Finite Group Databasebeta

← #14482827

Subgroups — #14482827

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×#92034C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3C4×Q8×D15C211yesmaximal, characteristic, complemented
4C5×#5576C211yesmaximal, characteristic, complemented
5C3×#65910C211yesmaximal, characteristic, complemented
6#11755247C211yesmaximal, characteristic, complemented
7#11755244C211yesmaximal, characteristic, complemented
8#11753884C213yesmaximal, complemented
9#11753850C213yesmaximal, complemented
10#11753703C213yesmaximal, complemented
11#11753698C213yesmaximal, complemented
12#11752751C213yesmaximal, complemented
13C4×#6777C213yesmaximal, complemented
14#11752555C213yesmaximal, complemented
15#11752553C213yesmaximal, complemented
16D5×#548—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic, complemented
19C2×C5×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#713C2211yescharacteristic, complemented
21C2×C3×Q8×D5C2211yescharacteristic, complemented
22#92034—28no—
23D3×Q8×D5—28no—
24C2×#6777C2213yes—
25C2×#6777C2213yes—
26C2×C4×D3×D5C2213yes—
27C2×C4×D3×D5C2213yes—
28C2×#6772C2213yescomplemented
29C2×D15⋊Q8C2213yes—
30C2×D3×Dic10C2213yescomplemented
31C2×#6765C2213yescomplemented
32C2×D5×Dic6C2213yescomplemented
33C3×C4×C5×Q8C2211yescharacteristic, complemented
34Q8×Dic15C2211yescharacteristic, complemented
35C4⋊C4×D15C2213yes—
36#91776C2213yescomplemented
37C42×D15C2213yes—
38C4×Dic30C2213yescomplemented
39C5×#897C2213yescomplemented
40C5×#895C2213yescomplemented
41C5×#875C2213yescomplemented
42C4×C5×D12C2213yescomplemented
43C3×#4043C2213yescomplemented
44C3×#4041C2213yescomplemented
45C3×#4021C2213yescomplemented
46C3×C4×D20C2213yescomplemented
47#91473C2211yescharacteristic
48#91473C2213yes—
49#91473C2216yes—
50#91464C2216yescomplemented
51#91464C2216yescomplemented
52#91456C2213yescomplemented
53#91453C2216yescomplemented
54#91449C2213yescomplemented
55#91442C2213yescomplemented
56#91442C2213yescomplemented
57C4×#1201C2213yescomplemented
58C4×#1201C2213yescomplemented
59#91437C2213yes—
60#91436C2216yescomplemented
61#91435C2213yescomplemented
62#91434C2213yescomplemented
63#91430C2216yescomplemented
64#91408C2216yescomplemented
65#91370C2213yescomplemented
66#91369C2213yescomplemented
67#91368C2213yescomplemented
68#91359C2213yescomplemented
69D3×#548—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×Q8×D5—31no—
72C5×#548—31no—
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#65910D311yescharacteristic, complemented
82C4×Q8×D5—31no—
83#65886—33no—
84C4×D4×D5—33no—
85C22×D3×D5C2313yes—
86C22×D3×D5C2311yescharacteristic
87C2×C3×C5×Q8C2311yescharacteristic
88Q8×D15D418yescomplemented
89C2×C4×D15C2313yes—
90C2×C4×D15C2311yescharacteristic
91C2×C4×D15C2313yes—
92C2×Dic30C2313yes—
93C5×#239—24no—
94C5×D3×Q8—24no—
95C2×C5×D12C2313yes—
96C2×C5×D12C2313yes—
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×#1201C2313yes—
109C2×#1201C2316yes—
110C2×#1201C2313yes—
111C2×#1200C2311yescharacteristic
112C2×#1200C2313yes—
113C2×D3×Dic5C2313yes—
114C2×D3×Dic5C2313yes—
115C2×D5×Dic3C2313yes—
116C2×D5×Dic3C2313yes—
117#6777—212no—
118#6777—212no—
119C4×D3×D5—212no—
120C4×D3×D5—212no—
121#6772—212no—
122D15⋊Q8—212no—
123D3×Dic10—212no—
124#6765—212no—
