Finite Group Databasebeta

← #67×#713 #14483207

Subgroups — #67×#713 #14483207

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
1C22×C3×#713C211yesmaximal, characteristic, complemented
2C2×D3×#713C211yesmaximal, characteristic, complemented
3#11756576C211yesmaximal, characteristic, complemented
4C5×Q8×#67C211yesmaximal, characteristic, complemented
5#11755273C213yesmaximal, complemented
6#11755270C213yesmaximal, complemented
7#11755251C211yesmaximal, characteristic, complemented
8#11755247C211yesmaximal, characteristic, complemented
9Dic3×#713C211yesmaximal, characteristic, complemented
10#11755159C213yesmaximal, complemented
11#11755157C213yesmaximal, complemented
12#67×D20C213yesmaximal, complemented
13C4×D5×#67C213yesmaximal, complemented
14#11754527C213yesmaximal, complemented
15#11754308C213yesmaximal, complemented
16D4×#713—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×#6821C2211yescharacteristic, complemented
19C2×C5×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#713—28no—
21C2×C3×#713C2211yescharacteristic
22C2×C3×#713C2213yescomplemented
23C2×C3×#713C2213yescomplemented
24C2×C3×#713C2211yescharacteristic, complemented
25C22×C3×D20C2213yescomplemented
26C22×C3×C4×D5C2213yescomplemented
27C2×D5×#67C2213yes—
28D3×#713—28no—
29C2×D3×D20C2213yescomplemented
30C2×C4×D3×D5C2213yescomplemented
31C2×#6773C2213yescomplemented
32C2×#6766C2213yescomplemented
33#91836C2213yescomplemented
34#91835C2213yescomplemented
35Q8×Dic15C2211yescharacteristic, complemented
36#91819C2213yescomplemented
37C4×#1220C2213yescomplemented
38C5×#946C2213yescomplemented
39C5×Q8×Dic3C2211yescharacteristic, complemented
40C5×#944C2213yescomplemented
41C4×C5×#67C2213yes—
42C5×#924C2213yescomplemented
43#91564C2216yescomplemented
44#91552C2213yescomplemented
45Dic5×#67C2211yescharacteristic
46D5×#217C2213yescomplemented
47#91474C2216yescomplemented
48D5×(C2×D3)⋊C4C2213yescomplemented
49#91465C2213yescomplemented
50#91458C2213yescomplemented
51#91456C2213yescomplemented
52#91450C2213yescomplemented
53#91444C2216yescomplemented
54#91444C2213yescomplemented
55C4×#1202C2213yescomplemented
56#91440C2213yescomplemented
57C4×#1201C2213yescomplemented
58#91434C2213yescomplemented
59Dic3×D20C2213yescomplemented
60#91409C2216yescomplemented
61#91409C2216yescomplemented
62#91407C2216yescomplemented
63D5×Dic3⋊C4C2213yescomplemented
64C4×D5×Dic3C2213yescomplemented
65#91368C2213yescomplemented
66#91359C2213yescomplemented
67#91358C2213yescomplemented
68#91348C2216yescomplemented
69#41×#67—51nomaximal, Hall
70C22×#713—31no—
71C22×#713D311yescharacteristic, complemented
72C5×D4×Q8—31no—
73#66151—31no—
74#66151—31no—
75#66060—33no—
76#66059—33no—
77#65964—33no—
78#65964—33no—
79#65961—33no—
80#65961—33no—
81#65911—31no—
82C4×#713—31no—
83D4×D20—33no—
84C4×D4×D5—33no—
85C23×C3×D5C2313yes—
86C22×D3×D5C2313yes—
