Finite Group Databasebeta

← #14483053

Subgroups — #14483053

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C211yesmaximal, characteristic, complemented
2C22×#6821C211yesmaximal, characteristic, complemented
3C3×C5×#548C211yesmaximal, characteristic, complemented
4#11756593C211yesmaximal, characteristic, complemented
5Q8×#1220C211yesmaximal, characteristic, complemented
6#11756435C213yesmaximal, complemented
7#11756427C213yesmaximal, complemented
8#11756390C213yesmaximal, complemented
9#11756386C213yesmaximal, complemented
10#11756368C213yesmaximal, complemented
11#11756365C213yesmaximal, complemented
12#11756335C211yesmaximal, characteristic, complemented
13C4×#6821C211yesmaximal, characteristic, complemented
14#11756309C213yesmaximal, complemented
15C4×D4×D15C213yesmaximal, complemented
16#10618611—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19#41×D15—28no—
20C2×#6821—28no—
21C2×#6821C2211yescharacteristic
22C2×#6821C2211yescharacteristic, complemented
23C2×#6821C2213yescomplemented
24C2×#6821C2213yescomplemented
25C2×Q8×D15C2211yescharacteristic, complemented
26C2×#6819C2213yescomplemented
27C2×D4×D15C2213yes—
28C2×D4×D15C2213yescomplemented
29C2×#6817C2213yescomplemented
30C22×D60C2213yescomplemented
31C22×C4×D15C2213yescomplemented
32C22×C4×D15C2213yescomplemented
33C3×C5×#124C2213yescomplemented
34C3×C5×C22⋊Q8C2213yescomplemented
35C3×C5×#121C2213yescomplemented
36C3×C4×C5×Q8C2211yescharacteristic, complemented
37C3×C4×C5×D4C2213yescomplemented
38#91835C2213yescomplemented
39Q8×Dic15C2211yescharacteristic, complemented
40#91833C2213yescomplemented
41#91829C2213yescomplemented
42#91827C2213yescomplemented
43#91826C2216yescomplemented
44D4×Dic15C2213yescomplemented
45#91819C2213yescomplemented
46C4×#1220C2213yes—
47C4×#1220C2213yescomplemented
48#91813C2213yescomplemented
49#91786C2213yescomplemented
50#91784C2213yescomplemented
51#91783C2216yescomplemented
52#91782C2213yescomplemented
53#91782C2213yescomplemented
54#91781C2213yescomplemented
55C4⋊C4×D15C2213yescomplemented
56#91773C2216yescomplemented
57#91773C2216yescomplemented
58#91772C2216yescomplemented
59#91771C2216yescomplemented
60#91770C2211yescharacteristic
61#91770C2213yescomplemented
62#91770C2216yescomplemented
63C22⋊C4×D15C2213yescomplemented
64C22⋊C4×D15C2213yescomplemented
65#91764C2213yescomplemented
66C4×D60C2213yescomplemented
67C4×D60C2213yescomplemented
68C42×D15C2213yescomplemented
69#86710—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×#713—31no—
72C5×#548D311yescharacteristic, complemented
73#66168—31no—
74Q8×C22⋊D5—31no—
75#66010—33no—
76#66002—33no—
77#65965—33no—
78#65961—33no—
79#65943—33no—
80#65940—33no—
81#65910—31no—
82C4×#713—31no—
83#65884—33no—
84C4×D4×D5—33no—
85C23×D15C2313yes—
86C23×D15C2313yes—
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×#1220C2316yes—
97C2×#1220C2316yes—
