Finite Group Databasebeta

← D3×#65910 #14482828

Subgroups — D3×#65910 #14482828

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×D3×#713C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3#11756335C211yesmaximal, characteristic, complemented
4C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
5C3×#65910C211yesmaximal, characteristic, complemented
6#11755257C211yesmaximal, characteristic, complemented
7#11755128C211yesmaximal, characteristic, complemented
8D3×#4043C213yesmaximal, complemented
9D3×#4041C213yesmaximal, complemented
10#11753439C213yesmaximal, complemented
11#11753342C213yesmaximal, complemented
12D3×#4021C213yesmaximal, complemented
13C4×D3×D20C213yesmaximal, complemented
14#11752546C213yesmaximal, complemented
15#11752541C213yesmaximal, complemented
16C2×#65910—31nomaximal, Hall
17C2×#6821C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×D3×Q8C2211yescharacteristic
20C2×C3×#713C2211yescharacteristic, complemented
21C2×C3×Q8×D5C2211yescharacteristic, complemented
22D3×#713—28no—
23D3×Q8×D5—28no—
24C2×D3×D20C2213yes—
25C2×D3×D20C2213yes—
26C2×C4×D3×D5C2213yes—
27C2×C4×D3×D5C2213yes—
28C2×#6773C2213yescomplemented
29C2×D15⋊Q8C2213yescomplemented
30C2×D3×Dic10C2213yes—
31C2×#6766C2213yescomplemented
32C2×D5×Dic6C2213yescomplemented
33C3×C4×C5×Q8C2211yescharacteristic, complemented
34#91786C2213yescomplemented
35#91784C2213yescomplemented
36#91764C2213yescomplemented
37C4×D60C2213yescomplemented
38C5×Q8×Dic3C2211yescharacteristic, complemented
39C5×D3×C4⋊C4C2213yes—
40C5×#887C2213yescomplemented
41C42×C5×D3C2213yes—
42C4×C5×Dic6C2213yescomplemented
43C3×#4043C2213yescomplemented
44C3×#4041C2213yescomplemented
45C3×#4021C2213yescomplemented
46C3×C4×D20C2213yescomplemented
47D3×#685C2211yescharacteristic
48D3×#685C2213yes—
49D3×#685C2216yes—
50#91465C2213yescomplemented
51#91459C2216yescomplemented
52#91450C2213yescomplemented
53C4×#1202C2213yescomplemented
54C4×#1202C2213yescomplemented
55#91429C2216yescomplemented
56#91428C2213yescomplemented
57D3×C4⋊Dic5C2213yes—
58Dic3×D20C2213yescomplemented
59#91422C2216yescomplemented
60#91409C2216yescomplemented
61#91395C2213yescomplemented
62#91395C2213yescomplemented
63#91390C2213yescomplemented
64#91374C2213yescomplemented
65#91364C2213yescomplemented
66#91360C2213yescomplemented
67#91353C2216yescomplemented
68#91353C2216yescomplemented
69D3×#548—51nomaximal, Hall
70C22×#713—31no—
71C22×Q8×D5—31no—
72C2×C4×C5×Q8—31no—
73#65910—33no—
74#65910—33no—
75#65910—33no—
76#65910—33no—
77#65910—31no—
78#65910—31no—
79#65910—31no—
80#65910D311yescharacteristic, direct product factor
81C2×#4043—33no—
82C2×#4041—33no—
83C2×#4021—33no—
84C2×C4×D20—33no—
85C22×D3×D5C2313yes—
