Finite Group Databasebeta

← D5×#5572 #14479019

Subgroups — D5×#5572 #14479019

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Q8×D5C211yesmaximal, characteristic
2#11756331C211yesmaximal, characteristic, complemented
3C5×#5572C211yesmaximal, characteristic, complemented
4C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
5Q8×D5×Dic3C211yesmaximal, characteristic, complemented
6#11755144C211yesmaximal, characteristic, complemented
7#11755124C211yesmaximal, characteristic, complemented
8D5×#892C213yesmaximal
9#11753405C213yesmaximal, complemented
10D5×#887C213yesmaximal, complemented
11#11753381C213yesmaximal, complemented
12D5×#872C213yesmaximal
13#11752523C213yesmaximal, complemented
14C4×D5×Dic6C213yesmaximal, complemented
15#11752460C213yesmaximal, complemented
16D5×#519—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20D3×Q8×D5C4116yescomplemented
21C2×C4×D3×D5C2213yes—
22C2×D15⋊Q8C2213yes—
23C2×D3×Dic10C2213yes—
24C2×D5×Dic6C2213yes—
25C3×C4×C5×Q8C2211yescharacteristic, complemented
26Q8×Dic15C2211yescharacteristic, complemented
27#91781C2213yes—
28#91776C2213yescomplemented
29#91761C2213yes—
30C4×Dic30C2213yescomplemented
31C5×Q8×Dic3C2211yescharacteristic, complemented
32C5×#892C2213yes—
33C5×#887C2213yescomplemented
34C5×#872C2213yes—
35C4×C5×Dic6C2213yescomplemented
36C3×Q8×Dic5C2211yescharacteristic, complemented
37C3×D5×C4⋊C4C2213yes—
38C3×#4033C2213yescomplemented
39C3×C42×D5C2213yes—
40C3×C4×Dic10C2213yescomplemented
41D5×(C2×D3)⋊C4C2211yescharacteristic
42D5×(C2×D3)⋊C4C2213yes—
43C4×#1204C2216yescomplemented
44D5×C4⋊Dic3C2213yes—
45#91403C2216yes—
46#91402C2213yes—
47#91402C2213yes—
48#91400C2216yes—
49#91398C2213yes—
50#91398C2213yes—
51D5×Dic3⋊C4C2213yes—
52D5×Dic3⋊C4C2213yes—
53C4×D5×Dic3C2213yes—
54C4×D5×Dic3C2216yes—
55#91386C2213yes—
56#91371C2213yes—
57#91347C2213yes—
58#91344C2213yescomplemented
59#91340C2213yescomplemented
60#91338C2213yes—
61#91333C2213yescomplemented
62Dic5×Dic6C2213yescomplemented
63#91331C2213yescomplemented
64Dic3×Dic10C2213yescomplemented
65#91325C2216yescomplemented
66#91324C2216yescomplemented
67#91323C2216yescomplemented
68C2×#5572—51nomaximal, Hall
69C22×Q8×D5—31no—
70C5×#519—31no—
71#66146—31no—
72#65906—31no—
73#65906—33no—
74#65906—33no—
75#65906—31no—
76C4×Q8×D5—33no—
77C4×Q8×D5—33no—
78C4×Q8×D5—31no—
79C4×Q8×D5D311yescharacteristic, complemented
80D5×#117—33no—
81D5×#117—33no—
82#65850—33no—
83#65850—33no—
84C22×D3×D5C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86Q8×D15C2×C418yescomplemented
87C2×C4×D15C2313yes—
88C2×Dic30C2313yes—
89C5×D3×Q8C2×C418yescomplemented
90C2×C4×C5×D3C2313yes—
91C2×C5×Dic6C2313yes—
92C3×Q8×D5C2×C418yes—
93C2×C3×C4×D5C2311yescharacteristic
94C2×C3×C4×D5C2313yes—