98C2×#1220C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2313yes—
101#6821—24no—
102#6821—212no—
103#6821—212no—
104#6821D418yescomplemented
105Q8×D15—24no—
106#6819—212no—
107D4×D15—212no—
108D4×D15—212no—
109#6817—212no—
110C2×D60—212no—
111C2×D60C2313yes—
112C2×D60C2313yes—
113C2×D60C2316yes—
114C2×D60C2313yes—
115C2×C4×D15—212no—
116C2×C4×D15—212no—
117C2×C4×D15C2313yes—
118C2×C4×D15C2313yes—
119C2×C4×D15C2313yes—
120C2×C4×D15C2313yes—
121C2×C4×D15C2313yes—
122C2×C4×D15C2311yescharacteristic
123C2×C4×D15C2313yes—
124C2×C4×D15C2313yes—
125C2×C4×D15C2313yes—
126C2×Dic30C2313yes—
127C3×C5×C4⋊C4C2313yes—
128C3×C5×C4⋊C4C2313yes—
129C3×C5×C22⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4C2313yes—
131C3×C5×C22⋊C4C2316yes—
132C3×C42×C5C2313yes—
133#6719C2313yes—
134#6719C2313yes—
135#6714C2311yescharacteristic
136#6714C2313yes—
137#6714C2316yes—
138#6714C2316yes—
139#6714C2313yes—
140#6714C2313yes—
141C4⋊Dic15C2313yes—
142C4⋊Dic15C2313yes—
143#6712C2311yescharacteristic
144#6712C2316yes—
145#6712C2313yes—
146C4×Dic15C2311yescharacteristic
147C4×Dic15C2313yes—
148C4×Dic15C2313yes—
149C2×D3×#41—51no—
150C22×#239—51no—
151C3×#548D511yescharacteristic, complemented
152#5834—51no—
153Q8×#67—51no—
154#5676—53no—
155#5668—53no—
156#5631—53no—
157#5627—53no—
158#5609—53no—
159#5606—53no—
160#5576—51no—
161C4×#239—51no—
162#5550—53no—
163C4×D3×D4—53no—
164C2×C5×#41C2×D311yescharacteristic, complemented
165C22×C5×Q8C2×D311yescharacteristic, complemented
166D5×#41—68no—
167C2×#713—31no—
168C2×#713—31no—
169C2×#713—33no—
170C2×#713—33no—
171C2×#713—68no—
172C2×Q8×D5—31no—
173C2×#711—33no—
174C2×D4×D5—33no—
175C2×D4×D5—33no—
176C2×#709—33no—
177C22×D20—33no—
178C22×C4×D5—33no—
179C22×C4×D5—33no—
180C5×#124C2×D313yescomplemented
181C5×C22⋊Q8C2×D313yescomplemented
182C5×#121C2×D313yescomplemented
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C4×C5×D4C2×D313yescomplemented
185#4092—33no—
186Q8×Dic5—31no—
187#4090—33no—
188#4086—33no—
189#4084—33no—
190#4083—36no—
191D4×Dic5—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5—33no—
195#4070—33no—
196#4043—33no—
197#4041—33no—
198#4040—36no—
199#4039—33no—
200#4039—33no—
201#4038—33no—
202D5×C4⋊C4—33no—
203#4030—36no—
204#4030—36no—
205#4029—36no—
206#4028—36no—
207#4027—31no—
208#4027—33no—
209#4027—36no—
210D5×C22⋊C4—33no—
211D5×C22⋊C4—33no—
212#4021—33no—
213C4×D20—33no—
214C4×D20—33no—
215C42×D5—33no—
216D4×#41—151noSylow
217C23×C3×C5C2413yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—26no—
220C22×D15—26no—
221C22×D15—26no—
222C22×D15—26no—
223C22×D15—43no—
224C22×D15—43no—
225C22×D15C2413yes—
226C22×D15C2413yes—
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×C5C2413yes—
235C2×C3×C4×C5C2411yescharacteristic
236C2×C3×C4×C5C2413yes—
237C2×C3×C4×C5C2411yescharacteristic
238C2×C3×C4×C5C2413yes—
239#1220—212no—
240#1220—26no—
241#1220—46no—
242#1220#4114yescomplemented