86C22×D3×D5C2311yescharacteristic
87C2×C3×C5×Q8C2311yescharacteristic
88#6821—24no—
89Q8×D15—24no—
90C2×D60C2313yes—
91C2×D60C2313yes—
92C2×C4×D15C2313yes—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C5×D3×Q8D418yescomplemented
96C2×C4×C5×D3C2311yescharacteristic
97C2×C4×C5×D3C2313yes—
98C2×C4×C5×D3C2313yes—
99C2×C5×Dic6C2313yes—
100C3×#713—24no—
101C3×Q8×D5—24no—
102C2×C3×D20C2313yes—
103C2×C3×D20C2313yes—
104C2×C3×C4×D5C2313yes—
105C2×C3×C4×D5C2313yes—
106C2×C3×Dic10C2313yes—
107C2×#1204C2316yes—
108C2×#1202C2313yes—
109C2×#1202C2313yes—
110C2×#1202C2316yes—
111C2×#1200C2313yes—
112C2×#1200C2313yes—
113C2×D3×Dic5C2311yescharacteristic
114C2×D3×Dic5C2313yes—
115C2×D5×Dic3C2313yes—
116C2×D5×Dic3C2313yes—
117D3×D20—212no—
118D3×D20—212no—
119C4×D3×D5—212no—
120C4×D3×D5—212no—
121#6773—212no—
122D15⋊Q8—212no—
123D3×Dic10—212no—
124#6766—212no—
125D5×Dic6—212no—
126C3×C5×C4⋊C4C2313yes—
127C3×C42×C5C2313yes—
128#6714C2311yescharacteristic
129#6714C2313yes—
130#6714C2316yes—
131C4⋊Dic15C2313yes—
132C5×C4⋊Dic3C2313yes—
133C5×Dic3⋊C4C2316yes—
134C4×C5×Dic3C2313yes—
135C4×C5×Dic3C2313yes—
136C4×C5×Dic3C2313yes—
137C3×#685C2311yescharacteristic
138C3×#685C2313yes—
139C3×#685C2316yes—
140C3×C4⋊Dic5C2313yes—
141Dic3⋊Dic5C2313yes—
142Dic3⋊Dic5C2313yes—
143#6667C2311yescharacteristic
144#6667C2313yes—
145#6667C2316yes—
146#6665C2316yes—
147#6665C2311yescharacteristic
148#6665C2313yes—
149C2×D3×#41—51no—
150C22×D3×Q8—51no—
151C3×#548—51no—
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×Q8D511yescharacteristic, complemented
162#5552—53no—
163C4×D3×D4—53no—
164C22×C5×Q8—31no—
165C2×#713—31no—
166C2×#713—33no—
167C2×#713—33no—
168C2×#713—68no—
169C2×#713C2×D311yescharacteristic, complemented
170C2×Q8×D5—31no—
171C2×Q8×D5—33no—
172C2×Q8×D5—33no—
173C2×Q8×D5—68no—
174C2×Q8×D5C2×D311yescharacteristic, complemented
175C22×D20—33no—
176C22×D20—33no—
177C22×C4×D5—33no—
178C22×C4×D5—33no—
179C22×Dic10—33no—
180C4×C5×Q8—31no—
181C4×C5×Q8—33no—
182C4×C5×Q8—33no—
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C2×C5×C4⋊C4—33no—
185C2×C42×C5—33no—
186C2×#685—31no—
187C2×#685—33no—
188C2×#685—36no—
189C2×C4⋊Dic5—33no—
190#4043—33no—
191#4043—33no—
192#4043—33no—
193#4043—36no—
194#4043—36no—
195#4043C2×D313yescomplemented
196#4041—36no—
197#4041—33no—
198#4041—33no—
199#4041—33no—
200#4041—36no—
201#4041C2×D313yescomplemented
202#4021—33no—
203#4021—33no—
204#4021—33no—
205#4021—36no—
206#4021—36no—
207#4021C2×D313yescomplemented
208C4×D20—33no—
209C4×D20—33no—
210C4×D20—33no—
211C4×D20—33no—
212C4×D20—33no—
213C4×D20—33no—
214C4×D20—33no—
215C4×D20C2×D313yescomplemented
216C2×#548—151noSylow
217C22×D15C2413yes—
218C22×D15C2411yescharacteristic
