Finite Group Databasebeta

← D15×#548 #14482795

Subgroups — D15×#548 #14482795

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C211yesmaximal, characteristic, complemented
2C22×Q8×D15C211yesmaximal, characteristic, complemented
3C3×C5×#548C211yesmaximal, characteristic, complemented
4#11756590C211yesmaximal, characteristic, complemented
5#11756576C211yesmaximal, characteristic, complemented
6#11756436C213yesmaximal, complemented
7D15×#124C213yesmaximal, complemented
8#11756392C213yesmaximal, complemented
9D15×C22⋊Q8C213yesmaximal, complemented
10D15×#121C213yesmaximal, complemented
11#11756357C213yesmaximal, complemented
12#11756335C211yesmaximal, characteristic, complemented
13C4×Q8×D15C211yesmaximal, characteristic, complemented
14#11756311C213yesmaximal, complemented
15C4×D4×D15C213yesmaximal, complemented
16D5×#548—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19#41×D15—28no—
20C2×#6821C2211yescharacteristic, complemented
21C2×Q8×D15—28no—
22C2×Q8×D15C2213yes—
23C2×Q8×D15C2211yescharacteristic
24C2×Q8×D15C2211yescharacteristic, complemented
25C2×Q8×D15C2213yescomplemented
26C2×#6819C2213yescomplemented
27C2×D4×D15C2213yes—
28C2×D4×D15C2213yes—
29C2×#6817C2213yescomplemented
30C22×C4×D15C2213yes—
31C22×C4×D15C2213yes—
32C22×Dic30C2213yescomplemented
33C3×C5×#124C2213yescomplemented
34C3×C5×C22⋊Q8C2213yescomplemented
35C3×C5×#121C2213yescomplemented
36C3×C4×C5×Q8C2211yescharacteristic, complemented
37C3×C4×C5×D4C2213yescomplemented
38#91836C2213yescomplemented
39#91835C2213yescomplemented
40Q8×Dic15C2211yescharacteristic, complemented
41#91828C2216yescomplemented
42#91827C2213yescomplemented
43#91825C2213yescomplemented
44D4×Dic15C2213yescomplemented
45#91819C2213yescomplemented
46C4×#1220C2213yescomplemented
47C4×#1220C2213yescomplemented
48#91813C2213yescomplemented
49#91786C2213yescomplemented
50#91785C2216yescomplemented
51#91784C2213yescomplemented
52#91782C2213yescomplemented
53C4⋊C4×D15C2213yes—
54C4⋊C4×D15C2213yes—
55#91776C2213yescomplemented
56#91774C2216yescomplemented
57#91774C2216yescomplemented
58#91773C2216yescomplemented
59#91770C2213yescomplemented
60#91770C2213yescomplemented
61C22⋊C4×D15C2211yescharacteristic
62C22⋊C4×D15C2213yes—
63C22⋊C4×D15C2216yes—
64#91767C2216yescomplemented
65#91764C2213yescomplemented
66C4×D60C2213yescomplemented
67C42×D15C2213yes—
68C4×Dic30C2213yescomplemented
69D3×#548—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×Q8×D5—31no—
72C5×#548D311yescharacteristic, complemented
73#66165—31no—
74#66151—31no—
75#66011—33no—
76D5×#124—33no—
77#65967—33no—
78D5×C22⋊Q8—33no—
79D5×#121—33no—
80#65932—33no—
81#65910—31no—
82C4×Q8×D5—31no—
83#65886—33no—
84C4×D4×D5—33no—
85C23×D15C2313yes—
86C23×D15C2311yescharacteristic
87C3×C5×#41—24no—
88C2×C3×C5×Q8—24no—
89C2×C3×C5×Q8C2313yes—
90C2×C3×C5×Q8C2311yescharacteristic
91C2×C3×C5×D4C2313yes—
92C2×C3×C5×D4C2313yes—