243C2×Dic15—22no—
244C2×Dic15—26no—
245C2×Dic15C2413yes—
246C2×Dic15C2413yes—
247C2×Dic15C2411yescharacteristic
248C2×Dic15C2411yescharacteristic
249C2×Dic15C2411yescharacteristic
250D60—212no—
251D60—26no—
252D60—26no—
253D60C2×D4112yescomplemented
254C4×D15—26no—
255C4×D15—26no—
256C4×D15—26no—
257C4×D15—26no—
258C4×D15—22no—
259C4×D15—26no—
260C4×D15—26no—
261C4×D15—43no—
262C4×D15C2×D4112yescomplemented
263Dic30—26no—
264C2×C3×#41C2×D511yescharacteristic, complemented
265C22×C3×Q8C2×D511yescharacteristic, complemented
266D3×#41—108no—
267C2×#239—51no—
268C2×#239—53no—
269C2×#239—53no—
270C2×#239—51no—
271C2×#239—108no—
272C2×D3×Q8—51no—
273C2×#237—53no—
274C2×D3×D4—53no—
275C2×D3×D4—53no—
276C2×#235—53no—
277C22×D12—53no—
278C22×C4×D3—53no—
279C22×C4×D3—53no—
280C3×#124C2×D513yescomplemented
281C3×C22⋊Q8C2×D513yescomplemented
282C3×#121C2×D513yescomplemented
283C3×C4×Q8C2×D511yescharacteristic, complemented
284C3×C4×D4C2×D513yescomplemented
285#946—53no—
286Q8×Dic3—51no—
287#944—53no—
288#940—53no—
289#938—53no—
290#937—56no—
291D4×Dic3—53no—
292#930—53no—
293C4×#67—53no—
294C4×#67—53no—
295#924—53no—
296#897—53no—
297#895—53no—
298#894—56no—
299#893—53no—
300#893—53no—
301#892—53no—
302D3×C4⋊C4—53no—
303#884—56no—
304#884—56no—
305#883—56no—
306#882—56no—
307#67⋊C4—53no—
308#67⋊C4—56no—
309#67⋊C4—51no—
310D3×C22⋊C4—53no—
311D3×C22⋊C4—53no—
312#875—53no—
313C4×D12—53no—
314C4×D12—53no—
315C42×D3—53no—
316C23×D5—33no—
317C23×D5—33no—
318C5×#41—24no—
319C2×C5×Q8—24no—
320C2×C5×Q8C22×D313yes—
321C2×C5×Q8C22×D311yescharacteristic
322C2×C5×D4C22×D313yes—
323C2×C5×D4C22×D313yes—
324C22×C4×C5C22×D313yes—
325C22×C4×C5C22×D313yes—
326C2×C22⋊D5—31no—
327C2×C22⋊D5—36no—
328C2×C22⋊D5—33no—
329C2×C22⋊D5—36no—
330C22×Dic5—31no—
331C22×Dic5—33no—
332#713—38no—
333#713—612no—
334#713—612no—
335#713—64no—
336Q8×D5—64no—
337#711—612no—
338D4×D5—612no—
339D4×D5—612no—
340#709—612no—
341C2×D20—33no—
342C2×D20—33no—
343C2×D20—36no—
344C2×D20—33no—
345C2×D20—612no—
346C2×C4×D5—33no—
347C2×C4×D5—31no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—33no—
351C2×C4×D5—33no—
352C2×C4×D5—33no—
353C2×C4×D5—33no—
354C2×C4×D5—33no—
355C2×C4×D5—612no—
356C2×C4×D5—612no—
357C2×Dic10—33no—
358C5×C4⋊C4C22×D313yes—
359C5×C4⋊C4C22×D313yes—
360C5×C22⋊C4C22×D311yescharacteristic
361C5×C22⋊C4C22×D313yes—
362C5×C22⋊C4C22×D316yes—
363C42×C5C22×D313yes—
364C22⋊Dic5—33no—
365C22⋊Dic5—33no—
366#685—31no—
367#685—33no—
368#685—36no—
369#685—36no—
370#685—33no—
371#685—33no—
372C4⋊Dic5—33no—
373C4⋊Dic5—33no—
374#683—36no—
375#683—33no—
376#683—31no—
377C4×Dic5—31no—
378C4×Dic5—33no—
379C4×Dic5—33no—
380C22×#41—151no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—151no—
384#548—151no—
385#548D1511yescharacteristic, complemented
386#547—153no—
387#546—153no—
388#546—153no—
389D42—153no—
390#532—153no—
391#525—153no—
392#525—153no—
393C4×#41—151no—