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C2×#1220C2313yes—
92#6821—24no—
93C2×D60C2313yes—
94C2×C4×D15C2313yes—
95C2×C5×#67C2311yescharacteristic
96C5×D3×Q8—24no—
97C2×C4×C5×D3C2313yes—
98C2×C5×Dic6C2313yes—
99C22×C3×Dic5C2311yescharacteristic
100C3×#713—24no—
101C3×#713—212no—
102C3×#713—212no—
103C3×#713D418yescomplemented
104C2×C3×D20—212no—
105C2×C3×D20C2316yes—
106C2×C3×D20C2313yes—
107C2×C3×D20C2313yes—
108C2×C3×C4×D5—212no—
109C2×C3×C4×D5C2313yes—
110C2×C3×C4×D5C2313yes—
111C2×C3×C4×D5C2313yes—
112C2×C3×C4×D5C2313yes—
113D5×#67—212no—
114C2×#1202C2313yes—
115C2×#1202C2316yes—
116C2×#1202C2316yes—
117C2×#1201C2313yes—
118C2×#1200C2313yes—
119C2×D3×Dic5C2311yescharacteristic
120C2×D5×Dic3C2313yes—
121C2×D5×Dic3C2313yes—
122C2×D5×Dic3C2313yes—
123D3×D20—212no—
124C4×D3×D5—212no—
125#6773—212no—
126#6766—212no—
127#6719C2311yescharacteristic
128#6714C2313yes—
129#6714C2316yes—
130C4⋊Dic15C2313yes—
131#6712C2313yes—
132C4×Dic15C2313yes—
133C5×#217C2313yes—
134C5×(C2×D3)⋊C4C2313yes—
135C5×C4⋊Dic3C2313yes—
136C5×Dic3⋊C4C2313yes—
137C5×Dic3⋊C4C2316yes—
138C4×C5×Dic3C2313yes—
139Dic3⋊Dic5C2311yescharacteristic
140#6669C2313yes—
141#6667C2313yes—
142(C2×D3)⋊Dic5C2311yescharacteristic
143#6665C2313yes—
144#6665C2316yes—
145#6665C2316yes—
146#6665C2313yes—
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2311yescharacteristic
149C22×C3×#41—51no—
150C2×D3×#41—51no—
151#5834—51no—
152#5832—53no—
153#5831—51no—
154#5829—53no—
155#5828—53no—
156Dic3×#41—51no—
157#5824—53no—
158#5817—51no—
159Q8×#67D511yescharacteristic, complemented
160#5806—53no—
161D4×#67—53no—
162#5791—53no—
163C2×C4×#67—53no—
164C22×C5×Q8—31no—
165C22×C5×Q8C2×D311yescharacteristic, complemented
166C2×#713—28no—
167C2×#713—31no—
168C2×#713—33no—
169C2×#713—33no—
170C2×#713—68no—
171C2×#713C2×D311yescharacteristic
172C2×#713C2×D313yescomplemented
173C2×#713C2×D313yescomplemented
174C2×#713C2×D311yescharacteristic, complemented
175C2×D4×D5—33no—
176C22×D20—33no—
177C22×D20C2×D313yescomplemented
178C22×C4×D5—33no—
179C22×C4×D5C2×D313yescomplemented
180C5×C4⋊Q8—33no—
181C5×C22⋊Q8—33no—
182C5×C22⋊Q8—33no—
183C4×C5×Q8—31no—
184C4×C5×D4—33no—
185#4093—33no—
186#4093—33no—
187#4092—33no—
188#4092—33no—
189Q8×Dic5—31no—
190D4×Dic5—31no—
191#4076—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5—33no—
195#4041—36no—
196#4041—36no—
197#4041—33no—
198#4041—33no—
199#4040—36no—
200#4040—36no—
201#4039—33no—
202#4039—33no—
203#4039—36no—
204#4038—33no—
205D5×C4⋊C4—33no—
206#4028—36no—
207#4028—36no—
208#4027—33no—
209#4027—33no—
210D5×C22⋊C4—33no—
211D5×C22⋊C4—33no—
212#4020—33no—
213C4×D20—33no—
214C4×D20—33no—
215C42×D5—33no—
216D4×#41—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15C2413yes—
219C22×C5×D3C2411yescharacteristic
220C22×C3×D5—26no—
221C22×C3×D5—26no—
222C22×C3×D5—43no—
223C22×C3×D5C2413yes—
224C22×C3×D5C2413yes—
