Finite Group Databasebeta

← #14482824

Subgroups — #14482824

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
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3C5×#5831C211yesmaximal, characteristic, complemented
4C3×#66165C211yesmaximal, characteristic, complemented
5Q8×#1200C211yesmaximal, characteristic, complemented
6#11755131C211yesmaximal, characteristic, complemented
7#11755128C211yesmaximal, characteristic, complemented
8#11755026C213yesmaximal, complemented
9#11754831C213yesmaximal, complemented
10#11754827C213yesmaximal, complemented
11#11754816C213yesmaximal, complemented
12C4×#6790C213yesmaximal, complemented
13#11754383C213yesmaximal, complemented
14#11754378C213yesmaximal, complemented
15#11754367C213yesmaximal, complemented
16D5×#548—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18#41×D15—28no—
19C2×#6821C2211yescharacteristic, complemented
20C2×Q8×D15C2211yescharacteristic
21C2×#6819C2213yescomplemented
22C2×D4×D15C2213yes—
23C2×#6817C2213yescomplemented
24C22×C4×D15C2213yes—
25C2×C5×D3×Q8C2211yescharacteristic, complemented
26C2×C3×Q8×D5C2211yescharacteristic, complemented
27C2×#6790C2213yes—
28D3×Q8×D5—28no—
29C2×C4×D3×D5C2213yes—
30C2×D15⋊Q8C2213yes—
31C2×D3×Dic10C2213yescomplemented
32C2×D5×Dic6C2213yescomplemented
33C5×Q8×Dic3C2211yescharacteristic, complemented
34C5×#938C2213yescomplemented
35C5×#936C2213yescomplemented
36C4×C5×#67C2213yescomplemented
37C5×#924C2213yescomplemented
38C3×Q8×Dic5C2211yescharacteristic, complemented
39C3×#4084C2213yescomplemented
40C3×#4082C2213yescomplemented
41C3×C4×C22⋊D5C2213yescomplemented
42C3×#4070C2213yescomplemented
43#91576C2216yescomplemented
44#91561C2216yes—
45#91561C2213yes—
46#67⋊Dic5C2213yescomplemented
47#91559C2213yescomplemented
48#91558C2216yescomplemented
49#91550C2216yescomplemented
50#91526C2216yescomplemented
51#91526C2216yescomplemented
52#91473C2211yescharacteristic
53#91460C2213yescomplemented
54#91450C2213yescomplemented
55C4×#1203C2213yescomplemented
56C4×#1202C2213yescomplemented
57#91437C2213yes—
58#91406C2213yescomplemented
59#91404C2213yes—
60C4×#1200C2213yes—
61#91396C2213yescomplemented
62#91390C2213yescomplemented
63#91383C2213yescomplemented
64#91377C2216yescomplemented
65#91375C2213yescomplemented
66#91374C2213yescomplemented
67#91340C2213yescomplemented
68#91333C2213yescomplemented
69D3×#548—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×Q8×D5—31no—
72C5×#548—31no—
73#66165D311yescharacteristic, complemented
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—
86C22×D3×D5C2311yescharacteristic
87C3×C5×#41—24no—
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×#1220C2316yes—
92C22×Dic15C2313yes—
93#6821—24no—
94Q8×D15D418yescomplemented
95#6819—212no—
96D4×D15—212no—
97#6817—212no—
98C2×D60C2313yes—
99C2×C4×D15—212no—
100C2×C4×D15C2313yes—
101C2×C4×D15C2311yescharacteristic
102C2×C4×D15C2313yes—