394C2×C4×D4—153no—
395C22×C3×C5—21no—
396C22×C3×C5—21no—
397C22×C3×C5—23no—
398C22×C3×C5—23no—
399C22×C3×C5—23no—
400C22×C3×C5C2×#4112yescomplemented
401C22×C3×C5C2511yescharacteristic
402C2×D15—21no—
403C2×D15—23no—
404C2×D15—23no—
405C2×D15—21no—
406C2×D15—23no—
407C2×D15—23no—
408C2×D15—23no—
409C2×D15—412no—
410C2×D15—412no—
411C2×D15C22×D416yes—
412C2×D15C2×#4112yescomplemented
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5—23no—
416C3×C4×C5—21no—
417C3×C4×C5C22×D416yes—
418Dic15—23no—
419Dic15—21no—
420Dic15—23no—
421Dic15C22×D412yes—
422Dic15C2×#4112yescomplemented
423C23×D3—53no—
424C23×D3—53no—
425C3×#41—24no—
426C2×C3×Q8—24no—
427C2×C3×Q8C22×D513yes—
428C2×C3×Q8C22×D511yescharacteristic
429C2×C3×D4C22×D513yes—
430C2×C3×D4C22×D513yes—
431C22×C3×C4C22×D513yes—
432C22×C3×C4C22×D513yes—
433C2×#67—51no—
434C2×#67—53no—
435C2×#67—56no—
436C2×#67—56no—
437C22×Dic3—53no—
438C22×Dic3—51no—
439#239—58no—
440#239—1012no—
441#239—1012no—
442#239—104no—
443D3×Q8—104no—
444#237—1012no—
445D3×D4—1012no—
446D3×D4—1012no—
447#235—1012no—
448C2×D12—53no—
449C2×D12—53no—
450C2×D12—53no—
451C2×D12—56no—
452C2×D12—1012no—
453C2×C4×D3—53no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—53no—
458C2×C4×D3—53no—
459C2×C4×D3—53no—
460C2×C4×D3—51no—
461C2×C4×D3—53no—
462C2×C4×D3—1012no—
463C2×C4×D3—1012no—
464C2×Dic6—53no—
465C3×C4⋊C4C22×D513yes—
466C3×C4⋊C4C22×D513yes—
467C3×C22⋊C4C22×D511yescharacteristic
468C3×C22⋊C4C22×D513yes—
469C3×C22⋊C4C22×D516yes—
470C3×C42C22×D513yes—
471#217—53no—
472#217—53no—
473(C2×D3)⋊C4—51no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—56no—
476(C2×D3)⋊C4—56no—
477(C2×D3)⋊C4—53no—
478(C2×D3)⋊C4—53no—
479C4⋊Dic3—53no—
480C4⋊Dic3—53no—
481Dic3⋊C4—56no—
482Dic3⋊C4—53no—
483Dic3⋊C4—51no—
484C4×Dic3—51no—
485C4×Dic3—53no—
486C4×Dic3—53no—
487C23×C5C23×D313yes—
488C23×C5C23×D311yescharacteristic
489C22×D5—31no—
490C22×D5—33no—
491C22×D5—33no—
492C22×D5—66no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—66no—
496C22×D5—123no—
497C22×D5—123no—
498C5×Q8—26no—
499C5×Q8D3×D414yescomplemented
500C5×D4—26no—
501C5×D4—26no—
502C2×C4×C5—26no—
503C2×C4×C5—26no—
504C2×C4×C5C23×D313yes—
505C2×C4×C5C23×D311yescharacteristic
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D311yescharacteristic
508C2×C4×C5C23×D313yes—
509C22⋊D5—34no—
510C22⋊D5—66no—
511C22⋊D5—612no—
512C22⋊D5—126no—
513C2×Dic5—31no—
514C2×Dic5—31no—
515C2×Dic5—33no—
516C2×Dic5—33no—
517C2×Dic5—31no—
518C2×Dic5—62no—
519C2×Dic5—66no—
520D20—312no—
521D20—612no—
522D20—66no—
523D20—66no—
524C4×D5—312no—
525C4×D5—62no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5—66no—
529C4×D5—66no—
530C4×D5—66no—
531C4×D5—66no—
532C4×D5—123no—
533Dic10—66no—
534C2×#41—151no—
535C2×#41—153no—
536C2×#41—153no—
537C2×#41—151no—
538C2×#41—153no—
539C2×#41—153no—
540C2×#41—308no—
541C2×#41—308no—
542C2×#41C2×D1511yescharacteristic, complemented
