Finite Group Databasebeta

← #41×#1202 #14483156

Subgroups — #41×#1202 #14483156

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
2C2×C3×D5×#41C211yesmaximal, characteristic, complemented
3C5×Dic3×#41C211yesmaximal, characteristic, complemented
4#11755257C211yesmaximal, characteristic, complemented
5#11755251C211yesmaximal, characteristic, complemented
6Q8×#1202C211yesmaximal, characteristic, complemented
7#11755128C211yesmaximal, characteristic, complemented
8#11754980C213yesmaximal, complemented
9#11754972C213yesmaximal, complemented
10#11754963C213yesmaximal, complemented
11D4×#1202C213yesmaximal, complemented
12#11754590C213yesmaximal, complemented
13#11754581C213yesmaximal, complemented
14#11754564C213yesmaximal, complemented
15C2×C4×#1202C213yesmaximal, complemented
16#41×D20—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18#41×D15—28no—
19C2×#6821C2211yescharacteristic, complemented
20C2×Q8×D15C2211yescharacteristic, complemented
21C2×#6819C2213yescomplemented
22C2×D4×D15C2213yescomplemented
23C2×#6817C2213yescomplemented
24C22×C4×D15C2213yescomplemented
25C3×D5×#41—28no—
26C2×C3×#713C2211yescharacteristic, complemented
27C2×C3×Q8×D5C2211yescharacteristic, complemented
28C2×C3×#711C2213yescomplemented
29C2×C3×D4×D5C2213yescomplemented
30C2×C3×#709C2213yescomplemented
31C22×C3×C4×D5C2213yescomplemented
32C22×#1202C2213yes—
33C5×Q8×Dic3C2211yescharacteristic, complemented
34C5×Q8×Dic3C2211yescharacteristic, complemented
35C5×D4×Dic3C2213yescomplemented
36C5×D4×Dic3C2213yescomplemented
37C5×#926C2213yescomplemented
38C2×C4×C5×Dic3C2213yescomplemented
39#91572C2216yescomplemented
40#91569C2216yescomplemented
41#91569C2216yescomplemented
42#91564C2216yescomplemented
43#91546C2216yescomplemented
44C2×Dic3⋊Dic5C2213yescomplemented
45C2×#6667C2213yescomplemented
46#91537C2216yescomplemented
47C2×#6665C2213yescomplemented
48#91465C2213yescomplemented
49#91465C2213yescomplemented
50#91458C2213yescomplemented
51#91450C2213yescomplemented
52#91450C2213yescomplemented
53C4×#1202C2211yescharacteristic
54C4×#1202C2213yes—
55C4×#1202C2213yescomplemented
56C4×#1202C2213yescomplemented
57C4×#1202C2213yescomplemented
58C4×#1202C2213yescomplemented
59C4×#1202C2213yescomplemented
60C4×#1202C2213yescomplemented
61C4×#1202C2216yescomplemented
62#91390C2213yescomplemented
63#91390C2213yescomplemented
64#91389C2213yescomplemented
65#91374C2213yescomplemented
66#91364C2213yescomplemented
67#91360C2213yescomplemented
68#91360C2213yescomplemented
69#41×#67—51nomaximal, Hall
70C2×D5×#41—31no—
71C2×D5×#41D311yescharacteristic, complemented
72C4×C5×#41—31no—
73#65911—31no—
74#65910—31no—
75#65910—31no—
76Q8×D20—31no—
77#65889—33no—
78#65888—33no—
79#65888—33no—
80D4×D20—33no—
81#65858—33no—
82#65858—33no—
83#65811—33no—
84C2×C4×D20—33no—
85C23×D15C2313yes—
86C23×C3×D5C2313yes—
87C3×C5×#41D418yescomplemented
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×#1220C2316yes—