103C2×C4×D15C2313yes—
104C2×Dic30C2313yes—
105C2×C5×#67C2313yes—
106C5×D3×Q8—24no—
107C2×C4×C5×D3C2313yes—
108C2×C5×Dic6C2313yes—
109C2×C3×C22⋊D5C2313yes—
110C3×Q8×D5—24no—
111C2×C3×C4×D5C2313yes—
112C2×C3×Dic10C2313yes—
113#6790—212no—
114C2×#1204C2316yes—
115C2×#1203C2313yes—
116C2×#1202C2313yes—
117C2×#1200C2311yescharacteristic
118C2×#1200C2313yes—
119C2×#1200C2313yes—
120C2×D3×Dic5C2313yes—
121C2×D5×Dic3C2313yes—
122C4×D3×D5—212no—
123D15⋊Q8—212no—
124D3×Dic10—212no—
125D5×Dic6—212no—
126C5×#217C2316yes—
127C5×#217C2313yes—
128C5×(C2×D3)⋊C4C2311yescharacteristic
129C5×C4⋊Dic3C2313yes—
130C5×Dic3⋊C4C2313yes—
131C4×C5×Dic3C2313yes—
132C3×C22⋊Dic5C2313yes—
133C3×C22⋊Dic5C2316yes—
134C3×#685C2311yescharacteristic
135C3×C4⋊Dic5C2313yes—
136C3×#683C2313yes—
137C3×C4×Dic5C2313yes—
138Dic3⋊Dic5C2313yes—
139#6669C2316yes—
140#6668C2313yes—
141#6667C2313yes—
142#6667C2313yes—
143#6667C2316yes—
144#6667C2316yes—
145(C2×D3)⋊Dic5C2311yescharacteristic
146#6665C2311yescharacteristic
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C2×D3×#41—51no—
150C22×D3×Q8—51no—
151C3×#548—51no—
152#5831D511yescharacteristic, complemented
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×Q8—31no—
166D5×#41—68no—
167C2×#713—31no—
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×Q8—31no—
184C4×C5×D4—33no—
185#4093—33no—
186#4092—33no—
187Q8×Dic5C2×D311yescharacteristic, complemented
188#4085—36no—
189#4084C2×D313yescomplemented
190#4082C2×D313yescomplemented
191D4×Dic5—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5C2×D313yescomplemented
195#4070C2×D313yescomplemented
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—33no—
209D5×C22⋊C4—36no—
210D5×C22⋊C4—31no—
211#4024—36no—
212#4021—33no—
213C4×D20—33no—
214C42×D5—33no—
215C4×Dic10—33no—
216C2×#548—151noSylow
217C23×C3×C5C2413yes—
218C22×D15—26no—
219C22×D15—26no—
220C22×D15—26no—
221C22×D15C2413yes—
222C22×D15C2411yescharacteristic
223C22×C5×D3C2411yescharacteristic
224C22×C3×D5C2411yescharacteristic
225C2×D3×D5—22no—
226C2×D3×D5—22no—
227C2×D3×D5#4114yescomplemented
228C3×C5×Q8C2×D414yescomplemented
229C3×C5×D4—26no—
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2411yescharacteristic
232C2×C3×C4×C5C2413yes—
233#1220—212no—
234C2×Dic15—26no—
235C2×Dic15C2411yescharacteristic
236C2×Dic15C2413yes—
237D60—26no—
238C4×D15—22no—
239C4×D15—26no—
240C4×D15—26no—
241C4×D15C2×D4112yes—
242Dic30C2×D4112yescomplemented
243C5×#67—26no—
244C2×C5×Dic3C2411yescharacteristic
245C2×C5×Dic3C2413yes—
246C2×C5×Dic3C2413yes—
247C4×C5×D3—26no—
248C5×Dic6—26no—
249C3×C22⋊D5—26no—
250C2×C3×Dic5C2411yescharacteristic
251C2×C3×Dic5C2413yes—
252C2×C3×Dic5C2413yes—
253C3×C4×D5—26no—
254C3×Dic10—26no—
255#1204—212no—
256#1203—26no—
257#1202—26no—
258#1200—26no—
259#1200—26no—
260#1200—22no—
261D3×Dic5—26no—
262D5×Dic3—26no—
263C2×C3×#41C2×D511yescharacteristic, complemented
