Finite Group Databasebeta

← #14483216

Subgroups — #14483216

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×#92034C211yesmaximal, characteristic, complemented
2C2×D5×#239C211yesmaximal, characteristic, complemented
3#11756335C211yesmaximal, characteristic, complemented
4C4×C5×#239C211yesmaximal, characteristic, complemented
5C3×#65910C211yesmaximal, characteristic, complemented
6#11755251C211yesmaximal, characteristic, complemented
7Q8×#1202C211yesmaximal, characteristic, complemented
8#11753880C213yesmaximal, complemented
9#11753879C213yesmaximal, complemented
10#11753860C213yesmaximal, complemented
11#11753696C213yesmaximal, complemented
12#11752746C213yesmaximal, complemented
13#11752740C213yesmaximal, complemented
14C4×D3×D20C213yesmaximal, complemented
15#11752543C213yesmaximal, complemented
16#41×D20—31nomaximal, Hall
17C2×#6821C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×#239C2211yescharacteristic
20C2×C3×#713C2211yescharacteristic, complemented
21C2×C3×Q8×D5C2211yescharacteristic, complemented
22#92034—28no—
23D5×#239—28no—
24C2×#6777C2213yescomplemented
25C2×D3×D20C2213yes—
26C2×D5×D12C2213yescomplemented
27C2×C4×D3×D5C2213yescomplemented
28C2×C4×D3×D5C2213yescomplemented
29C2×#6772C2213yescomplemented
30C2×#6769C2213yescomplemented
31C2×#6768C2213yescomplemented
32C2×#6765C2213yescomplemented
33C3×C4×C5×Q8C2211yescharacteristic, complemented
34#91786C2213yescomplemented
35#91784C2213yescomplemented
36#91764C2213yescomplemented
37C4×D60C2213yescomplemented
38C5×Q8×Dic3C2211yescharacteristic, complemented
39C5×#893C2213yescomplemented
40C5×#892C2213yescomplemented
41C4×C5×D12C2213yescomplemented
42C42×C5×D3C2213yescomplemented
43C3×#4043C2213yescomplemented
44C3×#4041C2213yescomplemented
45C3×#4021C2213yescomplemented
46C3×C4×D20C2213yescomplemented
47#91476C2216yescomplemented
48#91474C2216yescomplemented
49D3×#685C2213yescomplemented
50D3×#685C2213yescomplemented
51#91465C2213yescomplemented
52#91458C2213yescomplemented
53#91457C2216yescomplemented
54#91454C2216yescomplemented
55#91454C2216yescomplemented
56#91450C2213yescomplemented
57C4×#1202C2213yes—
58C4×#1202C2213yescomplemented
59#91428C2213yescomplemented
60#91427C2216yescomplemented
61D3×C4⋊Dic5C2213yescomplemented
62Dic3×D20C2213yescomplemented
63#91395C2211yescharacteristic
64#91395C2213yescomplemented
65#91395C2216yescomplemented
66#91390C2213yescomplemented
67#91389C2213yescomplemented
68#91360C2213yescomplemented
69#86710—51nomaximal, Hall
70C2×D5×#41—31no—
71C2×D5×#41—31no—
72C4×C5×#41—31no—
73#65911—31no—
74#65910—31no—
75#65910D311yescharacteristic, complemented
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—
85C22×D3×D5C2313yes—
86C22×D3×D5C2313yes—
87C2×C3×C5×Q8C2311yescharacteristic
88#6821—24no—
89Q8×D15—24no—
90C2×D60C2313yes—
91C2×D60C2313yes—
92C2×C4×D15C2313yes—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C5×#239D418yescomplemented