543C22×Q8—151no—
544C22×Q8C2×D1511yescharacteristic, complemented
545C22×D4—153no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—153no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—153no—
553#124C2×D1513yescomplemented
554#123—156no—
555#123—156no—
556C22⋊Q8—153no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8C2×D1513yescomplemented
560#121—153no—
561#121—153no—
562#121—153no—
563#121—156no—
564#121—156no—
565#121C2×D1513yescomplemented
566#120—156no—
567#120—156no—
568C4×Q8—151no—
569C4×Q8C2×D1511yescharacteristic, complemented
570C4×D4—153no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—151no—
576C4×D4—153no—
577C4×D4—156no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4C2×D1513yescomplemented
581#117—153no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—153no—
586C2×C3×C5—22no—
587C2×C3×C5—43no—
588C2×C3×C5C23×D411yescharacteristic
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5#58511yescharacteristic
591D15—22no—
592D15—26no—
593D15—43no—
594C23×C3C23×D513yes—
595C23×C3C23×D511yescharacteristic
596C22×D3—51no—
597C22×D3—53no—
598C22×D3—53no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3—106no—
603C22×D3—203no—
604C22×D3—203no—
605C3×Q8—26no—
606C3×Q8D4×D514yescomplemented
607C3×D4—26no—
608C3×D4—26no—
609C2×C3×C4—26no—
610C2×C3×C4—26no—
611C2×C3×C4C23×D513yes—
612C2×C3×C4C23×D511yescharacteristic
613C2×C3×C4C23×D513yes—
614C2×C3×C4C23×D511yescharacteristic
615C2×C3×C4C23×D513yes—
616#67—54no—
617#67—106no—
618#67—1012no—
619#67—206no—
620C2×Dic3—51no—
621C2×Dic3—51no—
622C2×Dic3—53no—
623C2×Dic3—53no—
624C2×Dic3—51no—
625C2×Dic3—102no—
626C2×Dic3—106no—
627D12—512no—
628D12—1012no—
629D12—106no—
630D12—106no—
631C4×D3—512no—
632C4×D3—102no—
633C4×D3—106no—
634C4×D3—106no—
635C4×D3—106no—
636C4×D3—106no—
637C4×D3—106no—
638C4×D3—106no—
639C4×D3—203no—
640Dic6—106no—
641C22×C5—21no—
642C22×C5—21no—
643C22×C5—23no—
644C22×C5—23no—
645C22×C5—23no—
646C22×C5D3×#4112yescomplemented
647C22×C5C24×D311yescharacteristic
648C2×D5—36no—
649C2×D5—32no—
650C2×D5—61no—
651C2×D5—63no—
652C2×D5—63no—
653C2×D5—61no—
654C2×D5—63no—
655C2×D5—63no—
656C2×D5—63no—
657C2×D5—1212no—
658C2×D5—1212no—
659C4×C5—21no—
660C4×C5—23no—
661C4×C5—23no—
662C4×C5—21no—
663C4×C5C2×D3×D416yes—
664Dic5—32no—
665Dic5—32no—
666Dic5—63no—
667Dic5—61no—
668Dic5—63no—
669C24—153no—
670C24—153no—
671#41—24no—
672#41—158no—
673#41—3012no—
674#41—3012no—
675#41—3012no—
676#41—3012no—
677#41—304no—
678C2×Q8—24no—
679C2×Q8—153no—
680C2×Q8—304no—
681C2×Q8C22×D1513yes—
682C2×Q8C22×D1511yescharacteristic
683C2×D4—151no—
684C2×D4—153no—
685C2×D4—156no—
686C2×D4—156no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—156no—
690C2×D4—153no—
691C2×D4—3012no—
692C2×D4—3012no—
693C2×D4—3012no—
694C2×D4C22×D1513yes—
695C2×D4C22×D1513yes—
696C22×C4—153no—