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, 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×Q8—51no—
283C3×C4×D4—53no—
284#947—53no—
285#946—53no—
286Q8×Dic3C2×D511yescharacteristic, complemented
287#939—56no—
288#938C2×D513yescomplemented
289#936C2×D513yescomplemented
290D4×Dic3—53no—
291#930—53no—
292C4×#67—53no—
293C4×#67C2×D513yescomplemented
294#924C2×D513yescomplemented
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—33no—
319C2×C5×Q8—64no—
320C2×C5×Q8C22×D311yescharacteristic
321C2×C5×D4—33no—
322C2×C5×D4C22×D313yes—
323C22×C4×C5—33no—
324C22×C4×C5C22×D313yes—
325C2×C22⋊D5—36no—
326C2×C22⋊D5—33no—
327C2×C22⋊D5C22×D313yes—
328C22×Dic5—33no—
329C22×Dic5—33no—
330#713—64no—
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×D20—33no—
340C2×D20—33no—
341C2×C4×D5—33no—
342C2×C4×D5—33no—
343C2×C4×D5—31no—
344C2×C4×D5—33no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—33no—
348C2×C4×D5—31no—
349C2×C4×D5—612no—
350C2×C4×D5—612no—
351C2×C4×D5C22×D313yes—
352C2×Dic10—33no—
353C2×Dic10—36no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4—33no—
358C5×C22⋊C4—33no—
359C5×C22⋊C4—36no—
360C5×C22⋊C4—31no—
361C42×C5—33no—
362C22⋊Dic5—31no—
363C22⋊Dic5C22×D316yes—
364C22⋊Dic5C22×D313yes—
365#685—31no—
366#685—33no—
367#685—36no—
368#685—36no—
369#685—33no—
370#685C22×D311yescharacteristic
371C4⋊Dic5—33no—
372C4⋊Dic5C22×D313yes—
373#683—33no—
374#683—36no—
375#683C22×D313yes—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5C22×D313yes—
379C22×#41—151no—
380C23×Q8—151no—
381#548—31no—
382#548—51no—
383#548—153no—
384#548—153no—
385#548—151no—
386#548—151no—
387#548—153no—
388#548—153no—
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5—23no—
395C22×C3×C5—23no—
396C22×C3×C5—23no—
397C22×C3×C5C2511yescharacteristic
398C2×D15—23no—
399C2×D15—23no—
400C2×D15—23no—
401C2×D15—412no—
402C2×D15C22×D412yes—
403C2×D15C2×#4112yes—
404C2×D152−1+412yes—
405C2×C5×D3—21no—
406C2×C5×D3—21no—
407C2×C5×D3C2×#4112yescomplemented
408C2×C3×D5—21no—
409C2×C3×D5—21no—
410C2×C3×D5C2×#4112yescomplemented
411D3×D5—28no—
412C3×C4×C5—21no—
413C3×C4×C5C22×D416yes—
414Dic15—21no—
415Dic15C22×D416yes—
416C3×Dic5—23no—
417C3×Dic5—23no—
418C3×Dic5—21no—
419C5×Dic3—23no—
420C5×Dic3—23no—
421C5×Dic3—21no—
422C23×D3—51no—
423C23×D3—53no—
424C3×#41—24no—
425C2×C3×Q8—53no—
426C2×C3×Q8—104no—
427C2×C3×Q8C22×D511yescharacteristic
428C2×C3×D4—53no—
429C2×C3×D4C22×D513yes—
430C22×C3×C4—53no—
431C22×C3×C4C22×D513yes—
432C2×#67—56no—
433C2×#67—53no—
434C2×#67C22×D513yes—
435C22×Dic3—53no—
436C22×Dic3—53no—
437#239—104no—
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×D12—53no—
447C2×D12—53no—
448C2×C4×D3—53no—
449C2×C4×D3—53no—
450C2×C4×D3—53no—
451C2×C4×D3—51no—
452C2×C4×D3—53no—
453C2×C4×D3—51no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—1012no—
457C2×C4×D3—1012no—
458C2×C4×D3C22×D513yes—
459C2×Dic6—53no—
460C2×Dic6—56no—