95C2×C3×C4×D5C2313yes—
96C2×C3×Dic10C2313yes—
97C2×#1204C2316yes—
98C2×#1200C2313yes—
99C2×D3×Dic5C2313yes—
100C2×D5×Dic3C2311yescharacteristic
101C2×D5×Dic3C2313yes—
102C2×D5×Dic3C2313yes—
103C4×D3×D5C2×C4124yes—
104D15⋊Q8C2×C4124yescomplemented
105D3×Dic10C2×C4124yescomplemented
106D5×Dic6C2×C4124yes—
107C3×C5×C4⋊C4C2313yes—
108C3×C42×C5C2313yes—
109#6714C2311yescharacteristic
110#6714C2313yes—
111C4⋊Dic15C2313yes—
112#6712C2313yes—
113#6712C2313yes—
114C4×Dic15C2316yes—
115C4×Dic15C2313yes—
116C5×(C2×D3)⋊C4C2311yescharacteristic
117C5×(C2×D3)⋊C4C2313yes—
118C5×C4⋊Dic3C2313yes—
119C5×Dic3⋊C4C2313yes—
120C5×Dic3⋊C4C2313yes—
121C4×C5×Dic3C2316yes—
122C4×C5×Dic3C2313yes—
123C3×C4⋊Dic5C2313yes—
124C3×#683C2316yes—
125C3×C4×Dic5C2313yes—
126C3×C4×Dic5C2313yes—
127C3×C4×Dic5C2313yes—
128Dic3⋊Dic5C2313yes—
129Dic3⋊Dic5C2313yes—
130#6669C2313yes—
131#6669C2313yes—
132#6668C2316yes—
133#6667C2311yescharacteristic
134#6667C2313yes—
135(C2×D3)⋊Dic5C2311yescharacteristic
136(C2×D3)⋊Dic5C2313yes—
137Dic3×Dic5C2313yes—
138Dic3×Dic5C2313yes—
139Dic3×Dic5C2316yes—
140Dic3×Dic5C2316yes—
141C22×D3×Q8—51no—
142C2×C3×C4×Q8—51no—
143C2×Q8×Dic3—51no—
144#5572—51no—
145#5572—51no—
146#5572—51no—
147#5572—53no—
148#5572—53no—
149#5572—53no—
150#5572—53no—
151#5572D511yescharacteristic, direct product factor
152C2×#892—53no—
153C2×#887—53no—
154C2×#872—53no—
155C2×C4×Dic6—53no—
156C22×C5×Q8—31no—
157C2×Q8×D5—31no—
158C2×Q8×D5—316no—
159C2×Q8×D5—33no—
160C2×Q8×D5—33no—
161C2×Q8×D5C2×D311yescharacteristic
162C22×C4×D5—33no—
163C22×Dic10—33no—
164C4×C5×Q8—31no—
165C4×C5×Q8—33no—
166C4×C5×Q8—33no—
167C4×C5×Q8C2×D311yescharacteristic, complemented
168C5×#117—33no—
169C5×#117—33no—
170Q8×Dic5—31no—
171Q8×Dic5—33no—
172Q8×Dic5—33no—
173Q8×Dic5C2×D311yescharacteristic, complemented
174#4072—33no—
175#4072—33no—
176#4038—33no—
177#4038—33no—
178#4038—33no—
179#4038—33no—
180D5×C4⋊C4—33no—
181D5×C4⋊C4—33no—
182D5×C4⋊C4—33no—
183D5×C4⋊C4C2×D313yes—
184#4033—33no—
185#4033—33no—
186#4033—36no—
187#4033—36no—
188#4033—33no—
189#4033C2×D313yescomplemented
190D5×C22⋊C4—33no—
191D5×C22⋊C4—31no—
192#4023—36no—
193#4023—33no—
194#4023—33no—
195#4018—33no—
196#4018—36no—
197#4018—33no—
198C42×D5—36no—
199C42×D5—33no—
200C42×D5C2×D313yes—
201C4×Dic10—33no—
202C4×Dic10—33no—
203C4×Dic10—33no—
204C4×Dic10—36no—
205C4×Dic10—36no—
206C4×Dic10C2×D313yescomplemented
207C2×#519—151noSylow
208C22×D15C2411yescharacteristic
209C22×C5×D3C2411yescharacteristic
210C22×C3×D5C2411yescharacteristic
211C2×D3×D5—22no—
212C2×D3×D5—22no—
213C2×D3×D5C22×C414yes—
214C3×C5×Q8C22×C414yes—
215C2×C3×C4×C5C2411yescharacteristic
216C2×C3×C4×C5C2413yes—
217C2×C3×C4×C5C2413yes—
218C2×Dic15C2413yes—
219C2×Dic15C2411yescharacteristic