219C22×C5×D3C2411yescharacteristic
220C22×C3×D5C2413yes—
221C22×C3×D5C2411yescharacteristic
222C2×D3×D5—22no—
223C2×D3×D5—22no—
224C2×D3×D5—26no—
225C2×D3×D5—26no—
226C2×D3×D5—26no—
227C2×D3×D5#4114yescomplemented
228C3×C5×Q8C2×D414yescomplemented
229C2×C3×C4×C5C2413yes—
230C2×C3×C4×C5C2411yescharacteristic
231C2×C3×C4×C5C2413yes—
232C2×Dic15C2413yes—
233C2×Dic15C2411yescharacteristic
234D60—26no—
235D60—26no—
236C4×D15—26no—
237C4×D15—26no—
238Dic30—26no—
239C2×C5×Dic3C2411yescharacteristic
240C2×C5×Dic3C2413yes—
241C2×C5×Dic3C2413yes—
242C4×C5×D3—26no—
243C4×C5×D3—22no—
244C4×C5×D3C2×D4112yes—
245C5×Dic6C2×D4112yescomplemented
246C2×C3×Dic5C2413yes—
247C2×C3×Dic5C2411yescharacteristic
248C3×D20—26no—
249C3×D20—26no—
250C3×C4×D5—26no—
251C3×C4×D5—26no—
252C3×Dic10—26no—
253#1204—212no—
254#1202—26no—
255#1202—26no—
256#1202—212no—
257#1200—26no—
258#1200—26no—
259D3×Dic5—26no—
260D3×Dic5—22no—
261D5×Dic3—26no—
262D5×Dic3—26no—
263C2×C3×#41—51no—
264C22×C3×Q8—51no—
265D3×#41—108no—
266C2×#239—51no—
267C2×D3×Q8—51no—
268C2×D3×Q8—53no—
269C2×D3×Q8—53no—
270C2×D3×Q8—108no—
271C2×D3×Q8C2×D511yescharacteristic
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×#124—53no—
280C3×C22⋊Q8—53no—
281C3×#121—53no—
282C3×C4×Q8C2×D511yescharacteristic, complemented
283C3×C4×D4—53no—
284#947—53no—
285#946—53no—
286Q8×Dic3C2×D511yescharacteristic, complemented
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⋊C4C2×D513yes—
301#887C2×D513yescomplemented
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×D3C2×D513yes—
314C4×Dic6C2×D513yescomplemented
315C23×D5—31no—
316C23×D5—33no—
317C2×C5×Q8—38no—
318C2×C5×Q8—33no—
319C2×C5×Q8C22×D311yescharacteristic
320C22×C4×C5—33no—
321C22×C4×C5—31no—
322C22×C4×C5—33no—
323C22×Dic5—33no—
324C22×Dic5—31no—
325#713—24no—
326#713—612no—
327#713—612no—
328#713—64no—
329Q8×D5—24no—
330Q8×D5—612no—
331Q8×D5—612no—
332Q8×D5—64no—
333C2×D20—36no—
334C2×D20—33no—
335C2×D20—33no—
336C2×D20—33no—
337C2×D20—33no—
338C2×D20—612no—
339C2×D20—612no—
340C2×D20C22×D313yes—
341C2×D20C22×D313yes—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—33no—
348C2×C4×D5—612no—
349C2×C4×D5—612no—
350C2×C4×D5C22×D313yes—
351C2×C4×D5C22×D313yes—
352C2×Dic10—33no—
353C2×Dic10—36no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—36no—
357C5×C4⋊C4—33no—
358C5×C4⋊C4C22×D313yes—
359C42×C5—33no—
360C42×C5—33no—
361C42×C5—33no—
362C42×C5C22×D313yes—
363#685—31no—
364#685—33no—
365#685—36no—
366#685—31no—
367#685—33no—
368#685—36no—
369#685—31no—
370#685—33no—
371#685—36no—
372#685C22×D311yescharacteristic
373#685C22×D313yes—
374#685C22×D316yes—
375C4⋊Dic5—33no—
376C4⋊Dic5—33no—
377C4⋊Dic5—33no—
378C4⋊Dic5C22×D313yes—