93C22×C3×C4×C5C2313yes—
94C22×C3×C4×C5C2313yes—
95C2×#1220C2313yes—
96C2×#1220C2313yes—
97C2×#1220C2316yes—
98C22×Dic15C2313yes—
99C22×Dic15C2313yes—
100#6821—24no—
101Q8×D15—24no—
102Q8×D15—212no—
103Q8×D15—212no—
104Q8×D15D418yescomplemented
105#6819—212no—
106D4×D15—212no—
107D4×D15—212no—
108#6817—212no—
109C2×D60C2313yes—
110C2×D60C2313yes—
111C2×C4×D15—212no—
112C2×C4×D15—212no—
113C2×C4×D15C2311yescharacteristic
114C2×C4×D15C2313yes—
115C2×C4×D15C2313yes—
116C2×C4×D15C2313yes—
117C2×C4×D15C2313yes—
118C2×C4×D15C2311yescharacteristic
119C2×C4×D15C2313yes—
120C2×C4×D15C2313yes—
121C2×C4×D15C2313yes—
122C2×Dic30—212no—
123C2×Dic30C2313yes—
124C2×Dic30C2316yes—
125C2×Dic30C2313yes—
126C3×C5×C4⋊C4C2313yes—
127C3×C5×C4⋊C4C2313yes—
128C3×C5×C22⋊C4C2316yes—
129C3×C5×C22⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4C2313yes—
131C3×C42×C5C2313yes—
132#6719C2316yes—
133#6719C2313yes—
134#6719C2311yescharacteristic
135#6714C2311yescharacteristic
136#6714C2313yes—
137#6714C2316yes—
138#6714C2316yes—
139#6714C2313yes—
140#6714C2311yescharacteristic
141C4⋊Dic15C2313yes—
142C4⋊Dic15C2313yes—
143#6712C2316yes—
144#6712C2313yes—
145#6712C2313yes—
146C4×Dic15C2313yes—
147C4×Dic15C2313yes—
148C4×Dic15C2313yes—
149C2×D3×#41—51no—
150C22×D3×Q8—51no—
151C3×#548D511yescharacteristic, complemented
152#5831—51no—
153#5817—51no—
154#5677—53no—
155D3×#124—53no—
156#5633—53no—
157D3×C22⋊Q8—53no—
158D3×#121—53no—
159#5598—53no—
160#5576—51no—
161C4×D3×Q8—51no—
162#5552—53no—
163C4×D3×D4—53no—
164C2×C5×#41C2×D311yescharacteristic, complemented
165C22×C5×Q8C2×D311yescharacteristic, complemented
166D5×#41—68no—
167C2×#713—31no—
168C2×Q8×D5—31no—
169C2×Q8×D5—31no—
170C2×Q8×D5—33no—
171C2×Q8×D5—33no—
172C2×Q8×D5—68no—
173C2×#711—33no—
174C2×D4×D5—33no—
175C2×D4×D5—33no—
176C2×#709—33no—
177C22×C4×D5—33no—
178C22×C4×D5—33no—
179C22×Dic10—33no—
180C5×#124C2×D313yescomplemented
181C5×C22⋊Q8C2×D313yescomplemented
182C5×#121C2×D313yescomplemented
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C4×C5×D4C2×D313yescomplemented
185#4093—33no—
186#4092—33no—
187Q8×Dic5—31no—
188#4085—36no—
189#4084—33no—
190#4082—33no—
191D4×Dic5—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5—33no—
195#4070—33no—
196#4043—33no—
197#4042—36no—
198#4041—33no—
199#4039—33no—
200D5×C4⋊C4—33no—
201D5×C4⋊C4—33no—
202#4033—33no—
203#4031—36no—
204#4031—36no—
205#4030—36no—
206#4027—33no—
207#4027—33no—
208D5×C22⋊C4—31no—
209D5×C22⋊C4—33no—
210D5×C22⋊C4—36no—
211#4024—36no—
212#4021—33no—
213C4×D20—33no—
214C42×D5—33no—
215C4×Dic10—33no—
216C2×#548—151noSylow
217C23×C3×C5C2413yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—26no—
222C22×D15—26no—
223C22×D15—26no—
224C22×D15#4114yescomplemented
225C22×D15C2413yes—
226C22×D15C2411yescharacteristic
227C22×D15C2411yescharacteristic
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—26no—
231C3×C5×D4—26no—