92C22×Dic15C2313yes—
93#6821—24no—
94Q8×D15—24no—
95#6819—212no—
96D4×D15—212no—
97#6817—212no—
98C2×D60C2313yes—
99C2×C4×D15—212no—
100C2×C4×D15C2311yescharacteristic
101C2×C4×D15C2313yes—
102C2×C4×D15C2313yes—
103C2×C4×D15C2313yes—
104C2×Dic30C2313yes—
105C22×C5×Dic3C2313yes—
106C22×C5×Dic3C2313yes—
107C2×C3×C22⋊D5C2316yes—
108C22×C3×Dic5C2313yes—
109C3×#713—24no—
110C3×Q8×D5—24no—
111C3×#711—212no—
112C3×D4×D5—212no—
113C3×#709—212no—
114C2×C3×D20C2313yes—
115C2×C3×C4×D5—212no—
116C2×C3×C4×D5C2311yescharacteristic
117C2×C3×C4×D5C2313yes—
118C2×C3×C4×D5C2313yes—
119C2×C3×C4×D5C2313yes—
120C2×C3×Dic10C2313yes—
121C2×#1202—212no—
122C2×#1202C2313yes—
123C2×#1202C2313yes—
124C2×#1202C2313yes—
125C2×#1202C2316yes—
126C2×#1202C2311yescharacteristic
127C5×#217C2316yes—
128C5×C4⋊Dic3C2313yes—
129C5×C4⋊Dic3C2313yes—
130C4×C5×Dic3C2311yescharacteristic
131C4×C5×Dic3C2313yes—
132C4×C5×Dic3C2313yes—
133C4×C5×Dic3C2313yes—
134Dic3⋊Dic5C2311yescharacteristic
135Dic3⋊Dic5C2313yes—
136Dic3⋊Dic5C2313yes—
137Dic3⋊Dic5C2313yes—
138Dic3⋊Dic5C2316yes—
139#6667C2311yescharacteristic
140#6667C2313yes—
141#6667C2313yes—
142#6667C2313yes—
143#6667C2316yes—
144#6665C2311yescharacteristic
145#6665C2313yes—
146#6665C2313yes—
147#6665C2313yes—
148#6665C2316yes—
149C22×C3×#41—51no—
150C2×D3×#41—51no—
151#5834—51no—
152#5832—53no—
153#5831—51no—
154#5829—53no—
155#5828—53no—
156Dic3×#41D511yescharacteristic, complemented
157#5824—53no—
158#5817—51no—
159Q8×#67—51no—
160#5806—53no—
161D4×#67—53no—
162#5791—53no—
163C2×C4×#67—53no—
164C2×C5×#41C2×D311yescharacteristic
165D5×#41—28no—
166D5×#41—68no—
167C2×#713—31no—
168C2×#713C2×D311yescharacteristic, complemented
169C2×Q8×D5—31no—
170C2×Q8×D5C2×D311yescharacteristic, complemented
171C2×#711—33no—
172C2×#711C2×D313yescomplemented
173C2×D4×D5—33no—
174C2×D4×D5C2×D313yescomplemented
175C2×#709—33no—
176C2×#709C2×D313yescomplemented
177C22×D20—33no—
178C22×C4×D5—33no—
179C22×C4×D5C2×D313yescomplemented
180C4×C5×Q8—31no—
181C4×C5×Q8—31no—
182C4×C5×D4—33no—
183C4×C5×D4—33no—
184C5×#117—33no—
185C2×C42×C5—33no—
186#4076—36no—
187#4076—36no—
188C2×#685—33no—
189C2×#685—33no—
190C2×C4⋊Dic5—33no—
191#4043—33no—
192#4043—33no—
193#4043—33no—
194#4043—33no—
195#4041—33no—
196#4041—33no—
197#4041—33no—
198#4041—33no—
199#4032—36no—
200#4032—36no—
201#4028—36no—
202#4028—36no—
203#4021—33no—
204#4021—33no—
205#4020—33no—
206C4×D20—31no—
207C4×D20—33no—
208C4×D20—33no—
209C4×D20—33no—
210C4×D20—33no—
211C4×D20—33no—
212C4×D20—33no—
213C4×D20—33no—
214C4×D20—36no—
215#4015—33no—
216D4×#41—151noSylow
217C23×C3×C5C2413yes—
218C22×D15—26no—
219C22×D15—26no—
220C22×D15—43no—
221C22×D15C2413yes—
222C22×D15C2411yescharacteristic
223C22×C3×D5—26no—
224C22×C3×D5—26no—
225C22×C3×D5—43no—
226C22×C3×D5C2413yes—
227C22×C3×D5C2411yescharacteristic
228C3×C5×Q8C2×D414yescomplemented
229C3×C5×D4C2×D4112yescomplemented
230C2×C3×C4×C5C2×D4112yescomplemented