125D5×Dic6—212no—
126C3×C5×C4⋊C4C2313yes—
127C3×C42×C5C2313yes—
128C4⋊Dic15C2313yes—
129#6712C2316yes—
130C4×Dic15C2313yes—
131C4×Dic15C2313yes—
132C4×Dic15C2313yes—
133C5×(C2×D3)⋊C4C2316yes—
134C5×(C2×D3)⋊C4C2311yescharacteristic
135C5×(C2×D3)⋊C4C2313yes—
136C5×C4⋊Dic3C2313yes—
137C3×#685C2316yes—
138C3×#685C2311yescharacteristic
139C3×#685C2313yes—
140C3×C4⋊Dic5C2313yes—
141#6669C2313yes—
142#6669C2313yes—
143(C2×D3)⋊Dic5C2311yescharacteristic
144(C2×D3)⋊Dic5C2313yes—
145(C2×D3)⋊Dic5C2316yes—
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#5576D511yescharacteristic, complemented
161C4×D3×Q8—51no—
162#5552—53no—
163C4×D3×D4—53no—
164C2×C5×#41—31no—
165C22×C5×Q8—31no—
166D5×#41—68no—
167C2×#713C2×D311yescharacteristic, complemented
168C2×Q8×D5—31no—
169C2×Q8×D5—33no—
170C2×Q8×D5—33no—
171C2×Q8×D5—68no—
172C2×Q8×D5C2×D311yescharacteristic, complemented
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×#124—33no—
181C5×C22⋊Q8—33no—
182C5×#121—33no—
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C4×C5×D4—33no—
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#4043C2×D313yescomplemented
197#4042—36no—
198#4041C2×D313yescomplemented
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#4021C2×D313yescomplemented
213C4×D20C2×D313yescomplemented
214C42×D5—33no—
215C4×Dic10—33no—
216C2×#548—151noSylow
217C22×D15C2411yescharacteristic
218C22×C5×D3C2413yes—
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×Dic15C2411yescharacteristic
233C2×Dic15C2413yes—
234C2×Dic15C2413yes—
235C4×D15—26no—
236C4×D15—22no—
237C4×D15C2×D4112yes—
238Dic30C2×D4112yescomplemented
239C2×C5×Dic3C2413yes—
240C2×C5×Dic3C2411yescharacteristic
241C5×D12—26no—
242C5×D12—26no—
243C4×C5×D3—26no—
244C4×C5×D3—26no—
245C5×Dic6—26no—
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#1201—26no—
255#1201—26no—
256#1201—212no—
257#1200—26no—
258#1200—22no—
259D3×Dic5—26no—
260D3×Dic5—26no—
261D5×Dic3—26no—
262D5×Dic3—26no—
263C2×C3×#41—51no—
264C22×C3×Q8—51no—
265D3×#41—108no—
266C2×#239C2×D511yescharacteristic, complemented
267C2×D3×Q8—51no—
268C2×D3×Q8—53no—
269C2×D3×Q8—53no—
270C2×D3×Q8—108no—
271C2×D3×Q8C2×D511yescharacteristic, complemented
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×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#897C2×D513yescomplemented
296#896—56no—
297#895C2×D513yescomplemented
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#875C2×D513yescomplemented
312C4×D12C2×D513yescomplemented
313C42×D3—53no—
314C4×Dic6—53no—
315C23×D5—31no—
316C23×D5—33no—
317C5×#41—64no—
318C2×C5×Q8—33no—
319C2×C5×Q8—64no—
320C2×C5×Q8C22×D311yescharacteristic
321C2×C5×D4—33no—
322C2×C5×D4—33no—
323C22×C4×C5—33no—
324C22×C4×C5—33no—
325C2×C22⋊D5—36no—
326C2×C22⋊D5—33no—
327C2×C22⋊D5—33no—
328C22×Dic5—33no—
329C22×Dic5—33no—
330#713—24no—
331Q8×D5—24no—
332Q8×D5—38no—
333Q8×D5—612no—
334Q8×D5—612no—
335#711—612no—
336D4×D5—612no—
337D4×D5—612no—
338#709—612no—
339C2×D20C22×D313yes—
340C2×D20C22×D313yes—
341C2×C4×D5—33no—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—31no—
346C2×C4×D5—31no—
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—33no—
357C5×C4⋊C4C22×D313yes—
358C5×C22⋊C4—31no—
359C5×C22⋊C4—33no—
360C5×C22⋊C4—36no—
361C42×C5C22×D313yes—
362C22⋊Dic5—36no—
363C22⋊Dic5—33no—