232C2×C3×C4×C5—26no—
233C2×C3×C4×C5—26no—
234C2×C3×C4×C5C2411yescharacteristic
235C2×C3×C4×C5C2413yes—
236C2×C3×C4×C5C2411yescharacteristic
237C2×C3×C4×C5C2413yes—
238C2×C3×C4×C5C2413yes—
239#1220—26no—
240#1220—26no—
241#1220—212no—
242C2×Dic15—26no—
243C2×Dic15—26no—
244C2×Dic15C2411yescharacteristic
245C2×Dic15C2413yes—
246C2×Dic15C2411yescharacteristic
247C2×Dic15C2413yes—
248C2×Dic15C2413yes—
249D60—26no—
250D60—26no—
251C4×D15—22no—
252C4×D15—26no—
253C4×D15—26no—
254C4×D15—22no—
255C4×D15—26no—
256C4×D15—26no—
257C4×D15—26no—
258C4×D15—26no—
259C4×D15C2×D4112yes—
260Dic30—26no—
261Dic30—212no—
262Dic30C2×D4112yescomplemented
263C2×C3×#41C2×D511yescharacteristic, complemented
264C22×C3×Q8C2×D511yescharacteristic, complemented
265D3×#41—108no—
266C2×#239—51no—
267C2×D3×Q8—51no—
268C2×D3×Q8—53no—
269C2×D3×Q8—53no—
270C2×D3×Q8—51no—
271C2×D3×Q8—108no—
272C2×#237—53no—
273C2×D3×D4—53no—
274C2×D3×D4—53no—
275C2×#235—53no—
276C22×C4×D3—53no—
277C22×C4×D3—53no—
278C22×Dic6—53no—
279C3×#124C2×D513yescomplemented
280C3×C22⋊Q8C2×D513yescomplemented
281C3×#121C2×D513yescomplemented
282C3×C4×Q8C2×D511yescharacteristic, complemented
283C3×C4×D4C2×D513yescomplemented
284#947—53no—
285#946—53no—
286Q8×Dic3—51no—
287#939—56no—
288#938—53no—
289#936—53no—
290D4×Dic3—53no—
291#930—53no—
292C4×#67—53no—
293C4×#67—53no—
294#924—53no—
295#897—53no—
296#896—56no—
297#895—53no—
298#893—53no—
299D3×C4⋊C4—53no—
300D3×C4⋊C4—53no—
301#887—53no—
302#885—56no—
303#885—56no—
304#884—56no—
305#67⋊C4—53no—
306#67⋊C4—53no—
307D3×C22⋊C4—53no—
308D3×C22⋊C4—56no—
309D3×C22⋊C4—51no—
310#878—56no—
311#875—53no—
312C4×D12—53no—
313C42×D3—53no—
314C4×Dic6—53no—
315C23×D5—31no—
316C23×D5—33no—
317C5×#41—24no—
318C2×C5×Q8—24no—
319C2×C5×Q8C22×D313yes—
320C2×C5×Q8C22×D311yescharacteristic
321C2×C5×D4C22×D313yes—
322C2×C5×D4C22×D313yes—
323C22×C4×C5C22×D313yes—
324C22×C4×C5C22×D313yes—
325C2×C22⋊D5—36no—
326C2×C22⋊D5—33no—
327C2×C22⋊D5—33no—
328C22×Dic5—33no—
329C22×Dic5—33no—
330#713—64no—
331Q8×D5—38no—
332Q8×D5—612no—
333Q8×D5—612no—
334Q8×D5—64no—
335#711—612no—
336D4×D5—612no—
337D4×D5—612no—
338#709—612no—
339C2×D20—33no—
340C2×D20—33no—
341C2×C4×D5—33no—
342C2×C4×D5—31no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—33no—
348C2×C4×D5—33no—
349C2×C4×D5—31no—
350C2×C4×D5—612no—
351C2×C4×D5—612no—
352C2×Dic10—33no—
353C2×Dic10—33no—
354C2×Dic10—36no—
355C2×Dic10—612no—
356C5×C4⋊C4C22×D313yes—
357C5×C4⋊C4C22×D313yes—
358C5×C22⋊C4C22×D311yescharacteristic
359C5×C22⋊C4C22×D313yes—
360C5×C22⋊C4C22×D316yes—
361C42×C5C22×D313yes—
362C22⋊Dic5—36no—
363C22⋊Dic5—33no—
364C22⋊Dic5—31no—
365#685—31no—
366#685—33no—
367#685—36no—
368#685—36no—
369#685—33no—
370#685—31no—
371C4⋊Dic5—33no—
372C4⋊Dic5—33no—
373#683—36no—
374#683—33no—
375#683—33no—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5—33no—
379C22×#41—151no—
380C23×Q8—151no—
381#548—151no—
