Finite Group Databasebeta

← #14483215

Subgroups — #14483215

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×D3×#713C211yesmaximal, characteristic, complemented
2C2×D5×#239C211yesmaximal, characteristic, complemented
3C4×#6821C211yesmaximal, characteristic, complemented
4C5×#5576C211yesmaximal, characteristic, complemented
5C3×#65910C211yesmaximal, characteristic, complemented
6#11755254C211yesmaximal, characteristic, complemented
7Q8×#1201C211yesmaximal, characteristic, complemented
8#11753886C213yesmaximal, complemented
9#11753885C213yesmaximal, complemented
10#11753857C213yesmaximal, complemented
11#11753704C213yesmaximal, complemented
12#11752749C213yesmaximal, complemented
13#11752748C213yesmaximal, complemented
14C4×#6777C213yesmaximal, complemented
15#11752678C213yesmaximal, complemented
16#10618611—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic, complemented
19C2×C5×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#713C2211yescharacteristic, complemented
21C2×C3×Q8×D5C2211yescharacteristic, complemented
22D3×#713—28no—
23D5×#239—28no—
24C2×#6777C2213yes—
25C2×D3×D20C2213yescomplemented
26C2×D5×D12C2213yescomplemented
27C2×C4×D3×D5C2213yescomplemented
28C2×C4×D3×D5C2213yescomplemented
29C2×#6773C2213yescomplemented
30C2×#6769C2213yescomplemented
31C2×#6768C2213yescomplemented
32C2×#6766C2213yescomplemented
33C3×C4×C5×Q8C2211yescharacteristic, complemented
34Q8×Dic15C2211yescharacteristic, complemented
35#91782C2213yescomplemented
36#91781C2213yescomplemented
37C4×D60C2213yescomplemented
38C42×D15C2213yescomplemented
39C5×#897C2213yescomplemented
40C5×#895C2213yescomplemented
41C5×#875C2213yescomplemented
42C4×C5×D12C2213yescomplemented
43C3×#4043C2213yescomplemented
44C3×#4041C2213yescomplemented
45C3×#4021C2213yescomplemented
46C3×C4×D20C2213yescomplemented
47#91475C2216yescomplemented
48#91474C2216yescomplemented
49#91473C2213yescomplemented
50#91473C2213yescomplemented
51#91463C2213yescomplemented
52#91461C2216yescomplemented
53#91461C2216yescomplemented
54#91456C2213yescomplemented
55#91449C2213yescomplemented
56#91442C2211yescharacteristic
57#91442C2213yescomplemented
58#91442C2216yescomplemented
59C4×#1201C2213yes—
60C4×#1201C2213yescomplemented
61#91438C2216yescomplemented
62#91437C2213yescomplemented
63#91435C2213yescomplemented
64#91434C2213yescomplemented
65#91385C2213yescomplemented
66#91369C2213yescomplemented
67#91359C2213yescomplemented
68#91356C2216yescomplemented
69#86710—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×#713—31no—
72C5×#548—31no—
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#65910D311yescharacteristic, complemented
82C4×#713—31no—
83#65884—33no—
84C4×D4×D5—33no—
85C22×D3×D5C2313yes—
86C22×D3×D5C2313yes—
87C2×C3×C5×Q8C2311yescharacteristic
88#6821D418yescomplemented
89C2×D60C2313yes—
90C2×C4×D15C2313yes—
91C2×C4×D15C2313yes—
92C2×C4×D15C2313yes—
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×#1203C2316yes—
108C2×#1202C2316yes—
109C2×#1201C2313yes—
110C2×#1201C2316yes—
111C2×#1201C2311yescharacteristic
112C2×#1200C2313yes—
113C2×#1200C2313yes—