364C22⋊Dic5—31no—
365#685—36no—
366#685—33no—
367#685—31no—
368#685C22×D311yescharacteristic
369#685C22×D313yes—
370#685C22×D316yes—
371C4⋊Dic5—33no—
372C4⋊Dic5C22×D313yes—
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—31no—
382#548—51no—
383#548—153no—
384#548—153no—
385#548—153no—
386#548—153no—
387#548—151no—
388#548—151no—
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5C2511yescharacteristic
395C2×D15C22×D412yes—
396C2×D15C2×#4112yes—
397C2×D152−1+412yes—
398C2×C5×D3—21no—
399C2×C5×D3—21no—
400C2×C5×D3—23no—
401C2×C5×D3—23no—
402C2×C5×D3—23no—
403C2×C5×D3C2×#4112yescomplemented
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—23no—
416Dic15—21no—
417Dic15C22×D416yes—
418C3×Dic5—21no—
419C3×Dic5—23no—
420C5×Dic3—21no—
421C5×Dic3—23no—
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—24no—
438D3×Q8—24no—
439D3×Q8—58no—
440D3×Q8—1012no—
441D3×Q8—1012no—
442#237—1012no—
443D3×D4—1012no—
444D3×D4—1012no—
445#235—1012no—
446C2×D12C22×D513yes—
447C2×D12C22×D513yes—
448C2×C4×D3—53no—
449C2×C4×D3—53no—
450C2×C4×D3—53no—
451C2×C4×D3—51no—
452C2×C4×D3—53no—
453C2×C4×D3—53no—
454C2×C4×D3—51no—
455C2×C4×D3—1012no—
456C2×C4×D3—1012no—
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—56no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—51no—
475(C2×D3)⋊C4C22×D511yescharacteristic
476(C2×D3)⋊C4C22×D513yes—
477(C2×D3)⋊C4C22×D516yes—
478C4⋊Dic3—53no—
479C4⋊Dic3C22×D513yes—
480Dic3⋊C4—56no—
481Dic3⋊C4—53no—
482Dic3⋊C4—53no—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3—53no—
486C23×C5—31no—
487C23×C5—33no—
488C22×D5—31no—
489C22×D5—34no—
490C22×D5—62no—
491C22×D5—62no—
492C22×D5—66no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5C23×D313yes—
496C22×D5C23×D311yescharacteristic
497C5×Q8—66no—
498C5×Q8D3×D414yescomplemented
499C5×D4—66no—
500C5×D4—66no—
501C2×C4×C5—31no—
502C2×C4×C5—33no—
503C2×C4×C5—66no—
504C2×C4×C5—66no—
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—66no—
515C2×Dic5—66no—
516C2×Dic5C23×D311yescharacteristic
517C2×Dic5C23×D313yes—
518D20—26no—
519D20—26no—
520C4×D5—26no—
521C4×D5—26no—
522C4×D5—312no—
523C4×D5—62no—
524C4×D5—66no—
525C4×D5—66no—
526C4×D5—66no—
527C4×D5—62no—
528C4×D5—66no—
529Dic10—26no—
530Dic10—312no—
531Dic10—612no—
532C2×#41—31no—
533C2×#41—51no—
534C2×#41—153no—
535C2×#41—153no—
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—33no—
549#124—53no—
550#124—156no—
551#124—156no—
552#124—153no—
553#124—153no—
554C22⋊Q8—33no—
555C22⋊Q8—53no—
556C22⋊Q8—156no—
557C22⋊Q8—156no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—33no—
561#121—53no—
562#121—156no—
563#121—156no—
564#121—153no—
565#121—153no—
566C4×Q8—151no—
567C4×Q8—153no—
568C4×Q8—153no—
569C4×Q8D3×D511yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—53no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
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×C5C23×D411yescharacteristic
585C2×C3×C5C22×#4111yescharacteristic
586C2×C3×C5C2×2−1+411yescharacteristic
587D15#54814yescomplemented
588C3×D5—22no—
589C3×D5—43no—
590C5×D3—22no—
591C5×D3—43no—
592C23×C3—51no—
593C23×C3—53no—
594C22×D3—51no—
595C22×D3—54no—
596C22×D3—102no—
597C22×D3—102no—
598C22×D3—106no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3C23×D513yes—
602C22×D3C23×D511yescharacteristic