231C2×C3×C4×C5C2411yescharacteristic
232C2×C3×C4×C5C2413yes—
233#1220—212no—
234C2×Dic15—26no—
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237D60—26no—
238C4×D15—22no—
239C4×D15—26no—
240C4×D15—26no—
241C4×D15—26no—
242Dic30—26no—
243C2×C5×Dic3—26no—
244C2×C5×Dic3—43no—
245C2×C5×Dic3C2411yescharacteristic
246C2×C5×Dic3C2413yes—
247C2×C5×Dic3C2413yes—
248C2×C5×Dic3C2411yescharacteristic
249C3×C22⋊D5—212no—
250C2×C3×Dic5—26no—
251C2×C3×Dic5C2413yes—
252C2×C3×Dic5C2411yescharacteristic
253C3×D20—26no—
254C3×C4×D5—22no—
255C3×C4×D5—26no—
256C3×C4×D5—26no—
257C3×C4×D5—26no—
258C3×Dic10—26no—
259#1202—26no—
260#1202—26no—
261#1202—26no—
262#1202—46no—
263#1202#4114yesdirect product factor
264C2×C3×#41—51no—
265C2×C3×#41—53no—
266C2×C3×#41—53no—
267C2×C3×#41—108no—
268C2×C3×#41C2×D511yescharacteristic
269C22×C3×Q8—51no—
270C22×C3×D4—53no—
271C23×C3×C4—53no—
272C22×#67—53no—
273D3×#41—108no—
274C2×#239—51no—
275C2×D3×Q8—51no—
276C2×#237—53no—
277C2×D3×D4—53no—
278C2×#235—53no—
279C22×C4×D3—53no—
280#953—56no—
281C2×#217—53no—
282#947—53no—
283#946—53no—
284#946—53no—
285Q8×Dic3C2×D511yescharacteristic, complemented
286Q8×Dic3C2×D511yescharacteristic, complemented
287#944—53no—
288#940—53no—
289#939—56no—
290#939—56no—
291#938—53no—
292#938—53no—
293#937—56no—
294#936—53no—
295#935—56no—
296D4×Dic3C2×D513yescomplemented
297D4×Dic3C2×D513yescomplemented
298#930—53no—
299#930—53no—
300#929—56no—
301C4×#67—51no—
302C4×#67—53no—
303C4×#67—53no—
304C4×#67—53no—
305C4×#67—53no—
306C4×#67—53no—
307C4×#67—53no—
308C4×#67—53no—
309C4×#67—56no—
310C2×(C2×D3)⋊C4—53no—
311#926C2×D513yescomplemented
312#924—53no—
313#924—53no—
314C2×Dic3⋊C4—53no—
315C2×C4×Dic3C2×D513yescomplemented
316C23×D5—33no—
317C23×D5C22×D313yes—
318C5×#41#6718yescomplemented
319C2×C5×Q8C22×D311yescharacteristic
320C2×C5×D4C22×D313yes—
321C22×C4×C5—33no—
322C22×C4×C5—33no—
323C22×C4×C5C22×D313yes—
324C2×C22⋊D5—36no—
325C2×C22⋊D5C22×D316yes—
326C22×Dic5—33no—
327C22×Dic5C22×D313yes—
328#713—24no—
329#713—64no—
330Q8×D5—24no—
331Q8×D5—64no—
332#711—212no—
333#711—612no—
334D4×D5—212no—
335D4×D5—612no—
336#709—212no—
337#709—612no—
338C2×D20—31no—
339C2×D20—33no—
340C2×D20—33no—
341C2×D20—33no—
342C2×D20—33no—
343C2×D20—36no—
344C2×D20—612no—
345C2×D20C22×D313yes—
346C2×C4×D5—212no—
347C2×C4×D5—31no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—33no—
351C2×C4×D5—612no—
352C2×C4×D5C22×D311yescharacteristic
353C2×C4×D5C22×D313yes—
354C2×C4×D5C22×D313yes—
355C2×C4×D5C22×D313yes—
356C2×Dic10—33no—
357C2×Dic10C22×D313yes—
358C5×C4⋊C4—33no—
359C5×C4⋊C4—33no—
360C5×C22⋊C4—36no—
361C42×C5—31no—
362C42×C5—33no—
363C42×C5—33no—
364C42×C5—33no—
365#685—31no—
366#685—33no—
367#685—33no—
368#685—33no—
369#685—36no—
370#685—31no—
371#685—33no—
372#685—33no—
373#685—33no—
374#685—36no—
375C4⋊Dic5—33no—
376C4⋊Dic5—36no—
377C4⋊Dic5—31no—
378C4⋊Dic5—33no—
379C4⋊Dic5—33no—
