Finite Group Databasebeta

← D15×#480 #14431397

Subgroups — D15×#480 #14431397

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#121C211yesmaximal, characteristic
2C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
3C3×C5×#480C211yesmaximal, characteristic, complemented
4#11751134C211yesmaximal, characteristic, complemented
5#11751068C211yesmaximal, characteristic, complemented
6#11750983C212yesmaximal, complemented
7D15×#107C212yesmaximal, complemented
8#11750875C212yesmaximal, complemented
9D15×#102C212yesmaximal, complemented
10#11750837C211yesmaximal, characteristic, complemented
11D15×C22⋊C8C211yesmaximal, characteristic, complemented
12D5×#480—31nomaximal, Hall
13C2×D4×D15—21no—
14C2×D4×D15C2211yescharacteristic
15C22×C4×D15—21no—
16C22×C4×D15C2211yescharacteristic
17C3×C5×#121C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
19#91828—21no—
20#91827C2211yescharacteristic
21#91819C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic, complemented
23C2×#6712—21no—
24C2×C8×D15C2212yes—
25#91784C2211yescharacteristic
26C4⋊C4×D15—21no—
27C4⋊C4×D15—21no—
28C4⋊C4×D15C2211yescharacteristic
29C4⋊C4×D15C2212yes—
30C4⋊C4×D15C2212yescomplemented
31#91773—21no—
32C22⋊C4×D15—21no—
33C3×C5×#107C2212yescomplemented
34C3×C5×#102C2212yescomplemented
35C3×C5×C22⋊C8C2211yescharacteristic, complemented
36#91116C2212yescomplemented
37#91114C2211yescharacteristic, complemented
38#91105C2212yescomplemented
39#91104C2212yescomplemented
40#91102C2212yescomplemented
41#91093C2212yescomplemented
42#91091C2212yescomplemented
43#91091C2212yescomplemented
44D3×#480—51nomaximal, Hall
45D5×#121—31no—
46C2×D5×C4⋊C4—31no—
47C5×#480D311yescharacteristic, complemented
48#65322—31no—
49#65256—31no—
50#65171—32no—
51D5×#107—32no—
52#65063—32no—
53D5×#102—32no—
54#65025—31no—
55D5×C22⋊C8—31no—
56C23×D15—21no—
57C23×D15D411yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63C2×#1220—21no—
64C2×#1220—21no—
65C22×Dic15—21no—
66C22×Dic15D411yescharacteristic
67D4×D15—24no—
68D4×D15—44no—
69C2×D60—21no—
70C2×D60C2311yescharacteristic
71C2×C4×D15—24no—
72C2×C4×D15—21no—
73C2×C4×D15—22no—
74C2×C4×D15—22no—
75C2×C4×D15—44no—
76C2×C4×D15D411yescharacteristic
77C2×C4×D15D411yescharacteristic
78C2×C4×D15C2311yescharacteristic
79C2×C4×D15C2311yescharacteristic
80C2×C3×C5×C8C2312yes—
81C3×C5×C4⋊C4—21no—
82C3×C5×C4⋊C4C2312yes—
83C3×C5×C4⋊C4C2311yescharacteristic
84C3×C5×C22⋊C4—21no—
85#6719—21no—
86#6714—21no—
87#6714—21no—
88C4⋊Dic15—21no—
89C4⋊Dic15C2312yes—
90C4⋊Dic15C2311yescharacteristic
91#6712—21no—
92#6712—22no—
93#6712—22no—
94C2×C3⋊#168C2312yes—
95C8×D15—24no—
96D3×#121—51no—
97C2×D3×C4⋊C4—51no—
98C3×#480D511yescharacteristic, complemented
99#5033—51no—
100#4967—51no—
101#4882—52no—
102D3×#107—52no—
103#4774—52no—
104D3×#102—52no—
105#4736—51no—
106D3×C22⋊C8—51no—
107C2×D4×D5—31no—