697C22×C4—151no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—151no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—153no—
706C22×C4—153no—
707C22×C4—3012no—
708C22×C4—3012no—
709C22×C4C22×D1513yes—
710C22×C4C22×D1513yes—
711C4⋊C4—151no—
712C4⋊C4—153no—
713C4⋊C4—153no—
714C4⋊C4—153no—
715C4⋊C4—156no—
716C4⋊C4C22×D1513yes—
717C4⋊C4C22×D1513yes—
718C22⋊C4—153no—
719C22⋊C4—153no—
720C22⋊C4—151no—
721C22⋊C4—153no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—156no—
725C22⋊C4—156no—
726C22⋊C4C22×D1511yescharacteristic
727C22⋊C4C22×D1513yes—
728C22⋊C4C22×D1516yes—
729C42—151no—
730C42—153no—
731C42—153no—
732C42C22×D1513yes—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—23no—
737C22×C3—23no—
738C22×C3—23no—
739C22×C3D5×#4112yescomplemented
740C22×C3C24×D511yescharacteristic
741C2×D3—56no—
742C2×D3—52no—
743C2×D3—101no—
744C2×D3—103no—
745C2×D3—103no—
746C2×D3—101no—
747C2×D3—103no—
748C2×D3—103no—
749C2×D3—103no—
750C2×D3—2012no—
751C2×D3—2012no—
752C3×C4—21no—
753C3×C4—23no—
754C3×C4—23no—
755C3×C4—21no—
756C3×C4C2×D4×D516yes—
757Dic3—52no—
758Dic3—52no—
759Dic3—103no—
760Dic3—101no—
761Dic3—103no—
762C2×C5—22no—
763C2×C5—43no—
764C2×C5C22×D3×D411yescharacteristic
765C2×C5C2×D3×#4111yescharacteristic
766C2×C5#596811yescharacteristic
767D5—62no—
768D5—66no—
769D5—123no—
770C23—151no—
771C23—153no—
772C23—153no—
773C23—306no—
774C23—306no—
775C23—306no—
776C23—306no—
777C23—603no—
778C23—603no—
779C23C23×D1513yes—
780C23C23×D1511yescharacteristic
781Q8—26no—
782Q8—306no—
783Q8D4×D1514yescomplemented
784D4—26no—
785D4—26no—
786D4—154no—
787D4—1512no—
788D4—3012no—
789D4—306no—
790D4—306no—
791D4—3012no—
792D4—306no—
793D4—606no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—151no—
797C2×C4—151no—
798C2×C4—1512no—
799C2×C4—153no—
800C2×C4—151no—
801C2×C4—153no—
802C2×C4—302no—
803C2×C4—306no—
804C2×C4—306no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—302no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4—603no—
812C2×C4C23×D1511yescharacteristic
813C2×C4C23×D1513yes—
814C2×C4C23×D1511yescharacteristic
815C2×C4C23×D1513yes—
816C2×C4C23×D1513yes—
817C2×C3—22no—
818C2×C3—43no—
819C2×C3C22×D4×D511yescharacteristic
820C2×C3C2×D5×#4111yescharacteristic
821C2×C3#6628711yescharacteristic
822D3—102no—
823D3—106no—
824D3—203no—
825C5#8671011yescharacteristic, complemented, Sylow
826C22—21no—
827C22—21no—
828C22—23no—
829C22—23no—
830C22—23no—
831C22—156no—
832C22—152no—
833C22—301no—
834C22—303no—
835C22—303no—
836C22—301no—
837C22—303no—
838C22—303no—
839C22—303no—
840C22—6012no—
841C22—6012no—
842C22#41×D1512yescomplemented
843C22C24×D1511yescharacteristic
844C4—21no—
845C4—23no—
846C4—23no—
847C4—21no—
848C4—152no—
849C4—152no—
850C4—301no—
851C4—303no—
852C4—303no—
853C4C2×D4×D1516yes—
854C3#1061861111yescharacteristic, complemented, Sylow
855C2—22no—
856C2—43no—
857C2—302no—
858C2—306no—
859C2—603no—
860C2C22×D4×D1511yescharacteristic