114C2×D3×Dic5C2311yescharacteristic
115C2×D3×Dic5C2313yes—
116C2×D5×Dic3C2311yescharacteristic
117C2×D5×Dic3C2313yes—
118#6777—212no—
119D3×D20—212no—
120D5×D12—212no—
121C4×D3×D5—212no—
122C4×D3×D5—212no—
123#6773—212no—
124#6769—212no—
125#6768—212no—
126#6766—212no—
127C3×C5×C4⋊C4C2313yes—
128C3×C42×C5C2313yes—
129#6714C2316yes—
130C4⋊Dic15C2313yes—
131C4×Dic15C2313yes—
132C4×Dic15C2313yes—
133C4×Dic15C2311yescharacteristic
134C5×(C2×D3)⋊C4C2311yescharacteristic
135C5×(C2×D3)⋊C4C2313yes—
136C5×(C2×D3)⋊C4C2316yes—
137C5×C4⋊Dic3C2313yes—
138C3×#685C2311yescharacteristic
139C3×#685C2313yes—
140C3×#685C2316yes—
141C3×C4⋊Dic5C2313yes—
142#6669C2311yescharacteristic
143#6669C2313yes—
144#6669C2316yes—
145(C2×D3)⋊Dic5C2313yes—
146(C2×D3)⋊Dic5C2313yes—
147#6665C2313yes—
148#6665C2313yes—
149C2×D3×#41—51no—
150C22×#239—51no—
151C3×#548—51no—
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#5576D511yescharacteristic, complemented
161C4×#239—51no—
162#5550—53no—
163C4×D3×D4—53no—
164C2×C5×#41—31no—
165C22×C5×Q8—31no—
166D5×#41—68no—
167C2×#713—31no—
168C2×#713—33no—
169C2×#713—33no—
170C2×#713—68no—
171C2×#713C2×D311yescharacteristic, complemented
172C2×Q8×D5C2×D311yescharacteristic, complemented
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×#124—33no—
181C5×C22⋊Q8—33no—
182C5×#121—33no—
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C4×C5×D4—33no—
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#4043C2×D313yescomplemented
197#4041C2×D313yescomplemented
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#4021C2×D313yescomplemented
213C4×D20—33no—
214C4×D20C2×D313yescomplemented
215C42×D5—33no—
216D4×#41—151noSylow
217C22×D15C2413yes—
218C22×C5×D3C2413yes—
219C22×C5×D3C2411yescharacteristic
220C22×C3×D5C2413yes—
221C22×C3×D5C2411yescharacteristic
222C2×D3×D5—26no—
223C2×D3×D5—26no—
224C2×D3×D5—26no—
225C2×D3×D5—26no—
226C2×D3×D5—43no—
227C2×D3×D5—43no—
228C3×C5×Q8C2×D414yescomplemented
229C2×C3×C4×C5C2413yes—
230C2×C3×C4×C5C2411yescharacteristic
231C2×C3×C4×C5C2413yes—
232C2×Dic15C2413yes—
233C2×Dic15C2411yescharacteristic
234C2×Dic15C2411yescharacteristic
235D60C2×D4112yescomplemented
236C4×D15—26no—
237C4×D15—43no—
238C4×D15C2×D4112yescomplemented
239C2×C5×Dic3C2411yescharacteristic
240C2×C5×Dic3C2413yes—
241C5×D12—26no—
242C5×D12—26no—
243C4×C5×D3—26no—
244C4×C5×D3—26no—
245C5×Dic6—26no—
246C2×C3×Dic5C2411yescharacteristic
247C2×C3×Dic5C2413yes—
248C3×D20—26no—
249C3×D20—26no—
250C3×C4×D5—26no—
251C3×C4×D5—26no—
252C3×Dic10—26no—
253#1203—212no—
254#1202—212no—
255#1201—26no—
256#1201—46no—
257#1201#4114yescomplemented
258#1200—26no—
259#1200—26no—
260D3×Dic5—26no—
261D3×Dic5—22no—
262D5×Dic3—26no—
263D5×Dic3—22no—
264C2×C3×#41—51no—
265C22×C3×Q8—51no—
266D3×#41—108no—
267C2×#239—51no—
268C2×#239—53no—
269C2×#239—53no—
270C2×#239—108no—
271C2×#239C2×D511yescharacteristic, complemented
272C2×D3×Q8C2×D511yescharacteristic, complemented
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×#124—53no—
281C3×C22⋊Q8—53no—
282C3×#121—53no—
283C3×C4×Q8C2×D511yescharacteristic, complemented