108C2×D4×D5—61no—
109C22×C4×D5—31no—
110C22×C4×D5—61no—
111C5×#121C2×D311yescharacteristic
112C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
113#4085—61no—
114#4084—31no—
115#4076—31no—
116C2×C4⋊Dic5—31no—
117C2×#683—61no—
118C2×C8×D5—32no—
119#4041—31no—
120D5×C4⋊C4—32no—
121D5×C4⋊C4—32no—
122D5×C4⋊C4—31no—
123D5×C4⋊C4—61no—
124D5×C4⋊C4—61no—
125#4030—61no—
126D5×C22⋊C4—61no—
127C5×#107C2×D312yescomplemented
128C5×#102C2×D312yescomplemented
129C5×C22⋊C8C2×D311yescharacteristic, complemented
130#3964—32no—
131C22⋊#168—31no—
132#3953—32no—
133#3952—32no—
134#3950—32no—
135#3941—32no—
136#3939—32no—
137#3939—32no—
138C2×#480—151noSylow
139C23×C3×C5—21no—
140C23×C3×C5C2×D411yescharacteristic
141C22×D15—22no—
142C22×D15—22no—
143C22×D15—21no—
144C22×D15—42no—
145C22×D15—42no—
146C22×D15—42no—
147C22×D15D814yes—
148C22×D15C2×D411yescharacteristic
149C22×D15C2×D411yescharacteristic
150C3×C5×D4—22no—
151C3×C5×D4—42no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—42no—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2411yescharacteristic
158#1220—42no—
159#1220—42no—
160#1220—42no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—21no—
164C2×Dic15—42no—
165C2×Dic15C2×D411yescharacteristic
166C2×Dic15C2×D411yescharacteristic
167D60—22no—
168D60—42no—
169C4×D15—22no—
170C4×D15—22no—
171C4×D15—22no—
172C4×D15—44no—
173C4×D15—44no—
174C4×D15—42no—
175C4×D15#4114yes—
176C3×C5×C8—22no—
177C3⋊#168—22no—
178C2×D3×D4—51no—
179C2×D3×D4—101no—
180C22×C4×D3—51no—
181C22×C4×D3—101no—
182C3×#121C2×D511yescharacteristic
183C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
184#939—101no—
185#938—51no—
186#930—51no—
187C2×C4⋊Dic3—51no—
188C2×Dic3⋊C4—101no—
189C2×D3×C8—52no—
190#895—51no—
191D3×C4⋊C4—51no—
192D3×C4⋊C4—52no—
193D3×C4⋊C4—52no—
194D3×C4⋊C4—101no—
195D3×C4⋊C4—101no—
196#884—101no—
197D3×C22⋊C4—101no—
198C3×#107C2×D512yescomplemented
199C3×#102C2×D512yescomplemented
200C3×C22⋊C8C2×D511yescharacteristic, complemented
201#832—52no—
202#830—51no—
203#821—52no—
204(C2×D3)⋊C8—52no—
205#818—52no—
206#809—52no—
207#807—52no—
208#807—52no—
209C23×D5—31no—
210C23×D5—61no—
211C2×C5×D4—21no—
212C2×C5×D4C22×D311yescharacteristic
213C22×C4×C5—21no—
214C22×C4×C5C22×D311yescharacteristic
215C2×C22⋊D5—61no—
216C2×C22⋊D5—61no—
217C2×C22⋊D5—61no—
218C22×Dic5—31no—
219C22×Dic5—61no—
220D4×D5—64no—
221D4×D5—124no—
222C2×D20—31no—
223C2×D20—61no—
224C2×C4×D5—31no—
225C2×C4×D5—31no—
226C2×C4×D5—31no—
227C2×C4×D5—31no—
228C2×C4×D5—64no—
229C2×C4×D5—62no—
230C2×C4×D5—62no—
231C2×C4×D5—61no—
232C2×C4×D5—124no—
233C2×C5×C8C22×D312yes—
234C5×C4⋊C4—21no—
235C5×C4⋊C4C22×D312yes—
236C5×C4⋊C4C22×D311yescharacteristic
237C5×C22⋊C4—21no—
238C22⋊Dic5—61no—
239#685—61no—
240#685—61no—
241C4⋊Dic5—31no—
242C4⋊Dic5—32no—
243C4⋊Dic5—61no—
244#683—61no—
245#683—62no—
246#683—62no—