225C2×D3×D5—26no—
226C2×D3×D5—26no—
227C2×D3×D5—43no—
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2413yes—
232C2×C3×C4×C5C2413yes—
233#1220—26no—
234C2×Dic15C2413yes—
235C2×Dic15C2411yescharacteristic
236C2×Dic15C2411yescharacteristic
237D60—26no—
238C4×D15—26no—
239C5×#67#4114yescomplemented
240C2×C5×Dic3C2413yes—
241C2×C5×Dic3C2413yes—
242C2×C5×Dic3C2411yescharacteristic
243C4×C5×D3—26no—
244C5×Dic6—26no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5C2411yescharacteristic
247C2×C3×Dic5C2411yescharacteristic
248C3×D20—212no—
249C3×D20—26no—
250C3×D20C2×D4112yescomplemented
251C3×C4×D5—26no—
252C3×C4×D5—26no—
253C3×C4×D5—26no—
254C3×C4×D5C2×D4112yescomplemented
255#1202—212no—
256#1202—26no—
257#1202—46no—
258#1201—26no—
259#1200—26no—
260D3×Dic5—22no—
261D5×Dic3—26no—
262D5×Dic3—26no—
263D5×Dic3—43no—
264C2×C3×#41—51no—
265C2×C3×#41—53no—
266C2×C3×#41—53no—
267C2×C3×#41—51no—
268C2×C3×#41—108no—
269C22×C3×Q8C2×D511yescharacteristic, complemented
270C22×C3×D4—53no—
271C23×C3×C4—53no—
272C22×#67—53no—
273D3×#41—108no—
274C2×#239—51no—
275C2×D3×Q8C2×D511yescharacteristic, complemented
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#946C2×D513yescomplemented
285Q8×Dic3—51no—
286Q8×Dic3C2×D511yescharacteristic, complemented
287#944C2×D513yescomplemented
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×Dic3—53no—
297D4×Dic3—53no—
298#930—53no—
299#930—53no—
300#929—56no—
301C4×#67—53no—
302C4×#67—51no—
303C4×#67—53no—
304C4×#67—53no—
305C4×#67—53no—
306C4×#67—53no—
307C4×#67—56no—
308C4×#67—53no—
309C4×#67C2×D513yes—
310C2×(C2×D3)⋊C4—53no—
311#926—53no—
312#924—53no—
313#924C2×D513yescomplemented
314C2×Dic3⋊C4—53no—
315C2×C4×Dic3—53no—
316C23×D5—33no—
317C23×D5C22×D313yes—
318C2×C5×Q8—24no—
319C2×C5×Q8—33no—
320C2×C5×Q8—64no—
321C2×C5×Q8C22×D313yes—
322C2×C5×Q8C22×D311yescharacteristic
323C2×C5×D4—31no—
324C22×C4×C5—33no—
325C22×C4×C5C22×D313yes—
326C2×C22⋊D5—33no—
327C2×C22⋊D5—33no—
328C22×Dic5—31no—
329C22×Dic5C22×D311yescharacteristic
330#713—24no—
331#713—212no—
332#713—212no—
333#713—64no—
334#713—612no—
335#713—612no—
336#713#6718yesdirect product factor
337D4×D5—612no—
338C2×D20—212no—
339C2×D20—36no—
340C2×D20—33no—
341C2×D20—33no—
342C2×D20—36no—
343C2×D20—612no—
344C2×D20C22×D313yes—
345C2×D20C22×D316yes—
346C2×D20C22×D313yes—
347C2×C4×D5—212no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—33no—
351C2×C4×D5—33no—
352C2×C4×D5—33no—
353C2×C4×D5—612no—
354C2×C4×D5C22×D313yes—
355C2×C4×D5C22×D313yes—
356C2×C4×D5C22×D313yes—
357C2×C4×D5C22×D313yes—
358C5×C4⋊C4—33no—
359C5×C4⋊C4—33no—
360C5×C4⋊C4—36no—
361C5×C22⋊C4—33no—
362C5×C22⋊C4—33no—
363C42×C5—33no—
364C22⋊Dic5—31no—
365C22⋊Dic5—31no—
366#685—33no—
367#685—36no—
368#685—33no—
369#685—36no—
370#685—33no—
371#685—36no—
372#685—33no—
373C4⋊Dic5—33no—
374C4⋊Dic5—31no—
375#683—33no—
376#683—33no—
377C4×Dic5—33no—