284C3×C4×D4—53no—
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#897C2×D513yescomplemented
297#895C2×D513yescomplemented
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#875C2×D513yescomplemented
313C4×D12—53no—
314C4×D12C2×D513yescomplemented
315C42×D3—53no—
316C23×D5—33no—
317C23×D5—33no—
318C5×#41—64no—
319C2×C5×Q8—33no—
320C2×C5×Q8—64no—
321C2×C5×Q8C22×D311yescharacteristic
322C2×C5×D4—33no—
323C2×C5×D4—33no—
324C22×C4×C5—33no—
325C22×C4×C5—33no—
326C2×C22⋊D5—31no—
327C2×C22⋊D5—33no—
328C2×C22⋊D5—36no—
329C2×C22⋊D5—36no—
330C22×Dic5—31no—
331C22×Dic5—33no—
332#713—24no—
333#713—38no—
334#713—612no—
335#713—612no—
336Q8×D5—24no—
337#711—612no—
338D4×D5—612no—
339D4×D5—612no—
340#709—612no—
341C2×D20—33no—
342C2×D20—36no—
343C2×D20—612no—
344C2×D20C22×D313yes—
345C2×D20C22×D313yes—
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—612no—
354C2×C4×D5—612no—
355C2×C4×D5C22×D313yes—
356C2×C4×D5C22×D313yes—
357C2×Dic10C22×D313yes—
358C5×C4⋊C4—33no—
359C5×C4⋊C4C22×D313yes—
360C5×C22⋊C4—31no—
361C5×C22⋊C4—33no—
362C5×C22⋊C4—36no—
363C42×C5C22×D313yes—
364C22⋊Dic5—33no—
365C22⋊Dic5—33no—
366#685—33no—
367#685—33no—
368#685—36no—
369#685C22×D311yescharacteristic
370#685C22×D313yes—
371#685C22×D316yes—
372C4⋊Dic5—33no—
373C4⋊Dic5C22×D313yes—
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—31no—
385#548—51no—
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×C5C2511yescharacteristic
396C2×D15—23no—
397C2×D15—23no—
398C2×D15C22×D416yes—
399C2×C5×D3—21no—
400C2×C5×D3—21no—
401C2×C5×D3—23no—
402C2×C5×D3—23no—
403C2×C5×D3—23no—
404C2×C5×D3C2×#4112yescomplemented
405C2×C3×D5—21no—
406C2×C3×D5—21no—
407C2×C3×D5—23no—
408C2×C3×D5—23no—
409C2×C3×D5—23no—
410C2×C3×D5C2×#4112yescomplemented
411D3×D5—412no—
412D3×D5—412no—
413C3×C4×C5—23no—
414C3×C4×C5—21no—
415C3×C4×C5C22×D416yes—
416Dic15—23no—
417Dic15C22×D412yes—
418Dic15C2×#4112yescomplemented
419C3×Dic5—21no—
420C3×Dic5—23no—
421C5×Dic3—21no—
422C5×Dic3—23no—
423C23×D3—53no—
424C23×D3—53no—
425C3×#41—104no—
426C2×C3×Q8—53no—
427C2×C3×Q8—104no—
428C2×C3×Q8C22×D511yescharacteristic
429C2×C3×D4—53no—
430C2×C3×D4—53no—
431C22×C3×C4—53no—
432C22×C3×C4—53no—
433C2×#67—51no—
434C2×#67—53no—
435C2×#67—56no—
436C2×#67—56no—
437C22×Dic3—53no—
438C22×Dic3—51no—
439#239—24no—
440#239—58no—
441#239—1012no—
442#239—1012no—
443D3×Q8—24no—
444#237—1012no—
445D3×D4—1012no—
446D3×D4—1012no—
447#235—1012no—
448C2×D12—53no—
449C2×D12—56no—
450C2×D12—1012no—
451C2×D12C22×D513yes—
452C2×D12C22×D513yes—
453C2×C4×D3—53no—
454C2×C4×D3—53no—
455C2×C4×D3—51no—
456C2×C4×D3—53no—
457C2×C4×D3—53no—
458C2×C4×D3—53no—
459C2×C4×D3—53no—
460C2×C4×D3—1012no—
461C2×C4×D3—1012no—
462C2×C4×D3C22×D513yes—
463C2×C4×D3C22×D513yes—
464C2×Dic6C22×D513yes—
465C3×C4⋊C4—53no—
466C3×C4⋊C4C22×D513yes—
467C3×C22⋊C4—51no—
468C3×C22⋊C4—53no—
469C3×C22⋊C4—56no—
470C3×C42C22×D513yes—
471#217—53no—
472#217—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—56no—
476(C2×D3)⋊C4C22×D511yescharacteristic
477(C2×D3)⋊C4C22×D513yes—
478(C2×D3)⋊C4C22×D516yes—
479C4⋊Dic3—53no—
480C4⋊Dic3C22×D513yes—
481Dic3⋊C4—56no—