461C2×Dic6—1012no—
462C2×Dic6C22×D513yes—
463C3×C4⋊C4—53no—
464C3×C4⋊C4—53no—
465C3×C22⋊C4—56no—
466C3×C22⋊C4—53no—
467C3×C22⋊C4—51no—
468C3×C42—53no—
469#217—51no—
470#217C22×D516yes—
471#217C22×D513yes—
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)⋊C4C22×D511yescharacteristic
478C4⋊Dic3—53no—
479C4⋊Dic3C22×D513yes—
480Dic3⋊C4—56no—
481Dic3⋊C4—53no—
482Dic3⋊C4C22×D513yes—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3C22×D513yes—
486C23×C5—31no—
487C23×C5C23×D313yes—
488C22×D5—31no—
489C22×D5—34no—
490C22×D5—33no—
491C22×D5—62no—
492C22×D5—62no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—66no—
496C22×D5C23×D311yescharacteristic
497C5×Q8—66no—
498C5×Q8D3×D414yescomplemented
499C5×D4—26no—
500C5×D4—66no—
501C2×C4×C5—26no—
502C2×C4×C5—31no—
503C2×C4×C5—33no—
504C2×C4×C5—33no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D311yescharacteristic
507C2×C4×C5C23×D313yes—
508C22⋊D5—26no—
509C22⋊D5—66no—
510C22⋊D5—612no—
511C2×Dic5—33no—
512C2×Dic5—31no—
513C2×Dic5—66no—
514C2×Dic5—66no—
515C2×Dic5C23×D311yescharacteristic
516C2×Dic5C23×D313yes—
517C2×Dic5C23×D313yes—
518D20—66no—
519D20—66no—
520C4×D5—26no—
521C4×D5—312no—
522C4×D5—62no—
523C4×D5—66no—
524C4×D5—66no—
525C4×D5—66no—
526C4×D5—66no—
527C4×D5—62no—
528C4×D5—66no—
529Dic10—26no—
530Dic10—312no—
531Dic10—612no—
532C2×#41—151no—
533C2×#41—153no—
534C2×#41—153no—
535C2×#41—308no—
536C2×#41D3×D511yescharacteristic, complemented
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—153no—
551#124—153no—
552#124—156no—
553#124—156no—
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—31no—
567C4×Q8—51no—
568C4×Q8—153no—
569C4×Q8—153no—
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×C5—43no—
585C2×C3×C5C23×D411yescharacteristic
586C2×C3×C5C22×#4111yescharacteristic
587C2×C3×C5C2×2−1+411yescharacteristic
588D15—43no—
589D15#54814yescomplemented
590C3×D5—22no—
591C5×D3—22no—
592C23×C3—51no—
593C23×C3C23×D513yes—
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×Q8D4×D514yescomplemented
605C3×D4—26no—
606C3×D4—106no—
607C2×C3×C4—26no—
608C2×C3×C4—51no—
609C2×C3×C4—53no—
610C2×C3×C4—53no—
611C2×C3×C4—106no—
612C2×C3×C4C23×D511yescharacteristic
613C2×C3×C4C23×D513yes—
614#67—26no—
615#67—106no—
616#67—1012no—
617C2×Dic3—53no—
618C2×Dic3—51no—
619C2×Dic3—106no—
620C2×Dic3—106no—
621C2×Dic3C23×D511yescharacteristic
622C2×Dic3C23×D513yes—
623C2×Dic3C23×D513yes—
624D12—106no—
625D12—106no—
626C4×D3—26no—
627C4×D3—512no—
628C4×D3—102no—
629C4×D3—106no—
630C4×D3—106no—
631C4×D3—106no—
632C4×D3—106no—
633C4×D3—102no—
634C4×D3—106no—
635Dic6—26no—
636Dic6—512no—
637Dic6—1012no—
638C22×C5—23no—
639C22×C5—23no—
640C22×C5—23no—
641C22×C5—32no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5C24×D311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—32no—
648C2×D5—32no—
649C2×D5—32no—
650C2×D5—68no—
651C2×D5—63no—
652C2×D5—63no—