380C22×#41—51no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—151no—
384#548—151no—
385#548—151no—
386#547—153no—
387#546—153no—
388#546—153no—
389D42—153no—
390#532—153no—
391#525—153no—
392#525—153no—
393C4×#41—31no—
394C2×C4×D4—153no—
395C22×C3×C5—23no—
396C22×C3×C5—23no—
397C22×C3×C5C22×D416yes—
398C22×C3×C5C2511yescharacteristic
399C2×D15—21no—
400C2×D15—21no—
401C2×D15—23no—
402C2×D15—23no—
403C2×D15—23no—
404C2×D15—412no—
405C2×D15C2×#4112yescomplemented
406C2×C3×D5—21no—
407C2×C3×D5—21no—
408C2×C3×D5—23no—
409C2×C3×D5—23no—
410C2×C3×D5—23no—
411C2×C3×D5—412no—
412C2×C3×D5C2×#4112yescomplemented
413C3×C4×C5C22×D416yes—
414C3×C4×C5C22×D412yes—
415Dic15—23no—
416Dic15—21no—
417C3×Dic5—23no—
418C3×Dic5—21no—
419C5×Dic3—23no—
420C5×Dic3—23no—
421C5×Dic3—21no—
422C5×Dic3C2×#4112yescomplemented
423C24×C3—53no—
424C23×D3—53no—
425C3×#41—104no—
426C3×#41—1012no—
427C3×#41—1012no—
428C3×#41D2018yescomplemented
429C2×C3×Q8—53no—
430C2×C3×Q8—104no—
431C2×C3×Q8C22×D511yescharacteristic
432C2×C3×D4—56no—
433C2×C3×D4—53no—
434C2×C3×D4—1012no—
435C2×C3×D4C22×D513yes—
436C22×C3×C4—53no—
437C22×C3×C4—53no—
438C22×C3×C4—53no—
439C22×C3×C4—51no—
440C22×C3×C4—53no—
441C22×C3×C4—1012no—
442C22×C3×C4C22×D513yes—
443C2×#67—56no—
444C2×#67—51no—
445C2×#67—53no—
446C2×#67—53no—
447C2×#67—53no—
448C2×#67—56no—
449C2×#67—1012no—
450C22×Dic3—53no—
451C22×Dic3C22×D513yes—
452C22×Dic3C22×D513yes—
453#239—104no—
454D3×Q8—104no—
455#237—1012no—
456D3×D4—1012no—
457#235—1012no—
458C2×D12—53no—
459C2×C4×D3—51no—
460C2×C4×D3—53no—
461C2×C4×D3—53no—
462C2×C4×D3—53no—
463C2×C4×D3—1012no—
464C2×Dic6—53no—
465#217—53no—
466#217—56no—
467#217—51no—
468#217—53no—
469#217—53no—
470#217C22×D516yes—
471(C2×D3)⋊C4—51no—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—56no—
476C4⋊Dic3C22×D513yes—
477C4⋊Dic3C22×D513yes—
478Dic3⋊C4—51no—
479Dic3⋊C4—53no—
480Dic3⋊C4—53no—
481Dic3⋊C4—53no—
482Dic3⋊C4—56no—
483C4×Dic3C22×D511yescharacteristic
484C4×Dic3C22×D513yes—
485C4×Dic3C22×D513yes—
486C4×Dic3C22×D513yes—
487C23×C5C23×D313yes—
488C22×D5—26no—
489C22×D5—26no—
490C22×D5—31no—
491C22×D5—33no—
492C22×D5—43no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—123no—
496C22×D5C23×D313yes—
497C22×D5C23×D311yescharacteristic
498C5×Q8C2×#6714yescomplemented
499C5×D4C2×#67112yescomplemented
500C2×C4×C5—31no—
501C2×C4×C5—33no—
502C2×C4×C5—33no—
503C2×C4×C5—31no—
504C2×C4×C5—66no—
505C2×C4×C5—123no—
506C2×C4×C5C2×#67112yescomplemented
507C2×C4×C5C23×D313yes—
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—212no—
510C22⋊D5—612no—
511C2×Dic5—26no—
512C2×Dic5—33no—
513C2×Dic5—31no—
514C2×Dic5—66no—
515C2×Dic5C23×D313yes—
516C2×Dic5C23×D311yescharacteristic
517D20—26no—
518D20—34no—
519D20—66no—
520D20—66no—
521D20—66no—
522D20—66no—
523D20—126no—
524C4×D5—22no—
525C4×D5—26no—
526C4×D5—26no—
527C4×D5—26no—
528C4×D5—62no—
529C4×D5—66no—
530C4×D5—66no—
531C4×D5—66no—
532Dic10—26no—
533Dic10—66no—
534C2×#41—51no—