482Dic3⋊C4—53no—
483Dic3⋊C4—51no—
484C4×Dic3—51no—
485C4×Dic3—53no—
486C4×Dic3—53no—
487C23×C5—31no—
488C23×C5—33no—
489C22×D5—33no—
490C22×D5—66no—
491C22×D5—66no—
492C22×D5—66no—
493C22×D5—66no—
494C22×D5—123no—
495C22×D5—123no—
496C22×D5C23×D313yes—
497C22×D5C23×D311yescharacteristic
498C5×Q8—66no—
499C5×Q8D3×D414yescomplemented
500C5×D4—66no—
501C5×D4—66no—
502C2×C4×C5—33no—
503C2×C4×C5—31no—
504C2×C4×C5—66no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D311yescharacteristic
508C2×C4×C5C23×D313yes—
509C22⋊D5—34no—
510C22⋊D5—612no—
511C22⋊D5—66no—
512C22⋊D5—126no—
513C2×Dic5—31no—
514C2×Dic5—31no—
515C2×Dic5—33no—
516C2×Dic5—62no—
517C2×Dic5—66no—
518C2×Dic5C23×D313yes—
519C2×Dic5C23×D311yescharacteristic
520D20—26no—
521D20—26no—
522D20—312no—
523D20—612no—
524C4×D5—26no—
525C4×D5—26no—
526C4×D5—312no—
527C4×D5—66no—
528C4×D5—66no—
529C4×D5—66no—
530C4×D5—62no—
531C4×D5—66no—
532C4×D5—123no—
533Dic10—26no—
534C2×#41—31no—
535C2×#41—51no—
536C2×#41—153no—
537C2×#41—153no—
538C2×#41—153no—
539C2×#41—153no—
540C2×#41—151no—
541C2×#41—308no—
542C2×#41—308no—
543C22×Q8—31no—
544C22×Q8—51no—
545C22×D4—153no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—153no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—33no—
553#124—53no—
554#123—156no—
555#123—156no—
556C22⋊Q8—33no—
557C22⋊Q8—53no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—33no—
561#121—53no—
562#121—156no—
563#121—156no—
564#121—153no—
565#121—153no—
566#120—156no—
567#120—156no—
568C4×Q8—151no—
569C4×Q8D3×D511yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—53no—
572C4×D4—151no—
573C4×D4—153no—
574C4×D4—156no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—153no—
581#117—153no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—153no—
586C2×C3×C5C23×D411yescharacteristic
587C2×C3×C5C22×#4111yescharacteristic
588C2×C3×C5#58511yescharacteristic
589D15—26no—
590C3×D5—22no—
591C3×D5—43no—
592C5×D3—22no—
593C5×D3—43no—
594C23×C3—51no—
595C23×C3—53no—
596C22×D3—53no—
597C22×D3—106no—
598C22×D3—106no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3—203no—
602C22×D3—203no—
603C22×D3C23×D513yes—
604C22×D3C23×D511yescharacteristic
605C3×Q8—106no—
606C3×Q8D4×D514yescomplemented
607C3×D4—106no—
608C3×D4—106no—
609C2×C3×C4—53no—
610C2×C3×C4—51no—
611C2×C3×C4—106no—
612C2×C3×C4—106no—
613C2×C3×C4C23×D513yes—
614C2×C3×C4C23×D511yescharacteristic
615C2×C3×C4C23×D513yes—
616#67—54no—
617#67—1012no—
618#67—106no—
619#67—206no—
620C2×Dic3—51no—
621C2×Dic3—51no—
622C2×Dic3—53no—
623C2×Dic3—102no—
624C2×Dic3—106no—
625C2×Dic3C23×D513yes—
626C2×Dic3C23×D511yescharacteristic
627D12—26no—
628D12—26no—
629D12—512no—
630D12—1012no—
631C4×D3—26no—
632C4×D3—26no—
633C4×D3—512no—
634C4×D3—106no—
635C4×D3—106no—
636C4×D3—106no—
637C4×D3—102no—
638C4×D3—106no—
639C4×D3—203no—
640Dic6—26no—
641C22×C5—32no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5—63no—
645C22×C5—63no—
646C22×C5—63no—
647C22×C5C24×D311yescharacteristic
648C2×D5—21no—
649C2×D5—21no—
650C2×D5—23no—
651C2×D5—23no—
652C2×D5—23no—
653C2×D5—36no—
654C2×D5—63no—
655C2×D5—63no—