653C2×D5—63no—
654C2×D5—1212no—
655C2×D5D3×#4112yescomplemented
656C4×C5—21no—
657C4×C5—63no—
658C4×C5—63no—
659C4×C5—61no—
660C4×C5C2×D3×D416yes—
661Dic5—23no—
662Dic5—23no—
663Dic5—21no—
664Dic5—36no—
665Dic5—61no—
666C24—151no—
667C24—153no—
668#41—24no—
669#41—3012no—
670#41—3012no—
671#41—304no—
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—53no—
685C2×D4—153no—
686C2×D4—153no—
687C2×D4—156no—
688C2×D4—153no—
689C2×D4—3012no—
690C2×D4—3012no—
691C2×D4C2×D3×D513yes—
692C22×C4—33no—
693C22×C4—53no—
694C22×C4—151no—
695C22×C4—153no—
696C22×C4—153no—
697C22×C4—153no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—151no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—3012no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—33no—
708C4⋊C4—33no—
709C4⋊C4—53no—
710C4⋊C4—53no—
711C4⋊C4—153no—
712C4⋊C4—153no—
713C4⋊C4—156no—
714C22⋊C4—33no—
715C22⋊C4—36no—
716C22⋊C4—31no—
717C22⋊C4—53no—
718C22⋊C4—56no—
719C22⋊C4—51no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—156no—
723C22⋊C4—156no—
724C22⋊C4—151no—
725C22⋊C4—151no—
726C42—33no—
727C42—53no—
728C42—153no—
729C42—153no—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—23no—
732C22×C3—23no—
733C22×C3—23no—
734C22×C3—52no—
735C22×C3—101no—
736C22×C3—101no—
737C22×C3C24×D511yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—52no—
741C2×D3—52no—
742C2×D3—52no—
743C2×D3—108no—
744C2×D3—103no—
745C2×D3—103no—
746C2×D3—103no—
747C2×D3—2012no—
748C2×D3D5×#4112yescomplemented
749C3×C4—21no—
750C3×C4—103no—
751C3×C4—103no—
752C3×C4—101no—
753C3×C4C2×D4×D516yes—
754Dic3—23no—
755Dic3—23no—
756Dic3—21no—
757Dic3—56no—
758Dic3—101no—
759C2×C5—43no—
760C2×C5—62no—
761C2×C5C22×D3×D411yescharacteristic
762C2×C5C2×D3×#4111yescharacteristic
763C2×C5D3×2−1+411yescharacteristic
764D5—22no—
765D5—34no—
766D5—123no—
767C23—31no—
768C23—51no—
769C23—154no—
770C23—151no—
771C23—153no—
772C23—306no—
773C23—306no—
774C23—306no—
775C23—302no—
776C23—302no—
777C23C22×D3×D513yes—
778Q8—66no—
779Q8—106no—
780Q8—1512no—
781Q8—3012no—
782Q8#679014yescomplemented
783D4—26no—
784D4—66no—
785D4—106no—
786D4—306no—
787D4—306no—
788D4—3012no—
789D4—306no—
790C2×C4—26no—
791C2×C4—31no—
792C2×C4—33no—
793C2×C4—33no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—53no—
797C2×C4—66no—
798C2×C4—106no—
799C2×C4—153no—
800C2×C4—1512no—
801C2×C4—151no—
802C2×C4—306no—
803C2×C4—302no—
804C2×C4—306no—
805C2×C4—306no—
806C2×C4—302no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4C22×D3×D511yescharacteristic
812C2×C4C22×D3×D513yes—
813C2×C3—43no—
814C2×C3—102no—
815C2×C3C22×D4×D511yescharacteristic
816C2×C3C2×D5×#4111yescharacteristic
817C2×C3D5×2−1+411yescharacteristic
818D3—22no—
819D3—54no—
820D3—203no—
821C5D3×#54811yescharacteristic, complemented, Sylow
822C22—23no—
823C22—23no—
824C22—23no—
825C22—32no—
826C22—52no—
827C22—61no—
828C22—61no—
829C22—101no—
830C22—101no—