382#548—151no—
383#548—153no—
384#548—153no—
385#548—153no—
386#548—151no—
387#548—153no—
388#548D1511yescharacteristic, direct product factor
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5—23no—
397C22×C3×C5—23no—
398C22×C3×C5—23no—
399C22×C3×C5C2×#4112yescomplemented
400C22×C3×C5C2511yescharacteristic
401C2×D15—21no—
402C2×D15—21no—
403C2×D15—28no—
404C2×D15—23no—
405C2×D15—23no—
406C2×D15—23no—
407C2×D15—412no—
408C2×D15C22×D412yes—
409C2×D15C2×#4112yes—
410C2×D15C2×#4112yescomplemented
411C2×D152−1+412yes—
412C3×C4×C5—23no—
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5—21no—
416C3×C4×C5C22×D416yes—
417Dic15—23no—
418Dic15—21no—
419Dic15—23no—
420Dic15—21no—
421Dic15C22×D416yes—
422C23×D3—51no—
423C23×D3—53no—
424C3×#41—24no—
425C2×C3×Q8—24no—
426C2×C3×Q8C22×D513yes—
427C2×C3×Q8C22×D511yescharacteristic
428C2×C3×D4C22×D513yes—
429C2×C3×D4C22×D513yes—
430C22×C3×C4C22×D513yes—
431C22×C3×C4C22×D513yes—
432C2×#67—53no—
433C2×#67—53no—
434C2×#67—56no—
435C22×Dic3—53no—
436C22×Dic3—53no—
437#239—104no—
438D3×Q8—58no—
439D3×Q8—1012no—
440D3×Q8—1012no—
441D3×Q8—104no—
442#237—1012no—
443D3×D4—1012no—
444D3×D4—1012no—
445#235—1012no—
446C2×D12—53no—
447C2×D12—53no—
448C2×C4×D3—53no—
449C2×C4×D3—51no—
450C2×C4×D3—53no—
451C2×C4×D3—53no—
452C2×C4×D3—53no—
453C2×C4×D3—53no—
454C2×C4×D3—51no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—1012no—
458C2×C4×D3—1012no—
459C2×Dic6—53no—
460C2×Dic6—53no—
461C2×Dic6—56no—
462C2×Dic6—1012no—
463C3×C4⋊C4C22×D513yes—
464C3×C4⋊C4C22×D513yes—
465C3×C22⋊C4C22×D516yes—
466C3×C22⋊C4C22×D511yescharacteristic
467C3×C22⋊C4C22×D513yes—
468C3×C42C22×D513yes—
469#217—56no—
470#217—53no—
471#217—51no—
472(C2×D3)⋊C4—51no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—56no—
475(C2×D3)⋊C4—56no—
476(C2×D3)⋊C4—53no—
477(C2×D3)⋊C4—51no—
478C4⋊Dic3—53no—
479C4⋊Dic3—53no—
480Dic3⋊C4—56no—
481Dic3⋊C4—53no—
482Dic3⋊C4—53no—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3—53no—
486C23×C5C23×D313yes—
487C23×C5C23×D311yescharacteristic
488C22×D5—31no—
489C22×D5—34no—
490C22×D5—31no—
491C22×D5—33no—
492C22×D5—62no—
493C22×D5—62no—
494C22×D5—66no—
495C22×D5—66no—
496C22×D5—66no—
497C5×Q8—26no—
498C5×Q8D3×D414yescomplemented
499C5×D4—26no—
500C5×D4—26no—
501C2×C4×C5—26no—
502C2×C4×C5—26no—
503C2×C4×C5C23×D311yescharacteristic
504C2×C4×C5C23×D313yes—
505C2×C4×C5C23×D311yescharacteristic
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D313yes—
508C22⋊D5—612no—
509C22⋊D5—66no—
510C22⋊D5—66no—
511C2×Dic5—33no—
512C2×Dic5—31no—
513C2×Dic5—33no—
514C2×Dic5—31no—
515C2×Dic5—33no—
516C2×Dic5—66no—
517C2×Dic5—66no—
518D20—66no—
519D20—66no—
520C4×D5—312no—
521C4×D5—66no—
522C4×D5—66no—
523C4×D5—62no—
524C4×D5—62no—
525C4×D5—66no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5—66no—
529Dic10—312no—
530Dic10—612no—
531Dic10—66no—
532C2×#41—151no—
533C2×#41—153no—
534C2×#41—153no—