247C2×#168—32no—
248C8×D5—64no—
249C2×#121—151no—
250C22×C4⋊C4—151no—
251#480—151no—
252#480—151no—
253#480—152no—
254#480—152no—
255#480—151no—
256#480D1511yescharacteristic, direct product factor
257C2×#107—152no—
258C2×#102—152no—
259C2×C22⋊C8—151no—
260C22×C3×C5—21no—
261C22×C3×C5—21no—
262C22×C3×C5—41no—
263C22×C3×C5—41no—
264C22×C3×C5—41no—
265C22×C3×C5C2×D812yes—
266C22×C3×C5C22×D411yescharacteristic
267C2×D15—21no—
268C2×D15—21no—
269C2×D15—28no—
270C2×D15—41no—
271C2×D15—41no—
272C2×D15—41no—
273C2×D15—84no—
274C2×D15#12312yes—
275C2×D15C2×D812yes—
276C2×D15C2×D812yes—
277C2×D15#13712yes—
278C3×C4×C5—21no—
279C3×C4×C5—42no—
280C3×C4×C5—41no—
281C3×C4×C5C2×#4112yes—
282Dic15—21no—
283Dic15—42no—
284Dic15—41no—
285Dic15#12312yes—
286C23×D3—51no—
287C23×D3—101no—
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—101no—
293C2×#67—101no—
294C2×#67—101no—
295C22×Dic3—51no—
296C22×Dic3—101no—
297D3×D4—104no—
298D3×D4—204no—
299C2×D12—51no—
300C2×D12—101no—
301C2×C4×D3—51no—
302C2×C4×D3—51no—
303C2×C4×D3—51no—
304C2×C4×D3—51no—
305C2×C4×D3—104no—
306C2×C4×D3—101no—
307C2×C4×D3—102no—
308C2×C4×D3—102no—
309C2×C4×D3—204no—
310C2×C3×C8C22×D512yes—
311C3×C4⋊C4—21no—
312C3×C4⋊C4C22×D511yescharacteristic
313C3×C4⋊C4C22×D512yes—
314C3×C22⋊C4—21no—
315#217—101no—
316(C2×D3)⋊C4—101no—
317(C2×D3)⋊C4—101no—
318C4⋊Dic3—51no—
319C4⋊Dic3—52no—
320C4⋊Dic3—101no—
321Dic3⋊C4—101no—
322Dic3⋊C4—102no—
323Dic3⋊C4—102no—
324C2×C3⋊C8—52no—
325D3×C8—104no—
326C23×C5—21no—
327C23×C5D3×D411yescharacteristic
328C22×D5—31no—
329C22×D5—34no—
330C22×D5—31no—
331C22×D5—62no—
332C22×D5—62no—
333C22×D5—61no—
334C22×D5—122no—
335C22×D5—122no—
336C22×D5—122no—
337C5×D4—22no—
338C5×D4—42no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—21no—
342C2×C4×C5—42no—
343C2×C4×C5D3×D411yescharacteristic
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—122no—
346C22⋊D5—122no—
347C22⋊D5—122no—
348C2×Dic5—31no—
349C2×Dic5—31no—
350C2×Dic5—62no—
351C2×Dic5—62no—
352C2×Dic5—61no—
353C2×Dic5—122no—
354D20—62no—
355D20—122no—
356C4×D5—34no—
357C4×D5—62no—
358C4×D5—62no—
359C4×D5—62no—
360C4×D5—124no—
361C4×D5—124no—
362C4×D5—122no—
363C5×C8—22no—
364#168—62no—
365C22×D4—151no—
366C22×D4—301no—
367C23×C4—151no—
368C23×C4—301no—
369C22×C8—152no—
370#121—151no—
371#121—151no—
372#121—151no—
373#121—301no—
374#121—301no—
375#121C2×D1511yescharacteristic
376C2×C4⋊C4—151no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—301no—
381C2×C4⋊C4—301no—
382C2×C4⋊C4—301no—
383C2×C4⋊C4C2×D1511yescharacteristic, complemented
384C2×C22⋊C4—301no—
385#107—152no—
386#107—152no—
387#107—152no—
388#107C2×D1512yescomplemented
389#102—152no—
390#102—152no—
391#102—152no—
392#102C2×D1512yescomplemented
393C22⋊C8—151no—
394C22⋊C8—152no—
395C22⋊C8C2×D1511yescharacteristic, complemented
396C2×C3×C5—22no—
397C2×C3×C5—81no—