96C2×C5×D12C2313yes—
97C2×C4×C5×D3C2313yes—
98C2×C4×C5×D3C2313yes—
99C2×C4×C5×D3C2313yes—
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×#1202C2313yes—
109C2×#1202C2316yes—
110C2×#1202C2311yescharacteristic
111C2×#1201C2316yes—
112C2×#1200C2311yescharacteristic
113C2×#1200C2313yes—
114C2×D3×Dic5C2313yes—
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#6772—212no—
124#6769—212no—
125#6768—212no—
126#6765—212no—
127C3×C5×C4⋊C4C2313yes—
128C3×C42×C5C2313yes—
129#6714C2311yescharacteristic
130#6714C2316yes—
131#6714C2313yes—
132C4⋊Dic15C2313yes—
133C5×(C2×D3)⋊C4C2316yes—
134C5×C4⋊Dic3C2313yes—
135C4×C5×Dic3C2311yescharacteristic
136C4×C5×Dic3C2313yes—
137C4×C5×Dic3C2313yes—
138C3×#685C2311yescharacteristic
139C3×#685C2313yes—
140C3×#685C2316yes—
141C3×C4⋊Dic5C2313yes—
142Dic3⋊Dic5C2311yescharacteristic
143Dic3⋊Dic5C2313yes—
144Dic3⋊Dic5C2316yes—
145#6667C2313yes—
146#6667C2313yes—
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#5576—51no—
161C4×#239D511yescharacteristic, complemented
162#5550—53no—
163C4×D3×D4—53no—
164C2×C5×#41—31no—
165D5×#41—68no—
166D5×#41—68no—
167C2×#713—31no—
168C2×#713C2×D311yescharacteristic, complemented
169C2×Q8×D5—31no—
170C2×Q8×D5C2×D311yescharacteristic, complemented
171C2×#711—33no—
172C2×#711—33no—
173C2×D4×D5—33no—
174C2×D4×D5—33no—
175C2×#709—33no—
176C2×#709—33no—
177C22×D20—33no—
178C22×C4×D5—33no—
179C22×C4×D5—33no—
180C4×C5×Q8—31no—
181C4×C5×Q8C2×D311yescharacteristic, complemented
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#4043C2×D313yescomplemented
195#4041—33no—
196#4041—33no—
197#4041—33no—
198#4041C2×D313yescomplemented
199#4032—36no—
200#4032—36no—
201#4028—36no—
202#4028—36no—
203#4021—33no—
204#4021C2×D313yescomplemented
205#4020—33no—
206C4×D20—33no—
207C4×D20—33no—
208C4×D20—33no—
209C4×D20—33no—
210C4×D20—31no—
211C4×D20—33no—
212C4×D20—36no—
213C4×D20—33no—
214C4×D20C2×D313yescomplemented
215#4015—33no—
216D4×#41—151noSylow
217C22×D15C2413yes—
218C22×D15C2411yescharacteristic
219C22×C5×D3C2413yes—
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×Dic15C2411yescharacteristic
233C2×Dic15C2413yes—
234D60—26no—
235D60—26no—
236C4×D15—26no—
237C4×D15—26no—
238Dic30—26no—
239C2×C5×Dic3C2413yes—
240C2×C5×Dic3C2411yescharacteristic
241C2×C5×Dic3C2411yescharacteristic
242C5×D12C2×D4112yescomplemented
243C4×C5×D3—26no—
244C4×C5×D3—43no—
245C4×C5×D3C2×D4112yescomplemented
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—26no—
255#1202—46no—
256#1202#4114yescomplemented
257#1201—212no—
258#1200—26no—
259#1200—22no—
260D3×Dic5—26no—
261D3×Dic5—26no—
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
272C2×D3×Q8—51no—
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×Dic3C2×D511yescharacteristic, complemented
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#897—53no—
297#895—53no—