535C2×#41—308no—
536C2×#41C2×D1511yescharacteristic, complemented
537C22×Q8—151no—
538C22×Q8—153no—
539C22×Q8—153no—
540C22×Q8—151no—
541C22×Q8—153no—
542C22×Q8—308no—
543C22×Q8C2×D1511yescharacteristic, complemented
544C22×D4—153no—
545C22×D4—153no—
546C23×C4—153no—
547C23×C4—153no—
548#124—153no—
549#124—153no—
550#124—156no—
551#124—156no—
552#124—153no—
553#124C2×D1513yescomplemented
554C22⋊Q8—153no—
555C22⋊Q8—153no—
556C22⋊Q8—156no—
557C22⋊Q8—153no—
558C22⋊Q8—156no—
559C22⋊Q8C2×D1513yescomplemented
560#121—153no—
561#121—156no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121C2×D1513yescomplemented
566C4×Q8—151no—
567C4×Q8—153no—
568C4×Q8—153no—
569C4×Q8C2×D1511yescharacteristic, complemented
570C4×D4—153no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4C2×D1513yescomplemented
578C2×C4⋊C4—153no—
579C2×C4⋊C4—153no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—153no—
582C2×C22⋊C4—156no—
583C2×C42—153no—
584C2×C3×C5—22no—
585C2×C3×C5—43no—
586C2×C3×C5C23×D411yescharacteristic
587C2×C3×C5C22×#4111yescharacteristic
588C2×C3×C5C2×2−1+411yescharacteristic
589D15—22no—
590D15—43no—
591D15#54814yesdirect product factor
592C23×C3C23×D513yes—
593C23×C3C23×D511yescharacteristic
594C22×D3—51no—
595C22×D3—54no—
596C22×D3—51no—
597C22×D3—53no—
598C22×D3—102no—
599C22×D3—102no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3—106no—
603C3×Q8—26no—
604C3×Q8D4×D514yescomplemented
605C3×D4—26no—
606C3×D4—26no—
607C2×C3×C4—26no—
608C2×C3×C4—26no—
609C2×C3×C4C23×D511yescharacteristic
610C2×C3×C4C23×D513yes—
611C2×C3×C4C23×D511yescharacteristic
612C2×C3×C4C23×D513yes—
613C2×C3×C4C23×D513yes—
614#67—1012no—
615#67—106no—
616#67—106no—
617C2×Dic3—53no—
618C2×Dic3—51no—
619C2×Dic3—53no—
620C2×Dic3—51no—
621C2×Dic3—53no—
622C2×Dic3—106no—
623C2×Dic3—106no—
624D12—106no—
625D12—106no—
626C4×D3—512no—
627C4×D3—106no—
628C4×D3—106no—
629C4×D3—102no—
630C4×D3—102no—
631C4×D3—106no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3—106no—
635Dic6—512no—
636Dic6—1012no—
637Dic6—106no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—23no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5D3×#4112yescomplemented
644C22×C5C24×D311yescharacteristic
645C2×D5—32no—
646C2×D5—32no—
647C2×D5—32no—
648C2×D5—32no—
649C2×D5—68no—
650C2×D5—61no—
651C2×D5—61no—
652C2×D5—63no—
653C2×D5—63no—
654C2×D5—63no—
655C2×D5—1212no—
656C4×C5—23no—
657C4×C5—21no—
658C4×C5—23no—
659C4×C5—21no—
660C4×C5C2×D3×D416yes—
661Dic5—36no—
662Dic5—63no—
663Dic5—61no—
664Dic5—63no—
665Dic5—61no—
666C24—151no—
667C24—153no—
668#41—24no—
669#41—3012no—
670#41—3012no—
671#41—304no—
672C2×Q8—24no—
673C2×Q8—158no—
674C2×Q8—153no—
675C2×Q8—156no—
676C2×Q8—153no—
677C2×Q8—3012no—
678C2×Q8—3012no—
679C2×Q8—3012no—
680C2×Q8—304no—
681C2×Q8C22×D1513yes—
682C2×Q8C22×D1511yescharacteristic
683C2×D4—153no—
684C2×D4—153no—
685C2×D4—156no—
686C2×D4—153no—
687C2×D4—153no—