398C2×C3×C5C2×#12311yescharacteristic
399C2×C3×C5C22×D811yescharacteristic
400C2×C3×C5C2×#13711yescharacteristic
401D15—22no—
402D15—81no—
403D15#48014yesdirect product factor
404C23×C3—21no—
405C23×C3D4×D511yescharacteristic
406C22×D3—51no—
407C22×D3—51no—
408C22×D3—54no—
409C22×D3—102no—
410C22×D3—102no—
411C22×D3—101no—
412C22×D3—202no—
413C22×D3—202no—
414C22×D3—202no—
415C3×D4—22no—
416C3×D4—42no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—42no—
421C2×C3×C4D4×D511yescharacteristic
422C2×C3×C4C23×D511yescharacteristic
423#67—202no—
424#67—202no—
425#67—202no—
426C2×Dic3—51no—
427C2×Dic3—51no—
428C2×Dic3—102no—
429C2×Dic3—102no—
430C2×Dic3—101no—
431C2×Dic3—202no—
432D12—102no—
433D12—202no—
434C4×D3—54no—
435C4×D3—102no—
436C4×D3—102no—
437C4×D3—102no—
438C4×D3—204no—
439C4×D3—204no—
440C4×D3—202no—
441C3×C8—22no—
442C3⋊C8—102no—
443C22×C5—21no—
444C22×C5—21no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5D3×D812yes—
449C22×C5C2×D3×D411yescharacteristic
450C2×D5—32no—
451C2×D5—32no—
452C2×D5—32no—
453C2×D5—32no—
454C2×D5—68no—
455C2×D5—61no—
456C2×D5—61no—
457C2×D5—121no—
458C2×D5—121no—
459C2×D5—121no—
460C2×D5—244no—
461C4×C5—21no—
462C4×C5—42no—
463C4×C5—41no—
464C4×C5D3×#4112yes—
465Dic5—32no—
466Dic5—61no—
467Dic5—122no—
468Dic5—121no—
469C24—151no—
470C24—301no—
471C2×D4—21no—
472C2×D4—151no—
473C2×D4—301no—
474C2×D4—304no—
475C2×D4—301no—
476C2×D4—301no—
477C2×D4—301no—
478C2×D4—604no—
479C2×D4C22×D1511yescharacteristic
480C22×C4—21no—
481C22×C4—151no—
482C22×C4—151no—
483C22×C4—151no—
484C22×C4—151no—
485C22×C4—151no—
486C22×C4—304no—
487C22×C4—301no—
488C22×C4—302no—
489C22×C4—302no—
490C22×C4—301no—
491C22×C4—604no—
492C22×C4C22×D1511yescharacteristic
493C2×C8—152no—
494C2×C8—304no—
495C2×C8C22×D1512yes—
496C4⋊C4—21no—
497C4⋊C4—152no—
498C4⋊C4—151no—
499C4⋊C4—302no—
500C4⋊C4—302no—
501C4⋊C4—301no—
502C4⋊C4—301no—
503C4⋊C4C22×D1512yes—
504C4⋊C4C22×D1511yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—301no—
507C22⋊C4—301no—
508C22⋊C4—301no—
509C3×C5C2×#48011yescharacteristic, complemented, Hall
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3D5×D812yes—
516C22×C3C2×D4×D511yescharacteristic
517C2×D3—52no—
518C2×D3—52no—
519C2×D3—52no—
520C2×D3—52no—
521C2×D3—108no—
522C2×D3—101no—
523C2×D3—101no—
524C2×D3—201no—
525C2×D3—201no—
526C2×D3—201no—
527C2×D3—404no—
528C3×C4—21no—
529C3×C4—42no—
530C3×C4—41no—
531C3×C4D5×#4112yes—
532Dic3—52no—
533Dic3—101no—
534Dic3—202no—
535Dic3—201no—
536C2×C5—22no—
537C2×C5—81no—
538C2×C5D3×#12311yescharacteristic
539C2×C5C2×D3×D811yescharacteristic
540C2×C5D3×#13711yescharacteristic
541D5—34no—
542D5—62no—
543D5—241no—
544C23—21no—
545C23—151no—
546C23—154no—
547C23—151no—
548C23—302no—
549C23—302no—
550C23—301no—
551C23—602no—
552C23—602no—
553C23—602no—
554C23D4×D1511yescharacteristic