378C4×Dic5—31no—
379C4×Dic5—33no—
380C22×#41—51no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—31no—
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—151no—
394C2×C4×D4—153no—
395C22×C3×C5—21no—
396C22×C3×C5—21no—
397C22×C3×C5C2×#4112yescomplemented
398C22×C3×C5C2511yescharacteristic
399C2×D15—23no—
400C2×D15—23no—
401C2×D15—23no—
402C2×C5×D3—21no—
403C2×C5×D3—21no—
404C2×C5×D3C2×#4112yescomplemented
405C2×C3×D5—23no—
406C2×C3×D5—23no—
407C2×C3×D5—23no—
408C2×C3×D5—23no—
409C2×C3×D5—23no—
410C2×C3×D5—412no—
411C2×C3×D5C22×D416yes—
412D3×D5—412no—
413C3×C4×C5—23no—
414C3×C4×C5C22×D416yes—
415Dic15—21no—
416Dic15—23no—
417Dic15—21no—
418C3×Dic5—21no—
419C3×Dic5C22×D412yes—
420C5×Dic3—23no—
421C5×Dic3—23no—
422C5×Dic3C2×#4112yescomplemented
423C24×C3—53no—
424C23×D3—53no—
425C3×#41—58no—
426C3×#41—1012no—
427C3×#41—1012no—
428C3×#41—104no—
429C2×C3×Q8—24no—
430C2×C3×Q8C22×D513yes—
431C2×C3×Q8C22×D511yescharacteristic
432C2×C3×D4—53no—
433C2×C3×D4—56no—
434C2×C3×D4—53no—
435C2×C3×D4—1012no—
436C22×C3×C4—53no—
437C22×C3×C4—51no—
438C22×C3×C4—53no—
439C22×C3×C4—53no—
440C22×C3×C4—53no—
441C22×C3×C4—1012no—
442C22×C3×C4C22×D513yes—
443C2×#67—53no—
444C2×#67—53no—
445C2×#67—53no—
446C2×#67—56no—
447C2×#67—56no—
448C2×#67—1012no—
449C2×#67C22×D511yescharacteristic
450C22×Dic3—53no—
451C22×Dic3—53no—
452C22×Dic3—53no—
453#239—104no—
454D3×Q8—24no—
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—1012no—
463C2×C4×D3C22×D513yes—
464C2×Dic6C22×D513yes—
465#217—51no—
466#217—56no—
467#217—56no—
468#217—53no—
469#217—53no—
470#217C22×D513yes—
471(C2×D3)⋊C4—51no—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—56no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4C22×D513yes—
476C4⋊Dic3—53no—
477C4⋊Dic3C22×D513yes—
478Dic3⋊C4—53no—
479Dic3⋊C4—53no—
480Dic3⋊C4—51no—
481Dic3⋊C4C22×D513yes—
482Dic3⋊C4C22×D516yes—
483C4×Dic3—53no—
484C4×Dic3—51no—
485C4×Dic3—53no—
486C4×Dic3C22×D513yes—
487C23×C5—31no—
488C23×C5C23×D311yescharacteristic
489C22×D5—26no—
490C22×D5—26no—
491C22×D5—33no—
492C22×D5—43no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—123no—
496C22×D5C23×D313yes—
497C22×D5C23×D313yes—
498C5×Q8—26no—
499C5×Q8—66no—
500C5×Q8C2×#6714yescomplemented
501C5×D4—34no—
502C2×C4×C5—26no—
503C2×C4×C5—31no—
504C2×C4×C5—33no—
505C2×C4×C5—33no—
506C2×C4×C5—66no—
507C2×C4×C5C23×D313yes—
508C2×C4×C5C23×D313yes—
509C22⋊D5—66no—
510C22⋊D5—66no—
511C2×Dic5—22no—
512C2×Dic5—31no—
513C2×Dic5—33no—
514C2×Dic5—31no—
515C2×Dic5—62no—
516C2×Dic5C23×D311yescharacteristic
517C2×Dic5C23×D311yescharacteristic
518D20—212no—
519D20—26no—
520D20—66no—
521D20—612no—
522D20—66no—
523D20—126no—
524D20C2×#67112yescomplemented
525C4×D5—26no—
526C4×D5—26no—
527C4×D5—26no—
528C4×D5—66no—
529C4×D5—66no—
530C4×D5—66no—
531C4×D5—66no—
532C4×D5—123no—
533C4×D5C2×#67112yescomplemented
534C2×#41—51no—
535C2×#41—53no—