298#894—56no—
299#893—53no—
300#893C2×D513yescomplemented
301#892C2×D513yescomplemented
302D3×C4⋊C4—53no—
303#884—56no—
304#884—56no—
305#883—56no—
306#882—56no—
307#67⋊C4—51no—
308#67⋊C4—53no—
309#67⋊C4—56no—
310D3×C22⋊C4—53no—
311D3×C22⋊C4—53no—
312#875—53no—
313C4×D12—53no—
314C4×D12C2×D513yescomplemented
315C42×D3C2×D513yescomplemented
316C23×D5—33no—
317C23×D5—33no—
318C5×#41—38no—
319C2×C5×Q8C22×D311yescharacteristic
320C2×C5×D4—33no—
321C22×C4×C5—33no—
322C22×C4×C5—33no—
323C22×C4×C5—33no—
324C2×C22⋊D5—36no—
325C2×C22⋊D5—36no—
326C22×Dic5—33no—
327C22×Dic5—33no—
328#713—24no—
329#713—64no—
330Q8×D5—24no—
331Q8×D5—64no—
332#711—612no—
333#711—612no—
334D4×D5—612no—
335D4×D5—612no—
336#709—612no—
337#709—612no—
338C2×D20—31no—
339C2×D20—33no—
340C2×D20—33no—
341C2×D20—33no—
342C2×D20—36no—
343C2×D20—612no—
344C2×D20C22×D313yes—
345C2×D20C22×D313yes—
346C2×C4×D5—31no—
347C2×C4×D5—33no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—31no—
351C2×C4×D5—33no—
352C2×C4×D5—612no—
353C2×C4×D5—612no—
354C2×C4×D5C22×D313yes—
355C2×C4×D5C22×D313yes—
356C2×Dic10—33no—
357C2×Dic10C22×D313yes—
358C5×C4⋊C4—33no—
359C5×C4⋊C4C22×D313yes—
360C5×C22⋊C4—36no—
361C42×C5—31no—
362C42×C5—33no—
363C42×C5—33no—
364C42×C5C22×D313yes—
365#685—33no—
366#685—33no—
367#685—31no—
368#685—33no—
369#685—36no—
370#685—33no—
371#685—33no—
372#685C22×D311yescharacteristic
373#685C22×D313yes—
374#685C22×D316yes—
375C4⋊Dic5—33no—
376C4⋊Dic5—33no—
377C4⋊Dic5—36no—
378C4⋊Dic5—31no—
379C4⋊Dic5C22×D313yes—
380C22×#41—151no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—151no—
384#548—51no—
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×C5C2511yescharacteristic
396C2×D15—21no—
397C2×D15—21no—
398C2×D15—23no—
399C2×D15—23no—
400C2×D15—23no—
401C2×D15C2×#4112yescomplemented
402C2×C5×D3—23no—
403C2×C5×D3—23no—
404C2×C5×D3C22×D416yes—
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—21no—
417Dic15—23no—
418C3×Dic5—21no—
419C3×Dic5—23no—
420C5×Dic3—23no—
421C5×Dic3C22×D412yes—
422C5×Dic3C2×#4112yescomplemented
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—56no—
434C2×#67—51no—
435C2×#67—53no—
436C2×#67—56no—
437C22×Dic3—53no—
438C22×Dic3—51no—
439#239—104no—
440#239—1012no—
441#239—1012no—
442#239D2018yescomplemented
443D3×Q8—104no—
444#237—1012no—
445D3×D4—1012no—
446D3×D4—1012no—
447#235—1012no—
448C2×D12—56no—
449C2×D12—53no—
450C2×D12—53no—
451C2×D12—1012no—
452C2×D12C22×D513yes—
453C2×C4×D3—53no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—53no—
458C2×C4×D3—51no—
459C2×C4×D3—1012no—
460C2×C4×D3—1012no—
461C2×C4×D3C22×D513yes—
462C2×C4×D3C22×D513yes—
463C2×C4×D3C22×D513yes—
464C2×Dic6—53no—
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—51no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—56no—
476(C2×D3)⋊C4—53no—
477(C2×D3)⋊C4—53no—
478(C2×D3)⋊C4C22×D516yes—
479C4⋊Dic3—53no—
480C4⋊Dic3C22×D513yes—