379C22×#41—151no—
380C23×Q8—151no—
381#548—51no—
382#548—153no—
383#548—153no—
384#548—153no—
385#548—153no—
386#548—151no—
387#548—151no—
388#548—151no—
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—31no—
393C2×C4×D4—153no—
394C22×C3×C5C2511yescharacteristic
395C2×D15—21no—
396C2×D15—21no—
397C2×D15—23no—
398C2×D15—23no—
399C2×D15—23no—
400C2×D15C2×#4112yescomplemented
401C2×C5×D3C22×D412yes—
402C2×C5×D3C2×#4112yes—
403C2×C5×D32−1+412yes—
404C2×C3×D5—21no—
405C2×C3×D5—21no—
406C2×C3×D5—23no—
407C2×C3×D5—23no—
408C2×C3×D5—23no—
409C2×C3×D5C2×#4112yescomplemented
410D3×D5—28no—
411D3×D5—412no—
412C3×C4×C5—23no—
413C3×C4×C5—21no—
414C3×C4×C5C22×D416yes—
415Dic15—21no—
416Dic15—23no—
417C3×Dic5—21no—
418C3×Dic5—23no—
419C5×Dic3—23no—
420C5×Dic3—21no—
421C5×Dic3C22×D416yes—
422C23×D3—51no—
423C23×D3—53no—
424C3×#41—104no—
425C2×C3×Q8—53no—
426C2×C3×Q8—104no—
427C2×C3×Q8C22×D511yescharacteristic
428C2×C3×D4—53no—
429C2×C3×D4—53no—
430C22×C3×C4—53no—
431C22×C3×C4—53no—
432C2×#67—53no—
433C2×#67—53no—
434C2×#67—56no—
435C22×Dic3—53no—
436C22×Dic3—53no—
437#239—104no—
438D3×Q8—104no—
439D3×Q8—1012no—
440D3×Q8—1012no—
441D3×Q8D2018yescomplemented
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—1012no—
455C2×C4×D3—1012no—
456C2×C4×D3C22×D511yescharacteristic
457C2×C4×D3C22×D513yes—
458C2×C4×D3C22×D513yes—
459C2×Dic6—53no—
460C2×Dic6—56no—
461C2×Dic6—1012no—
462C2×Dic6C22×D513yes—
463C3×C4⋊C4—53no—
464C3×C4⋊C4C22×D513yes—
465C3×C22⋊C4—56no—
466C3×C22⋊C4—51no—
467C3×C22⋊C4—53no—
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⋊Dic3C22×D513yes—
480Dic3⋊C4—53no—
481Dic3⋊C4—53no—
482Dic3⋊C4C22×D516yes—
483C4×Dic3C22×D513yes—
484C4×Dic3C22×D513yes—
485C4×Dic3C22×D513yes—
486C23×C5—31no—
487C22×D5—31no—
488C22×D5—34no—
489C22×D5—33no—
490C22×D5—62no—
491C22×D5—62no—
492C22×D5—66no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5C23×D313yes—
496C22×D5C23×D311yescharacteristic
497C5×Q8—312no—
498C5×Q8D3×D414yescomplemented
499C2×C4×C5—33no—
500C2×C4×C5—312no—
501C2×C4×C5—33no—
502C2×C4×C5—31no—
503C2×C4×C5—66no—
504C2×C4×C5—62no—
505C2×C4×C5C23×D313yes—
506C2×C4×C5C23×D311yescharacteristic
507C2×C4×C5C23×D313yes—
508C2×Dic5—31no—
509C2×Dic5—33no—
510C2×Dic5—66no—
511C2×Dic5—62no—
512C2×Dic5C23×D311yescharacteristic
513C2×Dic5C23×D313yes—
514D20—26no—
515D20—26no—
516D20—66no—
517D20—612no—
518D20—66no—
519D20—66no—
520D20—66no—
521C4×D5—26no—
522C4×D5—26no—
523C4×D5—66no—
524C4×D5—66no—
525C4×D5—66no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5—66no—
529Dic10—26no—
530Dic10—612no—
531Dic10—66no—
532C2×#41—51no—
533C2×#41—153no—
534C2×#41—153no—
535C2×#41—151no—
536C2×#41—308no—
537C22×Q8—31no—
538C22×Q8—51no—