536C2×#41—53no—
537C2×#41—51no—
538C2×#41—108no—
539C2×#41—153no—
540C2×#41—153no—
541C2×#41—151no—
542C2×#41—308no—
543C22×Q8—31no—
544C22×Q8D3×D511yescharacteristic, complemented
545C22×D4—53no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—53no—
549C23×C4—153no—
550C4⋊Q8—33no—
551#127—153no—
552#124—153no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—33no—
557C22⋊Q8—33no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—153no—
561#121—153no—
562#121—156no—
563#121—156no—
564#121—153no—
565#121—153no—
566#120—156no—
567#120—156no—
568C4×Q8—31no—
569C4×Q8—151no—
570C4×D4—33no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—156no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—151no—
580C4×D4—153no—
581#117—153no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—153no—
586C2×C3×C5—22no—
587C2×C3×C5C23×D411yescharacteristic
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5#58511yescharacteristic
590D15—43no—
591C3×D5—26no—
592C3×D5—43no—
593C5×D3—22no—
594C23×C3—53no—
595C23×C3—53no—
596C23×C3—106no—
597C23×C3—106no—
598C23×C3—203no—
599C23×C3C23×D511yescharacteristic
600C22×D3—53no—
601C22×D3—106no—
602C22×D3—106no—
603C22×D3—203no—
604C22×D3C23×D511yescharacteristic
605C3×Q8—26no—
606C3×Q8D4×D514yescomplemented
607C3×D4—512no—
608C3×D4—1012no—
609C3×D4—106no—
610C2×C3×C4—26no—
611C2×C3×C4—51no—
612C2×C3×C4—512no—
613C2×C3×C4—51no—
614C2×C3×C4—106no—
615C2×C3×C4—106no—
616C2×C3×C4—102no—
617C2×C3×C4—106no—
618C2×C3×C4C23×D513yes—
619C2×C3×C4C23×D513yes—
620#67—1012no—
621#67—106no—
622#67—106no—
623#67—106no—
624#67—206no—
625#67#71314yesdirect product factor
626C2×Dic3—51no—
627C2×Dic3—53no—
628C2×Dic3—51no—
629C2×Dic3—106no—
630C2×Dic3—106no—
631C2×Dic3—203no—
632C2×Dic3C23×D513yes—
633C2×Dic3C23×D513yes—
634C2×Dic3C23×D511yescharacteristic
635D12—106no—
636C4×D3—26no—
637C4×D3—106no—
638C4×D3—102no—
639C4×D3—106no—
640Dic6—26no—
641C22×C5—21no—
642C22×C5—21no—
643C22×C5—32no—
644C22×C5—61no—
645C22×C5—61no—
646C22×C5D3×#4112yescomplemented
647C22×C5C24×D311yescharacteristic
648C2×D5—23no—
649C2×D5—23no—
650C2×D5—23no—
651C2×D5—23no—
652C2×D5—23no—
653C2×D5—412no—
654C2×D5—63no—
655C2×D5—63no—
656C2×D5—63no—
657C2×D5—1212no—
658C2×D5C22×#6716yes—
659C4×C5—23no—
660C4×C5—32no—
661C4×C5—63no—
662C4×C5—63no—
663C4×C5C22×#6716yes—
664Dic5—21no—
665Dic5—63no—
666Dic5—61no—
667Dic5—61no—
668Dic5C22×#6712yes—
669C24—53no—
670C24—153no—
671#41—58no—
672#41—1012no—
673#41—1012no—
674#41—104no—
675#41—3012no—
676#41—3012no—
677#41—304no—
678C2×Q8—24no—
679C2×Q8—33no—
680C2×Q8—64no—
681C2×Q8C2×D3×D513yes—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—31no—
684C2×D4—53no—
685C2×D4—56no—
686C2×D4—53no—
687C2×D4—1012no—
688C2×D4—153no—
689C2×D4—156no—
690C2×D4—156no—
691C2×D4—153no—
692C2×D4—153no—
693C2×D4—153no—
694C2×D4—3012no—
695C2×D4—3012no—
696C22×C4—33no—