535C2×#41—53no—
536C2×#41—53no—
537C2×#41—108no—
538C2×#41—151no—
539C2×#41—153no—
540C2×#41—153no—
541C2×#41—308no—
542C2×#41D3×D511yescharacteristic
543C22×Q8—51no—
544C22×Q8—151no—
545C22×D4—53no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—53no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—153no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—153no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—153no—
561#121—153no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—156no—
566#120—156no—
567#120—156no—
568C4×Q8—31no—
569C4×Q8—31no—
570C4×D4—33no—
571C4×D4—33no—
572C4×D4—151no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—156no—
581#117—33no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—33no—
586C2×C3×C5—26no—
587C2×C3×C5C23×D411yescharacteristic
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5#58511yescharacteristic
590D15—22no—
591D15—43no—
592C3×D5—22no—
593C3×D5—43no—
594C23×C3—51no—
595C23×C3—53no—
596C23×C3—106no—
597C23×C3—106no—
598C23×C3—203no—
599C23×C3C23×D513yes—
600C22×D3—51no—
601C22×D3—53no—
602C22×D3—106no—
603C22×D3—106no—
604C22×D3—203no—
605C3×Q8—106no—
606C3×Q8C2×D2014yescomplemented
607C3×D4—1012no—
608C3×D4—106no—
609C3×D4C2×D20112yescomplemented
610C2×C3×C4—51no—
611C2×C3×C4—53no—
612C2×C3×C4—106no—
613C2×C3×C4—102no—
614C2×C3×C4—106no—
615C2×C3×C4—106no—
616C2×C3×C4—106no—
617C2×C3×C4C2×D20112yescomplemented
618C2×C3×C4C23×D513yes—
619C2×C3×C4C23×D511yescharacteristic
620#67—54no—
621#67—106no—
622#67—106no—
623#67—1012no—
624#67—106no—
625#67—206no—
626C2×Dic3—26no—
627C2×Dic3—43no—
628C2×Dic3—53no—
629C2×Dic3—51no—
630C2×Dic3—106no—
631C2×Dic3C23×D511yescharacteristic
632C2×Dic3C23×D513yes—
633C2×Dic3C23×D513yes—
634C2×Dic3C23×D511yescharacteristic
635D12—106no—
636C4×D3—102no—
637C4×D3—106no—
638C4×D3—106no—
639C4×D3—106no—
640Dic6—106no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5C22×#6716yes—
644C22×C5C24×D311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—23no—
648C2×D5—23no—
649C2×D5—23no—
650C2×D5—32no—
651C2×D5—412no—
652C2×D5—61no—
653C2×D5—61no—
654C2×D5—63no—
655C2×D5—63no—
656C2×D5—63no—
657C2×D5—1212no—
658C2×D5D3×#4112yescomplemented
659C4×C5—32no—
660C4×C5—63no—
661C4×C5—63no—
662C4×C5—61no—
663C4×C5C22×#6716yes—
664C4×C5C22×#6712yes—
665Dic5—23no—
666Dic5—21no—
667Dic5—63no—
668Dic5—61no—
669C24—53no—
670C24—153no—
671#41—104no—
672#41—1012no—
673#41—1012no—
674#41—304no—
675#41—3012no—
676#41—3012no—
677#41#120218yesdirect product factor
678C2×Q8—53no—
679C2×Q8—104no—
680C2×Q8—153no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—56no—
684C2×D4—53no—
685C2×D4—1012no—
686C2×D4—151no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—156no—
691C2×D4—156no—
692C2×D4—153no—
693C2×D4—3012no—
694C2×D4—3012no—
695C2×D4C2×D3×D513yes—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—53no—
699C22×C4—53no—
700C22×C4—53no—
701C22×C4—51no—
702C22×C4—53no—