539C22×Q8—153no—
540C22×Q8—153no—
541C22×Q8—153no—
542C22×Q8—151no—
543C22×Q8—308no—
544C22×D4—153no—
545C22×D4—153no—
546C23×C4—153no—
547C23×C4—153no—
548#124—53no—
549#124—156no—
550#124—156no—
551#124—153no—
552#124—153no—
553#124—153no—
554C22⋊Q8—53no—
555C22⋊Q8—156no—
556C22⋊Q8—156no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—53no—
561#121—156no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—153no—
566C4×Q8—31no—
567C4×Q8—33no—
568C4×Q8—33no—
569C4×Q8D3×D511yescharacteristic, complemented
570C4×D4—53no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C2×C4⋊C4—33no—
579C2×C4⋊C4—153no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—153no—
582C2×C22⋊C4—156no—
583C2×C42—33no—
584C2×C3×C5C23×D411yescharacteristic
585C2×C3×C5C22×#4111yescharacteristic
586C2×C3×C5C2×2−1+411yescharacteristic
587D15—22no—
588D15—43no—
589C3×D5—22no—
590C3×D5—43no—
591C5×D3#54814yescomplemented
592C23×C3—51no—
593C23×C3—53no—
594C22×D3—51no—
595C22×D3—54no—
596C22×D3—53no—
597C22×D3—102no—
598C22×D3—102no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3C23×D511yescharacteristic
603C3×Q8—106no—
604C3×Q8C2×D2014yescomplemented
605C3×D4—106no—
606C3×D4—106no—
607C2×C3×C4—51no—
608C2×C3×C4—53no—
609C2×C3×C4—106no—
610C2×C3×C4—106no—
611C2×C3×C4C23×D511yescharacteristic
612C2×C3×C4C23×D513yes—
613C2×C3×C4C23×D513yes—
614#67—106no—
615#67—106no—
616#67—1012no—
617C2×Dic3—51no—
618C2×Dic3—53no—
619C2×Dic3—106no—
620C2×Dic3—106no—
621C2×Dic3C23×D511yescharacteristic
622C2×Dic3C23×D513yes—
623C2×Dic3C23×D513yes—
624D12—106no—
625D12—106no—
626C4×D3—22no—
627C4×D3—26no—
628C4×D3—102no—
629C4×D3—106no—
630C4×D3—106no—
631C4×D3—106no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3C2×D20112yes—
635Dic6—106no—
636Dic6—1012no—
637Dic6C2×D20112yescomplemented
638C22×C5—32no—
639C22×C5—32no—
640C22×C5—32no—
641C22×C5C24×D311yescharacteristic
642C2×D5—21no—
643C2×D5—21no—
644C2×D5—23no—
645C2×D5—23no—
646C2×D5—23no—
647C2×D5—32no—
648C2×D5—68no—
649C2×D5—61no—
650C2×D5—61no—
651C2×D5—63no—
652C2×D5—63no—
653C2×D5—63no—
654C2×D5—1212no—
655C2×D5D3×#4112yescomplemented
656C4×C5—23no—
657C4×C5—21no—
658C4×C5—36no—
659C4×C5—63no—
660C4×C5—61no—
661C4×C5C2×D3×D416yes—
662Dic5—23no—
663Dic5—21no—
664Dic5—63no—
665Dic5—61no—
666C24—151no—
667C24—153no—
668#41—104no—
669#41—3012no—
670#41—3012no—
671#41—304no—
672C2×Q8—38no—
673C2×Q8—33no—
674C2×Q8—53no—
675C2×Q8—104no—
676C2×Q8—156no—
677C2×Q8—153no—
678C2×Q8—3012no—
679C2×Q8—3012no—
680C2×Q8—3012no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—53no—
684C2×D4—53no—
685C2×D4—153no—
686C2×D4—153no—
687C2×D4—156no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—3012no—