688C2×D4—3012no—
689C2×D4—3012no—
690C2×D4C22×D1513yes—
691C2×D4C22×D1513yes—
692C22×C4—153no—
693C22×C4—153no—
694C22×C4—153no—
695C22×C4—151no—
696C22×C4—153no—
697C22×C4—153no—
698C22×C4—151no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—153no—
703C22×C4—3012no—
704C22×C4—3012no—
705C22×C4C22×D1513yes—
706C22×C4C22×D1513yes—
707C4⋊C4—153no—
708C4⋊C4—153no—
709C4⋊C4—153no—
710C4⋊C4—156no—
711C4⋊C4—153no—
712C4⋊C4C22×D1513yes—
713C4⋊C4C22×D1513yes—
714C22⋊C4—151no—
715C22⋊C4—153no—
716C22⋊C4—156no—
717C22⋊C4—151no—
718C22⋊C4—151no—
719C22⋊C4—153no—
720C22⋊C4—153no—
721C22⋊C4—156no—
722C22⋊C4—156no—
723C22⋊C4C22×D1511yescharacteristic
724C22⋊C4C22×D1513yes—
725C22⋊C4C22×D1516yes—
726C42—153no—
727C42—153no—
728C42—153no—
729C42C22×D1513yes—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—23no—
734C22×C3—23no—
735C22×C3—23no—
736C22×C3D5×#4112yescomplemented
737C22×C3C24×D511yescharacteristic
738C2×D3—52no—
739C2×D3—52no—
740C2×D3—52no—
741C2×D3—52no—
742C2×D3—108no—
743C2×D3—101no—
744C2×D3—101no—
745C2×D3—103no—
746C2×D3—103no—
747C2×D3—103no—
748C2×D3—2012no—
749C3×C4—23no—
750C3×C4—21no—
751C3×C4—23no—
752C3×C4—21no—
753C3×C4C2×D4×D516yes—
754Dic3—56no—
755Dic3—103no—
756Dic3—101no—
757Dic3—103no—
758Dic3—101no—
759C2×C5—22no—
760C2×C5—43no—
761C2×C5C22×D3×D411yescharacteristic
762C2×C5C2×D3×#4111yescharacteristic
763C2×C5D3×2−1+411yescharacteristic
764D5—34no—
765D5—62no—
766D5—123no—
767C23—151no—
768C23—154no—
769C23—151no—
770C23—153no—
771C23—302no—
772C23—302no—
773C23—306no—
774C23—306no—
775C23—306no—
776C23C23×D1513yes—
777C23C23×D1511yescharacteristic
778Q8—26no—
779Q8—1512no—
780Q8—3012no—
781Q8—306no—
782Q8D4×D1514yescomplemented
783D4—26no—
784D4—26no—
785D4—306no—
786D4—3012no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—153no—
793C2×C4—1512no—
794C2×C4—151no—
795C2×C4—153no—
796C2×C4—153no—
797C2×C4—151no—
798C2×C4—306no—
799C2×C4—306no—
800C2×C4—302no—
801C2×C4—306no—
802C2×C4—306no—
803C2×C4—302no—
804C2×C4—306no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—306no—
808C2×C4C23×D1511yescharacteristic
809C2×C4C23×D1513yes—
810C2×C4C23×D1513yes—
811C2×C4C23×D1511yescharacteristic
812C2×C4C23×D1513yes—
813C2×C3—22no—
814C2×C3—43no—
815C2×C3C22×D4×D511yescharacteristic
816C2×C3C2×D5×#4111yescharacteristic
817C2×C3D5×2−1+411yescharacteristic
818D3—54no—
819D3—102no—
820D3—203no—
821C5D3×#54811yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—152no—
828C22—152no—
829C22—152no—
830C22—152no—
831C22—308no—
832C22—301no—
833C22—301no—
834C22—303no—
835C22—303no—
836C22—303no—
837C22—6012no—
838C22#41×D1512yescomplemented
839C22C24×D1511yescharacteristic
840C4—21no—
841C4—23no—
842C4—23no—
843C4—21no—
844C4—156no—
845C4—301no—
846C4—303no—
847C4—303no—
848C4—301no—
849C4C2×D4×D1516yes—
850C3D5×#54811yescharacteristic, complemented, Sylow
851C2—22no—
852C2—43no—
853C2—154no—
