—
766C2—601no—
767C2—1201no—
768C2D15×#12311yescharacteristic
769C2D15×#13511yescharacteristic
770C2D15×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#482C2
socleC22×C3×C5C22×D4
prime radicalD15×#121C2
hypercenter#482D15
hypocenterC3×C5C2×#482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. D15×#117C2semidirect
3. C3×C5×#482C2semidirect
4. #11751136C2semidirect
5. #11751104C2semidirect
6. #11750986C2semidirect
7. D15×#107C2semidirect
8. #11750967C2semidirect
9. D15×#106C2semidirect
10. #11750885C2semidirect
11. #11750880C2semidirect
12. D15×#102C2semidirect
13. D15×#102C2semidirect
14. #11750838C2semidirect
15. D15×C22⋊C8C2semidirect
21. C3×C5×#117C22semidirect
25. #91815C22semidirect
29. #91781C22semidirect
30. #91781C22semidirect
40. C3×C5×#107C22semidirect
41. C3×C5×#106C22semidirect
42. C3×C5×#102C22semidirect
43. C3×C5×#102C22semidirect
44. C3×C5×C22⋊C8C22semidirect
45. #91116C22semidirect
46. #91116C22semidirect
47. #91114C22semidirect
48. #91105C22semidirect
49. #91105C22semidirect
50. #91104C22semidirect
51. #91104C22semidirect
52. #91102C22semidirect
53. #91101C22semidirect
54. #91093C22semidirect
55. #91093C22semidirect
56. #91092C22semidirect
57. #91092C22semidirect
58. #91091C22semidirect
59. #91091C22semidirect
63. C5×#482D3semidirect
128. C3×#482D5semidirect
145. C5×#117C2×D3semidirect
164. C5×#107C2×D3semidirect
165. C5×#106C2×D3semidirect
166. C5×#102C2×D3semidirect
167. C5×#102C2×D3semidirect
168. C5×C22⋊C8C2×D3semidirect
235. C3×#117C2×D5semidirect
254. C3×#107C2×D5semidirect
255. C3×#106C2×D5semidirect
256. C3×#102C2×D5semidirect
257. C3×#102C2×D5semidirect
258. C3×C22⋊C8C2×D5semidirect
333. #482D15direct (N × H)
480. #117C2×D15semidirect
490. #107C2×D15semidirect
494. #106C2×D15semidirect
501. #102C2×D15semidirect
502. #102C2×D15semidirect
506. C22⋊C8C2×D15semidirect
514. D15#482direct (N × H)
640. C3×C5C2×#482semidirect
732. C5D3×#482semidirect
762. C3D5×#482semidirect

Maximal subgroups

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

subgroupindex
D15×#1212
D15×#1172
C3×C5×#4822
#117511362
#117511042
#117509862
D15×#1072
#117509672
D15×#1062
#117508852
#117508802
D15×#1022
#117508382
D15×C22⋊C82
D5×#4823
D3×#4825