603C3×Q8—106no—
604C3×Q8D4×D514yescomplemented
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—1012no—
615#67—106no—
616#67—106no—
617C2×Dic3—53no—
618C2×Dic3—51no—
619C2×Dic3—53no—
620C2×Dic3—106no—
621C2×Dic3—106no—
622C2×Dic3C23×D511yescharacteristic
623C2×Dic3C23×D513yes—
624D12—26no—
625D12—26no—
626C4×D3—26no—
627C4×D3—26no—
628C4×D3—512no—
629C4×D3—102no—
630C4×D3—106no—
631C4×D3—106no—
632C4×D3—106no—
633C4×D3—102no—
634C4×D3—106no—
635Dic6—26no—
636Dic6—512no—
637Dic6—1012no—
638C22×C5—32no—
639C22×C5—61no—
640C22×C5—61no—
641C22×C5—63no—
642C22×C5—63no—
643C22×C5—63no—
644C22×C5C24×D311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—23no—
648C2×D5—23no—
649C2×D5—23no—
650C2×D5—32no—
651C2×D5—32no—
652C2×D5—32no—
653C2×D5—68no—
654C2×D5—1212no—
655C2×D5D3×#4112yescomplemented
656C4×C5—23no—
657C4×C5—21no—
658C4×C5—63no—
659C4×C5—61no—
660C4×C5C2×D3×D416yes—
661Dic5—23no—
662Dic5—21no—
663Dic5—36no—
664Dic5—63no—
665Dic5—61no—
666C24—151no—
667C24—153no—
668#41—64no—
669#41—104no—
670#41—3012no—
671#41—3012no—
672C2×Q8—33no—
673C2×Q8—53no—
674C2×Q8—64no—
675C2×Q8—104no—
676C2×Q8—156no—
677C2×Q8—158no—
678C2×Q8—153no—
679C2×Q8—3012no—
680C2×Q8—3012no—
681C2×Q8—3012no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—53no—
686C2×D4—53no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—156no—
690C2×D4—3012no—
691C2×D4—3012no—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—53no—
695C22×C4—53no—
696C22×C4—153no—
697C22×C4—151no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—153no—
703C22×C4—151no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4—3012no—
707C4⋊C4—33no—
708C4⋊C4—53no—
709C4⋊C4—153no—
710C4⋊C4—153no—
711C4⋊C4—156no—
712C4⋊C4—153no—
713C4⋊C4C2×D3×D513yes—
714C22⋊C4—31no—
715C22⋊C4—33no—
716C22⋊C4—36no—
717C22⋊C4—51no—
718C22⋊C4—53no—
719C22⋊C4—56no—
720C22⋊C4—151no—
721C22⋊C4—153no—
722C22⋊C4—156no—
723C22⋊C4—151no—
724C22⋊C4—153no—
725C22⋊C4—156no—
726C42—153no—
727C42—153no—
728C42—153no—
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—21no—
739C2×D3—21no—
740C2×D3—23no—
741C2×D3—23no—
742C2×D3—23no—
743C2×D3—52no—
744C2×D3—52no—
745C2×D3—52no—
746C2×D3—108no—
747C2×D3—2012no—
748C2×D3D5×#4112yescomplemented
749C3×C4—23no—
750C3×C4—21no—
751C3×C4—103no—
752C3×C4—101no—
753C3×C4C2×D4×D516yes—
754Dic3—23no—
755Dic3—21no—
756Dic3—56no—
757Dic3—103no—
758Dic3—101no—
759C2×C5—62no—
760C2×C5—123no—
761C2×C5C22×D3×D411yescharacteristic
762C2×C5C2×D3×#4111yescharacteristic
763C2×C5D3×2−1+411yescharacteristic
764D5—22no—
765D5—34no—
766D5—43no—
767C23—31no—
768C23—33no—
769C23—51no—
770C23—53no—
771C23—154no—
772C23—151no—
773C23—302no—
774C23—302no—
775C23—306no—
776C23—306no—
777C23—306no—
778Q8—66no—
779Q8—106no—
780Q8—1512no—
781Q8—3012no—
782Q8#677714yescomplemented
783D4—66no—
784D4—66no—
785D4—106no—
786D4—106no—
787D4—3012no—
788D4—306no—
789D4—306no—
790C2×C4—33no—
791C2×C4—31no—
792C2×C4—53no—
793C2×C4—51no—
794C2×C4—66no—
795C2×C4—66no—
796C2×C4—106no—
797C2×C4—106no—
798C2×C4—153no—
799C2×C4—1512no—
800C2×C4—151no—
801C2×C4—153no—
802C2×C4—306no—
803C2×C4—302no—
804C2×C4—302no—
805C2×C4—306no—
806C2×C4—306no—
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×C3C22×D4×D511yescharacteristic
816C2×C3C2×D5×#4111yescharacteristic