854C2—302no—
855C2—603no—
856C2C22×D4×D1511yescharacteristic
857C2C2×#41×D1511yescharacteristic
858C2D15×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#548C2
hypercenter#548D15
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C22×Q8×D15C2semidirect
3. C3×C5×#548C2semidirect
4. #11756590C2semidirect
5. #11756576C2semidirect
6. #11756436C2semidirect
7. D15×#124C2semidirect
8. #11756392C2semidirect
9. D15×C22⋊Q8C2semidirect
10. D15×#121C2semidirect
11. #11756357C2semidirect
12. #11756335C2semidirect
13. C4×Q8×D15C2semidirect
14. #11756311C2semidirect
15. C4×D4×D15C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
20. C2×#6821C22semidirect
24. C2×Q8×D15C22semidirect
25. C2×Q8×D15C22semidirect
26. C2×#6819C22semidirect
29. C2×#6817C22semidirect
32. C22×Dic30C22semidirect
33. C3×C5×#124C22semidirect
34. C3×C5×C22⋊Q8C22semidirect
35. C3×C5×#121C22semidirect
36. C3×C4×C5×Q8C22semidirect
37. C3×C4×C5×D4C22semidirect
38. #91836C22semidirect
39. #91835C22semidirect
40. Q8×Dic15C22semidirect
41. #91828C22semidirect
42. #91827C22semidirect
43. #91825C22semidirect
44. D4×Dic15C22semidirect
45. #91819C22semidirect
46. C4×#1220C22semidirect
47. C4×#1220C22semidirect
48. #91813C22semidirect
49. #91786C22semidirect
50. #91785C22semidirect
51. #91784C22semidirect
52. #91782C22semidirect
55. #91776C22semidirect
56. #91774C22semidirect
57. #91774C22semidirect
58. #91773C22semidirect
59. #91770C22semidirect
60. #91770C22semidirect
64. #91767C22semidirect
65. #91764C22semidirect
66. C4×D60C22semidirect
68. C4×Dic30C22semidirect
72. C5×#548D3semidirect
104. Q8×D15D4semidirect
151. C3×#548D5semidirect
164. C2×C5×#41C2×D3semidirect
165. C22×C5×Q8C2×D3semidirect
180. C5×#124C2×D3semidirect
181. C5×C22⋊Q8C2×D3semidirect
182. C5×#121C2×D3semidirect
183. C4×C5×Q8C2×D3semidirect
184. C4×C5×D4C2×D3semidirect
224. C22×D15#41semidirect
229. C3×C5×Q8C2×D4semidirect
262. Dic30C2×D4semidirect
263. C2×C3×#41C2×D5semidirect
264. C22×C3×Q8C2×D5semidirect
279. C3×#124C2×D5semidirect
280. C3×C22⋊Q8C2×D5semidirect
281. C3×#121C2×D5semidirect
282. C3×C4×Q8C2×D5semidirect
283. C3×C4×D4C2×D5semidirect
388. #548D15direct (N × H)
399. C22×C3×C5C2×#41semidirect
410. C2×D15C2×#41semidirect
498. C5×Q8D3×D4semidirect
536. C2×#41C2×D15semidirect
543. C22×Q8C2×D15semidirect
553. #124C2×D15semidirect
559. C22⋊Q8C2×D15semidirect
565. #121C2×D15semidirect
569. C4×Q8C2×D15semidirect
577. C4×D4C2×D15semidirect
591. D15#548direct (N × H)
604. C3×Q8D4×D5semidirect
643. C22×C5D3×#41semidirect
730. C3×C5C2×#548semidirect
736. C22×C3D5×#41semidirect
782. Q8D4×D15semidirect
821. C5D3×#548semidirect
838. C22#41×D15semidirect
850. C3D5×#548semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C22×Q8×D152
C3×C5×#5482
#117565902
#117565762
#117564362
D15×#1242
#117563922
D15×C22⋊Q82
D15×#1212
#117563572
#117563352
C4×Q8×D152
#117563112
C4×D4×D152
D5×#5483
D3×#5485