481Dic3⋊C4—56no—
482Dic3⋊C4—53no—
483Dic3⋊C4—51no—
484C4×Dic3C22×D511yescharacteristic
485C4×Dic3C22×D513yes—
486C4×Dic3C22×D513yes—
487C23×C5—33no—
488C22×D5—31no—
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×Q8D3×D414yescomplemented
499C5×D4—312no—
500C2×C4×C5—31no—
501C2×C4×C5—31no—
502C2×C4×C5—312no—
503C2×C4×C5—33no—
504C2×C4×C5—66no—
505C2×C4×C5—123no—
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D311yescharacteristic
508C2×C4×C5C23×D313yes—
509C22⋊D5—612no—
510C22⋊D5—612no—
511C2×Dic5—33no—
512C2×Dic5—31no—
513C2×Dic5—66no—
514C2×Dic5—66no—
515C2×Dic5C23×D313yes—
516C2×Dic5C23×D311yescharacteristic
517D20—26no—
518D20—26no—
519D20—34no—
520D20—66no—
521D20—66no—
522D20—66no—
523D20—126no—
524C4×D5—26no—
525C4×D5—26no—
526C4×D5—62no—
527C4×D5—66no—
528C4×D5—62no—
529C4×D5—66no—
530C4×D5—66no—
531C4×D5—66no—
532Dic10—26no—
533Dic10—66no—
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—51no—
544C22×Q8—151no—
545C22×D4—153no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—153no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—53no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—53no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—53no—
561#121—156no—
562#121—156no—
563#121—153no—
564#121—153no—
565#121—153no—
566#120—156no—
567#120—156no—
568C4×Q8—31no—
569C4×Q8D3×D511yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—33no—
572C4×D4—53no—
573C4×D4—151no—
574C4×D4—153no—
575C4×D4—156no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—153no—
581#117—33no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—33no—
586C2×C3×C5C23×D411yescharacteristic
587C2×C3×C5C22×#4111yescharacteristic
588C2×C3×C5#58511yescharacteristic
589D15—22no—
590D15—43no—
591C3×D5—22no—
592C3×D5—43no—
593C5×D3—26no—
594C23×C3—51no—
595C23×C3—53no—
596C22×D3—51no—
597C22×D3—53no—
598C22×D3—106no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3—203no—
603C22×D3—203no—
604C22×D3C23×D513yes—
605C3×Q8—106no—
606C3×Q8C2×D2014yescomplemented
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—53no—
621C2×Dic3—51no—
622C2×Dic3—102no—
623C2×Dic3—106no—
624C2×Dic3C23×D513yes—
625C2×Dic3C23×D511yescharacteristic
626C2×Dic3C23×D511yescharacteristic
627D12—106no—
628D12—1012no—
629D12—106no—
630D12C2×D20112yescomplemented
631C4×D3—26no—
632C4×D3—43no—
633C4×D3—106no—
634C4×D3—106no—
635C4×D3—106no—
636C4×D3—106no—
637C4×D3—102no—
638C4×D3—106no—
639C4×D3C2×D20112yescomplemented
640Dic6—106no—
641C22×C5—36no—
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—61no—
652C2×D5—61no—
653C2×D5—63no—
654C2×D5—63no—
655C2×D5—63no—
656C2×D5—1212no—
657C2×D5—1212no—
658C2×D5D3×#4112yescomplemented
659C4×C5—23no—
660C4×C5—21no—
661C4×C5—32no—
662C4×C5—32no—
663C4×C5—63no—
664C4×C5C2×D3×D416yes—
665Dic5—23no—
666Dic5—21no—
667Dic5—63no—
668Dic5—61no—
669C24—153no—
670C24—153no—
671#41—38no—