817C2×C3D5×2−1+411yescharacteristic
818D3—22no—
819D3—43no—
820D3—54no—
821C5D3×#54811yescharacteristic, complemented, Sylow
822C22—32no—
823C22—52no—
824C22—61no—
825C22—61no—
826C22—63no—
827C22—63no—
828C22—63no—
829C22—101no—
830C22—101no—
831C22—103no—
832C22—103no—
833C22—103no—
834C22—152no—
835C22—152no—
836C22—152no—
837C22—308no—
838C22—6012no—
839C22C23×D3×D511yescharacteristic
840C4—21no—
841C4—23no—
842C4—61no—
843C4—63no—
844C4—101no—
845C4—103no—
846C4—156no—
847C4—301no—
848C4—303no—
849C4C2×#677716yes—
850C3D5×#54811yescharacteristic, complemented, Sylow
851C2—62no—
852C2—102no—
853C2—123no—
854C2—154no—
855C2—203no—
856C2C22×#677711yescharacteristic
857C2#1175704711yescharacteristic
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×#92034C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. C4×Q8×D15C2semidirect
4. C5×#5576C2semidirect
5. C3×#65910C2semidirect
6. #11755247C2semidirect
7. #11755244C2semidirect
8. #11753884C2semidirect
9. #11753850C2semidirect
10. #11753703C2semidirect
11. #11753698C2semidirect
12. #11752751C2semidirect
13. C4×#6777C2semidirect
14. #11752555C2semidirect
15. #11752553C2semidirect
18. C2×C5×#239C22semidirect
19. C2×C5×D3×Q8C22semidirect
20. C2×C3×#713C22semidirect
21. C2×C3×Q8×D5C22semidirect
28. C2×#6772C22semidirect
30. C2×D3×Dic10C22semidirect
31. C2×#6765C22semidirect
32. C2×D5×Dic6C22semidirect
33. C3×C4×C5×Q8C22semidirect
34. Q8×Dic15C22semidirect
36. #91776C22semidirect
38. C4×Dic30C22semidirect
39. C5×#897C22semidirect
40. C5×#895C22semidirect
41. C5×#875C22semidirect
42. C4×C5×D12C22semidirect
43. C3×#4043C22semidirect
44. C3×#4041C22semidirect
45. C3×#4021C22semidirect
46. C3×C4×D20C22semidirect
50. #91464C22semidirect
51. #91464C22semidirect
52. #91456C22semidirect
53. #91453C22semidirect
54. #91449C22semidirect
55. #91442C22semidirect
56. #91442C22semidirect
57. C4×#1201C22semidirect
58. C4×#1201C22semidirect
60. #91436C22semidirect
61. #91435C22semidirect
62. #91434C22semidirect
63. #91430C22semidirect
64. #91408C22semidirect
65. #91370C22semidirect
66. #91369C22semidirect
67. #91368C22semidirect
68. #91359C22semidirect
81. #65910D3semidirect
88. Q8×D15D4semidirect
160. #5576D5semidirect
167. C2×#713C2×D3semidirect
172. C2×Q8×D5C2×D3semidirect
183. C4×C5×Q8C2×D3semidirect
196. #4043C2×D3semidirect
198. #4041C2×D3semidirect
212. #4021C2×D3semidirect
213. C4×D20C2×D3semidirect
227. C2×D3×D5#41semidirect
228. C3×C5×Q8C2×D4semidirect
238. Dic30C2×D4semidirect
266. C2×#239C2×D5semidirect
271. C2×D3×Q8C2×D5semidirect
282. C3×C4×Q8C2×D5semidirect
295. #897C2×D5semidirect
297. #895C2×D5semidirect
311. #875C2×D5semidirect
312. C4×D12C2×D5semidirect
403. C2×C5×D3C2×#41semidirect
409. C2×C3×D5C2×#41semidirect
498. C5×Q8D3×D4semidirect
569. C4×Q8D3×D5semidirect
587. D15#548semidirect
604. C3×Q8D4×D5semidirect
655. C2×D5D3×#41semidirect
730. C3×C5C2×#548semidirect
748. C2×D3D5×#41semidirect
782. Q8#6777semidirect
821. C5D3×#548semidirect
850. C3D5×#548semidirect

Maximal subgroups

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

subgroupindex
C2×#920342
C2×D3×Q8×D52
C4×Q8×D152
C5×#55762
C3×#659102
#117552472
#117552442
#117538842
#117538502
#117537032
#117536982
#117527512
C4×#67772
#117525552
#117525532
D5×#5483
D3×#5485