656C2×D5—1212no—
657C2×D5—1212no—
658C2×D5D3×#4112yescomplemented
659C4×C5—23no—
660C4×C5—21no—
661C4×C5—61no—
662C4×C5—63no—
663C4×C5C2×D3×D416yes—
664Dic5—23no—
665Dic5—21no—
666Dic5—32no—
667Dic5—32no—
668Dic5—63no—
669C24—153no—
670C24—153no—
671#41—64no—
672#41—104no—
673#41—158no—
674#41—3012no—
675#41—3012no—
676#41—3012no—
677#41—3012no—
678C2×Q8—33no—
679C2×Q8—53no—
680C2×Q8—64no—
681C2×Q8—104no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—53no—
686C2×D4—53no—
687C2×D4—156no—
688C2×D4—156no—
689C2×D4—151no—
690C2×D4—153no—
691C2×D4—156no—
692C2×D4—153no—
693C2×D4—3012no—
694C2×D4—3012no—
695C2×D4—3012no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—53no—
699C22×C4—53no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—151no—
703C22×C4—153no—
704C22×C4—151no—
705C22×C4—153no—
706C22×C4—153no—
707C22×C4—153no—
708C22×C4—153no—
709C22×C4—3012no—
710C22×C4—3012no—
711C4⋊C4—33no—
712C4⋊C4—53no—
713C4⋊C4—151no—
714C4⋊C4—153no—
715C4⋊C4—156no—
716C4⋊C4—153no—
717C4⋊C4C2×D3×D513yes—
718C22⋊C4—31no—
719C22⋊C4—33no—
720C22⋊C4—36no—
721C22⋊C4—51no—
722C22⋊C4—53no—
723C22⋊C4—56no—
724C22⋊C4—153no—
725C22⋊C4—153no—
726C22⋊C4—153no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—151no—
730C42—153no—
731C42—153no—
732C42C2×D3×D513yes—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—52no—
735C22×C3—101no—
736C22×C3—101no—
737C22×C3—103no—
738C22×C3—103no—
739C22×C3—103no—
740C22×C3C24×D511yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—23no—
744C2×D3—23no—
745C2×D3—23no—
746C2×D3—56no—
747C2×D3—103no—
748C2×D3—103no—
749C2×D3—2012no—
750C2×D3—2012no—
751C2×D3D5×#4112yescomplemented
752C3×C4—23no—
753C3×C4—21no—
754C3×C4—101no—
755C3×C4—103no—
756C3×C4C2×D4×D516yes—
757Dic3—23no—
758Dic3—21no—
759Dic3—52no—
760Dic3—52no—
761Dic3—103no—
762C2×C5—62no—
763C2×C5—123no—
764C2×C5C22×D3×D411yescharacteristic
765C2×C5C2×D3×#4111yescharacteristic
766C2×C5#596811yescharacteristic
767D5—22no—
768D5—43no—
769D5—66no—
770C23—31no—
771C23—33no—
772C23—51no—
773C23—53no—
774C23—153no—
775C23—306no—
776C23—306no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23—603no—
781Q8—66no—
782Q8—106no—
783Q8#677714yescomplemented
784D4—66no—
785D4—66no—
786D4—106no—
787D4—106no—
788D4—154no—
789D4—1512no—
790D4—3012no—
791D4—3012no—
792D4—306no—
793D4—606no—
794C2×C4—33no—
795C2×C4—31no—
796C2×C4—53no—
797C2×C4—51no—
798C2×C4—66no—
799C2×C4—66no—
800C2×C4—106no—
801C2×C4—106no—
802C2×C4—151no—
803C2×C4—151no—
804C2×C4—1512no—
805C2×C4—153no—
806C2×C4—306no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—302no—
810C2×C4—306no—
811C2×C4—302no—
812C2×C4—306no—
813C2×C4—603no—
814C2×C4C22×D3×D511yescharacteristic
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D513yes—
817C2×C3—102no—
818C2×C3—203no—
819C2×C3C22×D4×D511yescharacteristic
820C2×C3C2×D5×#4111yescharacteristic
821C2×C3#6628711yescharacteristic
822D3—22no—
823D3—43no—
824D3—106no—
825C5#8671011yescharacteristic, complemented, Sylow
826C22—32no—
827C22—52no—
828C22—61no—
829C22—61no—
830C22—63no—
831C22—63no—
832C22—63no—
833C22—101no—
834C22—101no—