831C22—152no—
832C22—152no—
833C22—152no—
834C22—308no—
835C22—303no—
836C22—303no—
837C22—303no—
838C22—6012no—
839C22C23×D3×D511yescharacteristic
840C4—21no—
841C4—61no—
842C4—63no—
843C4—63no—
844C4—101no—
845C4—103no—
846C4—103no—
847C4—156no—
848C4—301no—
849C4C2×#679016yes—
850C3D5×#54811yescharacteristic, complemented, Sylow
851C2—43no—
852C2—62no—
853C2—102no—
854C2—154no—
855C2—603no—
856C2D3×D5×#4111yescharacteristic
857C2#1175705711yescharacteristic
858C2C22×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. C5×#5831C2semidirect
4. C3×#66165C2semidirect
5. Q8×#1200C2semidirect
6. #11755131C2semidirect
7. #11755128C2semidirect
8. #11755026C2semidirect
9. #11754831C2semidirect
10. #11754827C2semidirect
11. #11754816C2semidirect
12. C4×#6790C2semidirect
13. #11754383C2semidirect
14. #11754378C2semidirect
15. #11754367C2semidirect
17. C2×C3×C5×#41C22semidirect
19. C2×#6821C22semidirect
21. C2×#6819C22semidirect
23. C2×#6817C22semidirect
25. C2×C5×D3×Q8C22semidirect
26. C2×C3×Q8×D5C22semidirect
31. C2×D3×Dic10C22semidirect
32. C2×D5×Dic6C22semidirect
33. C5×Q8×Dic3C22semidirect
34. C5×#938C22semidirect
35. C5×#936C22semidirect
36. C4×C5×#67C22semidirect
37. C5×#924C22semidirect
38. C3×Q8×Dic5C22semidirect
39. C3×#4084C22semidirect
40. C3×#4082C22semidirect
41. C3×C4×C22⋊D5C22semidirect
42. C3×#4070C22semidirect
43. #91576C22semidirect
46. #67⋊Dic5C22semidirect
47. #91559C22semidirect
48. #91558C22semidirect
49. #91550C22semidirect
50. #91526C22semidirect
51. #91526C22semidirect
53. #91460C22semidirect
54. #91450C22semidirect
55. C4×#1203C22semidirect
56. C4×#1202C22semidirect
58. #91406C22semidirect
61. #91396C22semidirect
62. #91390C22semidirect
63. #91383C22semidirect
64. #91377C22semidirect
65. #91375C22semidirect
66. #91374C22semidirect
67. #91340C22semidirect
68. #91333C22semidirect
73. #66165D3semidirect
94. Q8×D15D4semidirect
152. #5831D5semidirect
164. C2×C5×#41C2×D3semidirect
172. C2×Q8×D5C2×D3semidirect
187. Q8×Dic5C2×D3semidirect
189. #4084C2×D3semidirect
190. #4082C2×D3semidirect
194. C4×C22⋊D5C2×D3semidirect
195. #4070C2×D3semidirect
227. C2×D3×D5#41semidirect
228. C3×C5×Q8C2×D4semidirect
242. Dic30C2×D4semidirect
263. C2×C3×#41C2×D5semidirect
271. C2×D3×Q8C2×D5semidirect
286. Q8×Dic3C2×D5semidirect
288. #938C2×D5semidirect
289. #936C2×D5semidirect
293. C4×#67C2×D5semidirect
294. #924C2×D5semidirect
407. C2×C5×D3C2×#41semidirect
410. C2×C3×D5C2×#41semidirect
498. C5×Q8D3×D4semidirect
536. C2×#41D3×D5semidirect
589. D15#548semidirect
604. C3×Q8D4×D5semidirect
655. C2×D5D3×#41semidirect
730. C3×C5C2×#548semidirect
748. C2×D3D5×#41semidirect
782. Q8#6790semidirect
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×#41×D152
C2×D3×Q8×D52
C5×#58312
C3×#661652
Q8×#12002
#117551312
#117551282
#117550262
#117548312
#117548272
#117548162
C4×#67902
#117543832
#117543782
#117543672
D5×#5483
D3×#5485