672#41—104no—
673#41—3012no—
674#41—3012no—
675#41—3012no—
676#41—3012no—
677#41—304no—
678C2×Q8—53no—
679C2×Q8—104no—
680C2×Q8—153no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—53no—
685C2×D4—53no—
686C2×D4—151no—
687C2×D4—153no—
688C2×D4—156no—
689C2×D4—156no—
690C2×D4—156no—
691C2×D4—153no—
692C2×D4—153no—
693C2×D4—3012no—
694C2×D4—3012no—
695C2×D4—3012no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—53no—
700C22×C4—53no—
701C22×C4—151no—
702C22×C4—153no—
703C22×C4—151no—
704C22×C4—153no—
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—36no—
719C22⋊C4—51no—
720C22⋊C4—53no—
721C22⋊C4—56no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—153no—
725C22⋊C4—153no—
726C22⋊C4—151no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—31no—
730C42—33no—
731C42—33no—
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—23no—
742C2×D3—23no—
743C2×D3—52no—
744C2×D3—101no—
745C2×D3—101no—
746C2×D3—103no—
747C2×D3—103no—
748C2×D3—103no—
749C2×D3—2012no—
750C2×D3—2012no—
751C2×D3C22×D2016yes—
752C3×C4—23no—
753C3×C4—21no—
754C3×C4—101no—
755C3×C4—103no—
756C3×C4C22×D2016yes—
757Dic3—23no—
758Dic3—103no—
759Dic3—101no—
760Dic3C22×D2012yes—
761Dic3D5×#4112yescomplemented
762C2×C5—66no—
763C2×C5C22×D3×D411yescharacteristic
764C2×C5C2×D3×#4111yescharacteristic
765C2×C5#596811yescharacteristic
766D5—22no—
767D5—43no—
768D5—62no—
769D5—123no—
770C23—33no—
771C23—51no—
772C23—53no—
773C23—151no—
774C23—153no—
775C23—306no—
776C23—306no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23—603no—
781Q8—106no—
782Q8—306no—
783Q8D3×D2014yescomplemented
784D4—312no—
785D4—106no—
786D4—106no—
787D4—154no—
788D4—306no—
789D4—306no—
790D4—3012no—
791D4—3012no—
792D4—306no—
793D4—606no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—312no—
797C2×C4—33no—
798C2×C4—53no—
799C2×C4—51no—
800C2×C4—66no—
801C2×C4—106no—
802C2×C4—106no—
803C2×C4—123no—
804C2×C4—151no—
805C2×C4—153no—
806C2×C4—302no—
807C2×C4—306no—
808C2×C4—302no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4—306no—
812C2×C4—306no—
813C2×C4—306no—
814C2×C4C22×D3×D511yescharacteristic
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D513yes—
817C2×C3—102no—
818C2×C3—203no—
819C2×C3C23×D2011yescharacteristic
820C2×C3C2×D5×#4111yescharacteristic
821C2×C3#6628311yescharacteristic
822D3—26no—
823D3—102no—
824D3—203no—
825C5#8671011yescharacteristic, complemented, Sylow
826C22—36no—
827C22—52no—
828C22—63no—
829C22—63no—
830C22—101no—
831C22—101no—
832C22—103no—
833C22—103no—
834C22—103no—
835C22—152no—
836C22—301no—
837C22—301no—
838C22—303no—
839C22—303no—
840C22—303no—
841C22—6012no—
842C22—6012no—
843C22C23×D3×D511yescharacteristic
844C4—21no—
845C4—23no—
846C4—32no—
847C4—32no—
848C4—63no—
849C4—101no—
850C4—103no—
851C4—301no—
852C4—303no—
853C4C2×D3×D2016yes—
854C3#41×D2011yescharacteristic, complemented, Sylow
855C2—66no—