835C22—103no—
836C22—103no—
837C22—103no—
838C22—156no—
839C22—303no—
840C22—303no—
841C22—6012no—
842C22—6012no—
843C22C23×D3×D511yescharacteristic
844C4—21no—
845C4—23no—
846C4—61no—
847C4—63no—
848C4—101no—
849C4—103no—
850C4—152no—
851C4—152no—
852C4—303no—
853C4C2×#677716yes—
854C3#1061861111yescharacteristic, complemented, Sylow
855C2—62no—
856C2—102no—
857C2—123no—
858C2—203no—
859C2—306no—
860C2C22×#677711yescharacteristic
861C2#1175705011yescharacteristic
862C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5D4×#41
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×D3×#713C2semidirect
2. C2×D5×#239C2semidirect
3. C4×#6821C2semidirect
4. C5×#5576C2semidirect
5. C3×#65910C2semidirect
6. #11755254C2semidirect
7. Q8×#1201C2semidirect
8. #11753886C2semidirect
9. #11753885C2semidirect
10. #11753857C2semidirect
11. #11753704C2semidirect
12. #11752749C2semidirect
13. #11752748C2semidirect
14. C4×#6777C2semidirect
15. #11752678C2semidirect
18. C2×C5×#239C22semidirect
19. C2×C5×D3×Q8C22semidirect
20. C2×C3×#713C22semidirect
21. C2×C3×Q8×D5C22semidirect
25. C2×D3×D20C22semidirect
26. C2×D5×D12C22semidirect
27. C2×C4×D3×D5C22semidirect
28. C2×C4×D3×D5C22semidirect
29. C2×#6773C22semidirect
30. C2×#6769C22semidirect
31. C2×#6768C22semidirect
32. C2×#6766C22semidirect
33. C3×C4×C5×Q8C22semidirect
34. Q8×Dic15C22semidirect
35. #91782C22semidirect
36. #91781C22semidirect
37. C4×D60C22semidirect
38. C42×D15C22semidirect
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
47. #91475C22semidirect
48. #91474C22semidirect
49. #91473C22semidirect
50. #91473C22semidirect
51. #91463C22semidirect
52. #91461C22semidirect
53. #91461C22semidirect
54. #91456C22semidirect
55. #91449C22semidirect
57. #91442C22semidirect
58. #91442C22semidirect
60. C4×#1201C22semidirect
61. #91438C22semidirect
62. #91437C22semidirect
63. #91435C22semidirect
64. #91434C22semidirect
65. #91385C22semidirect
66. #91369C22semidirect
67. #91359C22semidirect
68. #91356C22semidirect
81. #65910D3semidirect
88. #6821D4semidirect
160. #5576D5semidirect
171. C2×#713C2×D3semidirect
172. C2×Q8×D5C2×D3semidirect
183. C4×C5×Q8C2×D3semidirect
196. #4043C2×D3semidirect
197. #4041C2×D3semidirect
212. #4021C2×D3semidirect
214. C4×D20C2×D3semidirect
228. C3×C5×Q8C2×D4semidirect
235. D60C2×D4semidirect
238. C4×D15C2×D4semidirect
257. #1201#41semidirect
271. C2×#239C2×D5semidirect
272. C2×D3×Q8C2×D5semidirect
283. C3×C4×Q8C2×D5semidirect
296. #897C2×D5semidirect
297. #895C2×D5semidirect
312. #875C2×D5semidirect
314. C4×D12C2×D5semidirect
404. C2×C5×D3C2×#41semidirect
410. C2×C3×D5C2×#41semidirect
418. Dic15C2×#41semidirect
499. C5×Q8D3×D4semidirect
569. C4×Q8D3×D5semidirect
606. C3×Q8D4×D5semidirect
658. C2×D5D3×#41semidirect
733. C3×C5D4×#41semidirect
751. C2×D3D5×#41semidirect
783. Q8#6777semidirect
825. C5#86710semidirect
854. C3#10618611semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7132
C2×D5×#2392
C4×#68212
C5×#55762
C3×#659102
#117552542
Q8×#12012
#117538862
#117538852
#117538572
#117537042
#117527492
#117527482
C4×#67772
#117526782
#106186113
#867105