691C2×D4—3012no—
692C22×C4—33no—
693C22×C4—31no—
694C22×C4—33no—
695C22×C4—53no—
696C22×C4—53no—
697C22×C4—153no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—151no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4—3012no—
707C4⋊C4—36no—
708C4⋊C4—33no—
709C4⋊C4—53no—
710C4⋊C4—153no—
711C4⋊C4—153no—
712C4⋊C4—153no—
713C4⋊C4C2×D3×D513yes—
714C22⋊C4—51no—
715C22⋊C4—53no—
716C22⋊C4—56no—
717C22⋊C4—151no—
718C22⋊C4—153no—
719C22⋊C4—156no—
720C22⋊C4—151no—
721C22⋊C4—153no—
722C22⋊C4—156no—
723C22⋊C4—151no—
724C22⋊C4—153no—
725C22⋊C4—156no—
726C42—33no—
727C42—33no—
728C42—33no—
729C42C2×D3×D513yes—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—52no—
732C22×C3—101no—
733C22×C3—101no—
734C22×C3—103no—
735C22×C3—103no—
736C22×C3—103no—
737C22×C3C24×D511yescharacteristic
738C2×D3—52no—
739C2×D3—101no—
740C2×D3—101no—
741C2×D3—108no—
742C2×D3—103no—
743C2×D3—103no—
744C2×D3—103no—
745C2×D3—2012no—
746C2×D3C22×D2012yes—
747C2×D3#414712yes—
748C2×D3D5×#4112yes—
749C3×C4—21no—
750C3×C4—23no—
751C3×C4—103no—
752C3×C4—101no—
753C3×C4C22×D2016yes—
754Dic3—21no—
755Dic3—23no—
756Dic3—103no—
757Dic3—101no—
758Dic3C22×D2016yes—
759C2×C5—34no—
760C2×C5C22×D3×D411yescharacteristic
761C2×C5C2×D3×#4111yescharacteristic
762C2×C5D3×2−1+411yescharacteristic
763D5—22no—
764D5—43no—
765D5—62no—
766D5—123no—
767C23—31no—
768C23—51no—
769C23—53no—
770C23—154no—
771C23—151no—
772C23—153no—
773C23—302no—
774C23—302no—
775C23—306no—
776C23—306no—
777C23—306no—
778Q8—312no—
779Q8—106no—
780Q8—3012no—
781Q8—306no—
782Q8D3×D2014yescomplemented
783D4—106no—
784D4—106no—
785D4—306no—
786D4—3012no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—33no—
791C2×C4—312no—
792C2×C4—31no—
793C2×C4—33no—
794C2×C4—53no—
795C2×C4—51no—
796C2×C4—66no—
797C2×C4—62no—
798C2×C4—106no—
799C2×C4—106no—
800C2×C4—153no—
801C2×C4—151no—
802C2×C4—306no—
803C2×C4—306no—
804C2×C4—306no—
805C2×C4—306no—
806C2×C4—302no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4C22×D3×D511yescharacteristic
811C2×C4C22×D3×D513yes—
812C2×C4C22×D3×D513yes—
813C2×C3—102no—
814C2×C3—203no—
815C2×C3C23×D2011yescharacteristic
816C2×C3C2×#414711yescharacteristic
817C2×C3C2×D5×#4111yescharacteristic
818D3—102no—
819D3—203no—
820D3#6591014yesdirect product factor
821C5D3×#54811yescharacteristic, complemented, Sylow
822C22—32no—
823C22—32no—
824C22—32no—
825C22—52no—
826C22—101no—
827C22—101no—
828C22—103no—
829C22—103no—
830C22—103no—
831C22—152no—
832C22—308no—
833C22—301no—
834C22—301no—
835C22—303no—
836C22—303no—
837C22—303no—
838C22—6012no—
839C22C23×D3×D511yescharacteristic
840C4—21no—
841C4—23no—
842C4—36no—
843C4—61no—
844C4—63no—
845C4—101no—
846C4—103no—
847C4—301no—
848C4—303no—