703C22×C4—1012no—
704C22×C4—153no—
705C22×C4—153no—
706C22×C4—153no—
707C22×C4—151no—
708C22×C4—153no—
709C22×C4—3012no—
710C22×C4C2×D3×D513yes—
711C4⋊C4—33no—
712C4⋊C4—33no—
713C4⋊C4—151no—
714C4⋊C4—153no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—156no—
718C22⋊C4—36no—
719C22⋊C4—151no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—153no—
723C22⋊C4—156no—
724C22⋊C4—151no—
725C22⋊C4—153no—
726C22⋊C4—153no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—33no—
730C42—33no—
731C42—31no—
732C42—33no—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—23no—
735C22×C3—23no—
736C22×C3—52no—
737C22×C3—101no—
738C22×C3—101no—
739C22×C3—103no—
740C22×C3—103no—
741C22×C3—103no—
742C22×C3—2012no—
743C22×C3C22×D2016yes—
744C22×C3C24×D511yescharacteristic
745C2×D3—52no—
746C2×D3—101no—
747C2×D3—101no—
748C2×D3—103no—
749C2×D3—103no—
750C2×D3—103no—
751C2×D3—2012no—
752C3×C4—101no—
753C3×C4—103no—
754C3×C4C22×D2016yes—
755C3×C4C22×D2012yes—
756Dic3—23no—
757Dic3—21no—
758Dic3—23no—
759Dic3—103no—
760Dic3—101no—
761Dic3D5×#4112yescomplemented
762C2×C5—26no—
763C2×C5C2×D3×#4111yescharacteristic
764C2×C5#596411yescharacteristic
765C2×C5C23×#6711yescharacteristic
766D5—22no—
767D5—43no—
768D5—62no—
769D5—123no—
770C23—51no—
771C23—53no—
772C23—106no—
773C23—106no—
774C23—151no—
775C23—153no—
776C23—203no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23C22×D3×D513yes—
781Q8—106no—
782Q8—306no—
783Q8C2×#120214yescomplemented
784D4—1012no—
785D4—106no—
786D4—154no—
787D4—306no—
788D4—306no—
789D4—306no—
790D4—3012no—
791D4—306no—
792D4—606no—
793D4C2×#1202112yescomplemented
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—33no—
797C2×C4—33no—
798C2×C4—51no—
799C2×C4—53no—
800C2×C4—66no—
801C2×C4—106no—
802C2×C4—102no—
803C2×C4—106no—
804C2×C4—106no—
805C2×C4—106no—
806C2×C4—123no—
807C2×C4—151no—
808C2×C4—153no—
809C2×C4—306no—
810C2×C4—302no—
811C2×C4—306no—
812C2×C4—306no—
813C2×C4—306no—
814C2×C4C2×#1202112yescomplemented
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D511yescharacteristic
817C2×C3—26no—
818C2×C3—102no—
819C2×C3—203no—
820C2×C3C23×D2011yescharacteristic
821C2×C3C2×D5×#4111yescharacteristic
822C2×C3#6628311yescharacteristic
823D3—102no—
824D3—203no—
825C5#41×#6711yescharacteristic, complemented, Sylow
826C22—23no—
827C22—23no—
828C22—52no—
829C22—101no—
830C22—101no—
831C22—103no—
832C22—103no—
833C22—103no—
834C22—152no—
835C22—2012no—
836C22—301no—
837C22—301no—
838C22—303no—
839C22—303no—
840C22—303no—
841C22—6012no—
842C22C22×#120216yes—
843C22C23×D3×D511yescharacteristic
844C4—32no—
845C4—61no—
846C4—63no—
847C4—63no—
848C4—101no—
849C4—103no—
850C4—301no—
851C4—303no—
852C4C22×#120212yes—
853C4C22×#120216yes—
854C3#41×D2011yescharacteristic, complemented, Sylow
855C2—26no—
856C2—102no—
857C2—203no—
858C2—302no—
859C2—603no—
860C2D3×D5×#4111yescharacteristic
861C2#1175705811yescharacteristic