861C2C2×#41×D1511yescharacteristic
862C2#1175715011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#548C2
hypercenter#548D15
hypocenterC3×C5D4×#41
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×#6821C2semidirect
3. C3×C5×#548C2semidirect
4. #11756593C2semidirect
5. Q8×#1220C2semidirect
6. #11756435C2semidirect
7. #11756427C2semidirect
8. #11756390C2semidirect
9. #11756386C2semidirect
10. #11756368C2semidirect
11. #11756365C2semidirect
12. #11756335C2semidirect
13. C4×#6821C2semidirect
14. #11756309C2semidirect
15. C4×D4×D15C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
22. C2×#6821C22semidirect
23. C2×#6821C22semidirect
24. C2×#6821C22semidirect
25. C2×Q8×D15C22semidirect
26. C2×#6819C22semidirect
28. C2×D4×D15C22semidirect
29. C2×#6817C22semidirect
30. C22×D60C22semidirect
31. C22×C4×D15C22semidirect
32. C22×C4×D15C22semidirect
33. C3×C5×#124C22semidirect
34. C3×C5×C22⋊Q8C22semidirect
35. C3×C5×#121C22semidirect
36. C3×C4×C5×Q8C22semidirect
37. C3×C4×C5×D4C22semidirect
38. #91835C22semidirect
39. Q8×Dic15C22semidirect
40. #91833C22semidirect
41. #91829C22semidirect
42. #91827C22semidirect
43. #91826C22semidirect
44. D4×Dic15C22semidirect
45. #91819C22semidirect
47. C4×#1220C22semidirect
48. #91813C22semidirect
49. #91786C22semidirect
50. #91784C22semidirect
51. #91783C22semidirect
52. #91782C22semidirect
53. #91782C22semidirect
54. #91781C22semidirect
55. C4⋊C4×D15C22semidirect
56. #91773C22semidirect
57. #91773C22semidirect
58. #91772C22semidirect
59. #91771C22semidirect
61. #91770C22semidirect
62. #91770C22semidirect
63. C22⋊C4×D15C22semidirect
64. C22⋊C4×D15C22semidirect
65. #91764C22semidirect
66. C4×D60C22semidirect
67. C4×D60C22semidirect
68. C42×D15C22semidirect
72. C5×#548D3semidirect
104. #6821D4semidirect
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
229. C3×C5×Q8C2×D4semidirect
242. #1220#41semidirect
253. D60C2×D4semidirect
262. C4×D15C2×D4semidirect
264. C2×C3×#41C2×D5semidirect
265. C22×C3×Q8C2×D5semidirect
280. C3×#124C2×D5semidirect
281. C3×C22⋊Q8C2×D5semidirect
282. C3×#121C2×D5semidirect
283. C3×C4×Q8C2×D5semidirect
284. C3×C4×D4C2×D5semidirect
385. #548D15semidirect
400. C22×C3×C5C2×#41semidirect
412. C2×D15C2×#41semidirect
422. Dic15C2×#41semidirect
499. C5×Q8D3×D4semidirect
542. C2×#41C2×D15semidirect
544. C22×Q8C2×D15semidirect
553. #124C2×D15semidirect
559. C22⋊Q8C2×D15semidirect
565. #121C2×D15semidirect
569. C4×Q8C2×D15semidirect
580. C4×D4C2×D15semidirect
606. C3×Q8D4×D5semidirect
646. C22×C5D3×#41semidirect
733. C3×C5D4×#41semidirect
739. C22×C3D5×#41semidirect
783. Q8D4×D15semidirect
825. C5#86710semidirect
842. C22#41×D15semidirect
854. C3#10618611semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C22×#68212
C3×C5×#5482
#117565932
Q8×#12202
#117564352
#117564272
#117563902
#117563862
#117563682
#117563652
#117563352
C4×#68212
#117563092
C4×D4×D152
#106186113
#867105