697C22×C4—53no—
698C22×C4—51no—
699C22×C4—53no—
700C22×C4—53no—
701C22×C4—53no—
702C22×C4—1012no—
703C22×C4—153no—
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—36no—
714C4⋊C4—151no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—153no—
718C22⋊C4—33no—
719C22⋊C4—33no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—153no—
723C22⋊C4—156no—
724C22⋊C4—156no—
725C22⋊C4—151no—
726C22⋊C4—151no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—33no—
730C42—151no—
731C42—153no—
732C42—153no—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—56no—
737C22×C3—103no—
738C22×C3—103no—
739C22×C3—103no—
740C22×C3—103no—
741C22×C3—103no—
742C22×C3—2012no—
743C22×C3C2×#71312yescomplemented
744C22×C3C24×D511yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—103no—
748C2×D3—103no—
749C2×D3—103no—
750C2×D3—2012no—
751C2×D3C2×#71312yescomplemented
752C3×C4—23no—
753C3×C4—52no—
754C3×C4—101no—
755C3×C4C2×D4×D516yes—
756Dic3—23no—
757Dic3—23no—
758Dic3—101no—
759Dic3—103no—
760Dic3—101no—
761Dic3C2×#71312yescomplemented
762C2×C5—22no—
763C2×C5—62no—
764C2×C5C2×D3×#4111yescharacteristic
765C2×C5#596411yescharacteristic
766C2×C5C23×#6711yescharacteristic
767D5—26no—
768D5—43no—
769D5—123no—
770C23—31no—
771C23—53no—
772C23—53no—
773C23—106no—
774C23—106no—
775C23—153no—
776C23—203no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23C22×D3×D511yescharacteristic
781Q8—26no—
782Q8—66no—
783Q8D5×#6714yescomplemented
784D4—34no—
785D4—512no—
786D4—1012no—
787D4—106no—
788D4—306no—
789D4—3012no—
790D4—306no—
791D4—306no—
792D4—306no—
793D4—606no—
794C2×C4—26no—
795C2×C4—31no—
796C2×C4—33no—
797C2×C4—33no—
798C2×C4—51no—
799C2×C4—512no—
800C2×C4—51no—
801C2×C4—66no—
802C2×C4—106no—
803C2×C4—106no—
804C2×C4—102no—
805C2×C4—106no—
806C2×C4—151no—
807C2×C4—153no—
808C2×C4—151no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4—302no—
812C2×C4—306no—
813C2×C4—306no—
814C2×C4—603no—
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D513yes—
817C2×C3—22no—
818C2×C3—106no—
819C2×C3—203no—
820C2×C3C22×D4×D511yescharacteristic
821C2×C3C22×#71311yescharacteristic
822C2×C3#6628711yescharacteristic
823D3—22no—
824D3—203no—
825C5#41×#6711yescharacteristic, complemented, Sylow
826C22—21no—
827C22—21no—
828C22—32no—
829C22—56no—
830C22—61no—
831C22—61no—
832C22—103no—
833C22—103no—
834C22—103no—
835C22—103no—
836C22—103no—
837C22—2012no—
838C22—303no—
839C22—303no—
840C22—303no—
841C22—6012no—
842C22D3×#71312yescomplemented
843C22C23×D3×D511yescharacteristic
844C4—23no—
845C4—32no—
846C4—52no—
847C4—63no—
848C4—63no—
849C4—101no—
850C4—301no—
851C4—303no—
852C4—301no—
853C4C2×D5×#6716yes—
854C3D4×#71311yescharacteristic, complemented, Sylow
855C2—22no—
856C2—62no—
857C2—106no—
858C2—203no—
859C2—603no—
860C2C2×D3×#71311yescharacteristic
861C2#1175704811yescharacteristic