856C2—102no—
857C2—203no—
858C2—302no—
859C2—603no—
860C2C22×D3×D2011yescharacteristic
861C2#1175704911yescharacteristic
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×#92034C2semidirect
2. C2×D5×#239C2semidirect
3. #11756335C2semidirect
4. C4×C5×#239C2semidirect
5. C3×#65910C2semidirect
6. #11755251C2semidirect
7. Q8×#1202C2semidirect
8. #11753880C2semidirect
9. #11753879C2semidirect
10. #11753860C2semidirect
11. #11753696C2semidirect
12. #11752746C2semidirect
13. #11752740C2semidirect
14. C4×D3×D20C2semidirect
15. #11752543C2semidirect
17. C2×#6821C22semidirect
18. C2×Q8×D15C22semidirect
20. C2×C3×#713C22semidirect
21. C2×C3×Q8×D5C22semidirect
24. C2×#6777C22semidirect
26. C2×D5×D12C22semidirect
27. C2×C4×D3×D5C22semidirect
28. C2×C4×D3×D5C22semidirect
29. C2×#6772C22semidirect
30. C2×#6769C22semidirect
31. C2×#6768C22semidirect
32. C2×#6765C22semidirect
33. C3×C4×C5×Q8C22semidirect
34. #91786C22semidirect
35. #91784C22semidirect
36. #91764C22semidirect
37. C4×D60C22semidirect
38. C5×Q8×Dic3C22semidirect
39. C5×#893C22semidirect
40. C5×#892C22semidirect
41. C4×C5×D12C22semidirect
42. C42×C5×D3C22semidirect
43. C3×#4043C22semidirect
44. C3×#4041C22semidirect
45. C3×#4021C22semidirect
46. C3×C4×D20C22semidirect
47. #91476C22semidirect
48. #91474C22semidirect
49. D3×#685C22semidirect
50. D3×#685C22semidirect
51. #91465C22semidirect
52. #91458C22semidirect
53. #91457C22semidirect
54. #91454C22semidirect
55. #91454C22semidirect
56. #91450C22semidirect
58. C4×#1202C22semidirect
59. #91428C22semidirect
60. #91427C22semidirect
61. D3×C4⋊Dic5C22semidirect
62. Dic3×D20C22semidirect
64. #91395C22semidirect
65. #91395C22semidirect
66. #91390C22semidirect
67. #91389C22semidirect
68. #91360C22semidirect
75. #65910D3semidirect
95. C5×#239D4semidirect
161. C4×#239D5semidirect
168. C2×#713C2×D3semidirect
170. C2×Q8×D5C2×D3semidirect
181. C4×C5×Q8C2×D3semidirect
194. #4043C2×D3semidirect
198. #4041C2×D3semidirect
204. #4021C2×D3semidirect
214. C4×D20C2×D3semidirect
228. C3×C5×Q8C2×D4semidirect
242. C5×D12C2×D4semidirect
245. C4×C5×D3C2×D4semidirect
256. #1202#41semidirect
283. C3×C4×Q8C2×D5semidirect
286. Q8×Dic3C2×D5semidirect
300. #893C2×D5semidirect
301. #892C2×D5semidirect
314. C4×D12C2×D5semidirect
315. C42×D3C2×D5semidirect
401. C2×D15C2×#41semidirect
410. C2×C3×D5C2×#41semidirect
422. C5×Dic3C2×#41semidirect
442. #239D20semidirect
498. C5×Q8D3×D4semidirect
569. C4×Q8D3×D5semidirect
606. C3×Q8C2×D20semidirect
630. D12C2×D20semidirect
639. C4×D3C2×D20semidirect
658. C2×D5D3×#41semidirect
733. C3×C5D4×#41semidirect
761. Dic3D5×#41semidirect
783. Q8D3×D20semidirect
825. C5#86710semidirect
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×#920342
C2×D5×#2392
#117563352
C4×C5×#2392
C3×#659102
#117552512
Q8×#12022
#117538802
#117538792
#117538602
#117536962
#117527462
#117527402
C4×D3×D202
#117525432
#41×D203
#867105