849C4C2×D3×D2016yes—
850C3C2×#6591011yescharacteristic, complemented, Sylow
851C2—34no—
852C2—102no—
853C2—203no—
854C2—302no—
855C2—603no—
856C2C22×D3×D2011yescharacteristic
857C2D3×#414711yescharacteristic
858C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#713C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. #11756335C2semidirect
4. C4×C5×D3×Q8C2semidirect
5. C3×#65910C2semidirect
6. #11755257C2semidirect
7. #11755128C2semidirect
8. D3×#4043C2semidirect
9. D3×#4041C2semidirect
10. #11753439C2semidirect
11. #11753342C2semidirect
12. D3×#4021C2semidirect
13. C4×D3×D20C2semidirect
14. #11752546C2semidirect
15. #11752541C2semidirect
17. C2×#6821C22semidirect
18. C2×Q8×D15C22semidirect
20. C2×C3×#713C22semidirect
21. C2×C3×Q8×D5C22semidirect
28. C2×#6773C22semidirect
29. C2×D15⋊Q8C22semidirect
31. C2×#6766C22semidirect
32. C2×D5×Dic6C22semidirect
33. C3×C4×C5×Q8C22semidirect
34. #91786C22semidirect
35. #91784C22semidirect
36. #91764C22semidirect
37. C4×D60C22semidirect
38. C5×Q8×Dic3C22semidirect
40. C5×#887C22semidirect
42. C4×C5×Dic6C22semidirect
43. C3×#4043C22semidirect
44. C3×#4041C22semidirect
45. C3×#4021C22semidirect
46. C3×C4×D20C22semidirect
50. #91465C22semidirect
51. #91459C22semidirect
52. #91450C22semidirect
53. C4×#1202C22semidirect
54. C4×#1202C22semidirect
55. #91429C22semidirect
56. #91428C22semidirect
58. Dic3×D20C22semidirect
59. #91422C22semidirect
60. #91409C22semidirect
61. #91395C22semidirect
62. #91395C22semidirect
63. #91390C22semidirect
64. #91374C22semidirect
65. #91364C22semidirect
66. #91360C22semidirect
67. #91353C22semidirect
68. #91353C22semidirect
80. #65910D3direct (N × H)
95. C5×D3×Q8D4semidirect
161. C4×D3×Q8D5semidirect
169. C2×#713C2×D3semidirect
174. C2×Q8×D5C2×D3semidirect
183. C4×C5×Q8C2×D3semidirect
195. #4043C2×D3semidirect
201. #4041C2×D3semidirect
207. #4021C2×D3semidirect
215. C4×D20C2×D3semidirect
227. C2×D3×D5#41semidirect
228. C3×C5×Q8C2×D4semidirect
245. C5×Dic6C2×D4semidirect
282. C3×C4×Q8C2×D5semidirect
286. Q8×Dic3C2×D5semidirect
301. #887C2×D5semidirect
314. C4×Dic6C2×D5semidirect
400. C2×D15C2×#41semidirect
409. C2×C3×D5C2×#41semidirect
441. D3×Q8D20semidirect
498. C5×Q8D3×D4semidirect
569. C4×Q8D3×D5semidirect
591. C5×D3#548semidirect
604. C3×Q8C2×D20semidirect
637. Dic6C2×D20semidirect
655. C2×D5D3×#41semidirect
730. C3×C5C2×#548semidirect
782. Q8D3×D20semidirect
820. D3#65910direct (N × H)
821. C5D3×#548semidirect
850. C3C2×#65910semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7132
C2×D3×Q8×D52
#117563352
C4×C5×D3×Q82
C3×#659102
#117552572
#117551282
D3×#40432
D3×#40412
#117534392
#117533422
D3×#40212
C4×D3×D202
#117525462
#117525412
C2×#659103
D3×#5485