862C2C22×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#713C2semidirect
2. C2×D3×#713C2semidirect
3. #11756576C2semidirect
4. C5×Q8×#67C2semidirect
5. #11755273C2semidirect
6. #11755270C2semidirect
7. #11755251C2semidirect
8. #11755247C2semidirect
9. Dic3×#713C2semidirect
10. #11755159C2semidirect
11. #11755157C2semidirect
12. #67×D20C2semidirect
13. C4×D5×#67C2semidirect
14. #11754527C2semidirect
15. #11754308C2semidirect
17. C22×C3×C5×Q8C22semidirect
18. C2×#6821C22semidirect
19. C2×C5×D3×Q8C22semidirect
22. C2×C3×#713C22semidirect
23. C2×C3×#713C22semidirect
24. C2×C3×#713C22semidirect
25. C22×C3×D20C22semidirect
26. C22×C3×C4×D5C22semidirect
29. C2×D3×D20C22semidirect
30. C2×C4×D3×D5C22semidirect
31. C2×#6773C22semidirect
32. C2×#6766C22semidirect
33. #91836C22semidirect
34. #91835C22semidirect
35. Q8×Dic15C22semidirect
36. #91819C22semidirect
37. C4×#1220C22semidirect
38. C5×#946C22semidirect
39. C5×Q8×Dic3C22semidirect
40. C5×#944C22semidirect
42. C5×#924C22semidirect
43. #91564C22semidirect
44. #91552C22semidirect
46. D5×#217C22semidirect
47. #91474C22semidirect
48. D5×(C2×D3)⋊C4C22semidirect
49. #91465C22semidirect
50. #91458C22semidirect
51. #91456C22semidirect
52. #91450C22semidirect
53. #91444C22semidirect
54. #91444C22semidirect
55. C4×#1202C22semidirect
56. #91440C22semidirect
57. C4×#1201C22semidirect
58. #91434C22semidirect
59. Dic3×D20C22semidirect
60. #91409C22semidirect
61. #91409C22semidirect
62. #91407C22semidirect
63. D5×Dic3⋊C4C22semidirect
64. C4×D5×Dic3C22semidirect
65. #91368C22semidirect
66. #91359C22semidirect
67. #91358C22semidirect
68. #91348C22semidirect
71. C22×#713D3semidirect
103. C3×#713D4semidirect
159. Q8×#67D5semidirect
165. C22×C5×Q8C2×D3semidirect
172. C2×#713C2×D3semidirect
173. C2×#713C2×D3semidirect
174. C2×#713C2×D3semidirect
177. C22×D20C2×D3semidirect
179. C22×C4×D5C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
239. C5×#67#41semidirect
250. C3×D20C2×D4semidirect
254. C3×C4×D5C2×D4semidirect
269. C22×C3×Q8C2×D5semidirect
275. C2×D3×Q8C2×D5semidirect
284. #946C2×D5semidirect
286. Q8×Dic3C2×D5semidirect
287. #944C2×D5semidirect
313. #924C2×D5semidirect
336. #713#67direct (N × H)
397. C22×C3×C5C2×#41semidirect
404. C2×C5×D3C2×#41semidirect
422. C5×Dic3C2×#41semidirect
500. C5×Q8C2×#67semidirect
524. D20C2×#67semidirect
533. C4×D5C2×#67semidirect
544. C22×Q8D3×D5semidirect
606. C3×Q8D4×D5semidirect
625. #67#713direct (N × H)
646. C22×C5D3×#41semidirect
733. C3×C5D4×#41semidirect
743. C22×C3C2×#713semidirect
751. C2×D3C2×#713semidirect
761. Dic3C2×#713semidirect
783. Q8D5×#67semidirect
825. C5#41×#67semidirect
842. C22D3×#713semidirect
854. C3D4×#713semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C2×D3×#7132
#117565762
C5×Q8×#672
#117552732
#117552702
#117552512
#117552472
Dic3×#7132
#117551592
#117551572
#67×D202
C4×D5×#672
#117545272
#117543082
D4×#7133
#41×#675