862C2C23×#120211yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C2×C3×D5×#41C2semidirect
3. C5×Dic3×#41C2semidirect
4. #11755257C2semidirect
5. #11755251C2semidirect
6. Q8×#1202C2semidirect
7. #11755128C2semidirect
8. #11754980C2semidirect
9. #11754972C2semidirect
10. #11754963C2semidirect
11. D4×#1202C2semidirect
12. #11754590C2semidirect
13. #11754581C2semidirect
14. #11754564C2semidirect
15. C2×C4×#1202C2semidirect
19. C2×#6821C22semidirect
20. C2×Q8×D15C22semidirect
21. C2×#6819C22semidirect
22. C2×D4×D15C22semidirect
23. C2×#6817C22semidirect
24. C22×C4×D15C22semidirect
26. C2×C3×#713C22semidirect
27. C2×C3×Q8×D5C22semidirect
28. C2×C3×#711C22semidirect
29. C2×C3×D4×D5C22semidirect
30. C2×C3×#709C22semidirect
31. C22×C3×C4×D5C22semidirect
33. C5×Q8×Dic3C22semidirect
34. C5×Q8×Dic3C22semidirect
35. C5×D4×Dic3C22semidirect
36. C5×D4×Dic3C22semidirect
37. C5×#926C22semidirect
38. C2×C4×C5×Dic3C22semidirect
39. #91572C22semidirect
40. #91569C22semidirect
41. #91569C22semidirect
42. #91564C22semidirect
43. #91546C22semidirect
44. C2×Dic3⋊Dic5C22semidirect
45. C2×#6667C22semidirect
46. #91537C22semidirect
47. C2×#6665C22semidirect
48. #91465C22semidirect
49. #91465C22semidirect
50. #91458C22semidirect
51. #91450C22semidirect
52. #91450C22semidirect
55. C4×#1202C22semidirect
56. C4×#1202C22semidirect
57. C4×#1202C22semidirect
58. C4×#1202C22semidirect
59. C4×#1202C22semidirect
60. C4×#1202C22semidirect
61. C4×#1202C22semidirect
62. #91390C22semidirect
63. #91390C22semidirect
64. #91389C22semidirect
65. #91374C22semidirect
66. #91364C22semidirect
67. #91360C22semidirect
68. #91360C22semidirect
71. C2×D5×#41D3semidirect
87. C3×C5×#41D4semidirect
156. Dic3×#41D5semidirect
168. C2×#713C2×D3semidirect
170. C2×Q8×D5C2×D3semidirect
172. C2×#711C2×D3semidirect
174. C2×D4×D5C2×D3semidirect
176. C2×#709C2×D3semidirect
179. C22×C4×D5C2×D3semidirect
228. C3×C5×Q8C2×D4semidirect
229. C3×C5×D4C2×D4semidirect
230. C2×C3×C4×C5C2×D4semidirect
263. #1202#41direct (N × H)
285. Q8×Dic3C2×D5semidirect
286. Q8×Dic3C2×D5semidirect
296. D4×Dic3C2×D5semidirect
297. D4×Dic3C2×D5semidirect
311. #926C2×D5semidirect
315. C2×C4×Dic3C2×D5semidirect
318. C5×#41#67semidirect
405. C2×D15C2×#41semidirect
412. C2×C3×D5C2×#41semidirect
422. C5×Dic3C2×#41semidirect
428. C3×#41D20semidirect
498. C5×Q8C2×#67semidirect
499. C5×D4C2×#67semidirect
506. C2×C4×C5C2×#67semidirect
606. C3×Q8C2×D20semidirect
609. C3×D4C2×D20semidirect
617. C2×C3×C4C2×D20semidirect
658. C2×D5D3×#41semidirect
677. #41#1202direct (N × H)
733. C3×C5D4×#41semidirect
761. Dic3D5×#41semidirect
783. Q8C2×#1202semidirect
793. D4C2×#1202semidirect
814. C2×C4C2×#1202semidirect
825. C5#41×#67semidirect
854. C3#41×D20semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C2×C3×D5×#412
C5×Dic3×#412
#117552572
#117552512
Q8×#12022
#117551282
#117549802
#117549722
#117549632
D4×#12022
#117545902
#117545812
#117545642
C2×C4×#12022
#41×D203
#41×#675