555D4—22no—
556D4—42no—
557D4—302no—
558D4—602no—
559D4—602no—
560D4—602no—
561D4—602no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—42no—
566C2×C4—151no—
567C2×C4—154no—
568C2×C4—151no—
569C2×C4—302no—
570C2×C4—302no—
571C2×C4—302no—
572C2×C4—302no—
573C2×C4—301no—
574C2×C4—302no—
575C2×C4—604no—
576C2×C4—604no—
577C2×C4—602no—
578C2×C4—602no—
579C2×C4D4×D1511yescharacteristic
580C2×C4C23×D1511yescharacteristic
581C8—22no—
582C8—302no—
583C2×C3—22no—
584C2×C3—81no—
585C2×C3D5×#12311yescharacteristic
586C2×C3C2×D5×D811yescharacteristic
587C2×C3D5×#13711yescharacteristic
588D3—54no—
589D3—102no—
590D3—401no—
591C5D3×#48011yescharacteristic, complemented, Sylow
592C22—21no—
593C22—21no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—152no—
598C22—152no—
599C22—152no—
600C22—152no—
601C22—308no—
602C22—301no—
603C22—301no—
604C22—601no—
605C22—601no—
606C22—601no—
607C22—1204no—
608C22D8×D1512yes—
609C22C2×D4×D1511yescharacteristic
610C4—21no—
611C4—42no—
612C4—41no—
613C4—152no—
614C4—301no—
615C4—602no—
616C4—601no—
617C4#41×D1512yes—
618C3D5×#48011yescharacteristic, complemented, Sylow
619C2—22no—
620C2—81no—
621C2—154no—
622C2—302no—
623C2—1201no—
624C2D15×#12311yescharacteristic
625C2C2×D8×D1511yescharacteristic
626C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#480C2
socleC22×C3×C5C22×D4
prime radicalD15×#121C2
hypercenter#480D15
hypocenterC3×C5C2×#480
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D15C2semidirect
3. C3×C5×#480C2semidirect
4. #11751134C2semidirect
5. #11751068C2semidirect
6. #11750983C2semidirect
7. D15×#107C2semidirect
8. #11750875C2semidirect
9. D15×#102C2semidirect
10. #11750837C2semidirect
11. D15×C22⋊C8C2semidirect
18. C2×C3×C5×C4⋊C4C22semidirect
22. C2×C4⋊Dic15C22semidirect
30. C4⋊C4×D15C22semidirect
33. C3×C5×#107C22semidirect
34. C3×C5×#102C22semidirect
35. C3×C5×C22⋊C8C22semidirect
36. #91116C22semidirect
37. #91114C22semidirect
38. #91105C22semidirect
39. #91104C22semidirect
40. #91102C22semidirect
41. #91093C22semidirect
42. #91091C22semidirect
43. #91091C22semidirect
47. C5×#480D3semidirect
98. C3×#480D5semidirect
112. C2×C5×C4⋊C4C2×D3semidirect
127. C5×#107C2×D3semidirect
128. C5×#102C2×D3semidirect
129. C5×C22⋊C8C2×D3semidirect
183. C2×C3×C4⋊C4C2×D5semidirect
198. C3×#107C2×D5semidirect
199. C3×#102C2×D5semidirect
200. C3×C22⋊C8C2×D5semidirect
256. #480D15direct (N × H)
383. C2×C4⋊C4C2×D15semidirect
388. #107C2×D15semidirect
392. #102C2×D15semidirect
395. C22⋊C8C2×D15semidirect
403. D15#480direct (N × H)
509. C3×C5C2×#480semidirect
591. C5D3×#480semidirect
618. C3D5×#480semidirect

Maximal subgroups

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

subgroupindex
D15×#1212
C2×C4⋊C4×D152
C3×C5×#4802
#117511342
#117510682
#117509832
D15×#1072
#117508752
D15×#1022
#117508372
D15×C22⋊C82
D5×#4803
D3×#4805