220C2×Dic15C2413yes—
221C4×D15C22×C4112yes—
222Dic30C22×C4112yes—
223C2×C5×Dic3C2413yes—
224C2×C5×Dic3C2411yescharacteristic
225C2×C5×Dic3C2413yes—
226C4×C5×D3C22×C4112yes—
227C5×Dic6C22×C4112yes—
228C2×C3×Dic5C2413yes—
229C2×C3×Dic5C2411yescharacteristic
230C2×C3×Dic5C2413yes—
231C3×C4×D5—22no—
232C3×C4×D5—26no—
233C3×C4×D5C22×C4112yes—
234C3×Dic10C22×C4112yes—
235#1204C22×C4124yes—
236#1200C22×C4112yes—
237D3×Dic5C22×C4112yes—
238D5×Dic3—26no—
239D5×Dic3—22no—
240D5×Dic3C22×C4112yes—
241C22×C3×Q8—51no—
242C2×D3×Q8—51no—
243C2×D3×Q8—516no—
244C2×D3×Q8—53no—
245C2×D3×Q8—53no—
246C2×D3×Q8C2×D511yescharacteristic
247C22×C4×D3—53no—
248C22×Dic6—53no—
249C3×C4×Q8—51no—
250C3×C4×Q8—53no—
251C3×C4×Q8—53no—
252C3×C4×Q8C2×D511yescharacteristic, complemented
253C2×C3×C4⋊C4—53no—
254C2×C3×C42—53no—
255Q8×Dic3—51no—
256Q8×Dic3—53no—
257Q8×Dic3—53no—
258Q8×Dic3C2×D511yescharacteristic, complemented
259C2×(C2×D3)⋊C4—51no—
260C2×(C2×D3)⋊C4—53no—
261C2×C4⋊Dic3—53no—
262C2×Dic3⋊C4—53no—
263C2×Dic3⋊C4—53no—
264C2×C4×Dic3—56no—
265C2×C4×Dic3—53no—
266#892—53no—
267#892—53no—
268#892—56no—
269#892—53no—
270#892—56no—
271#892C2×D513yes—
272#887—53no—
273#887—53no—
274#887—56no—
275#887—56no—
276#887—53no—
277#887C2×D513yescomplemented
278#872—53no—
279#872—53no—
280#872—53no—
281#872—53no—
282#872—53no—
283#872—53no—
284#872—53no—
285#872C2×D513yes—
286C4×Dic6—53no—
287C4×Dic6—53no—
288C4×Dic6—53no—
289C4×Dic6—56no—
290C4×Dic6—56no—
291C4×Dic6C2×D513yescomplemented
292C23×D5—31no—
293C2×C5×Q8—38no—
294C2×C5×Q8—33no—
295C2×C5×Q8C22×D311yescharacteristic
296C22×C4×C5—33no—
297C22×Dic5—33no—
298Q8×D5—38no—
299Q8×D5—324no—
300Q8×D5—324no—
301Q8×D5C4×D318yes—
302C2×C4×D5—33no—
303C2×C4×D5—33no—
304C2×C4×D5—33no—
305C2×C4×D5—324no—
306C2×C4×D5—33no—
307C2×C4×D5—31no—
308C2×C4×D5C22×D313yes—
309C2×C4×D5C22×D311yescharacteristic
310C2×C4×D5C22×D313yes—
311C2×Dic10—33no—
312C2×Dic10—36no—
313C2×Dic10—324no—
314C2×Dic10C22×D313yes—
315C5×C4⋊C4—33no—
316C5×C4⋊C4—33no—
317C5×C4⋊C4—33no—
318C5×C4⋊C4C22×D313yes—
319C5×C22⋊C4—33no—
320C5×C22⋊C4—31no—
321C42×C5—36no—
322C42×C5—33no—
323C42×C5C22×D313yes—
324C22⋊Dic5—33no—
325C22⋊Dic5—31no—
326#685—33no—
327#685—31no—
328#685—33no—
329#685—31no—
330C4⋊Dic5—33no—
331C4⋊Dic5—33no—
332C4⋊Dic5—33no—
333C4⋊Dic5C22×D313yes—
334#683—33no—
335#683—33no—
336#683—36no—
337#683—33no—
338#683—33no—
339#683C22×D316yes—
340C4×Dic5—36no—
341C4×Dic5—33no—
342C4×Dic5—36no—
343C4×Dic5—33no—
344C4×Dic5—33no—
345C4×Dic5—36no—
346C4×Dic5C22×D313yes—
347C4×Dic5C22×D313yes—
348C4×Dic5C22×D313yes—
349C23×Q8—151no—
350#519—31no—
351#519—153no—
352#519—153no—
353#519—151no—
354#519—153no—
355#519—153no—
356#519—151no—
357#519—151no—
358C2×C4×Q8—51no—
359C2×C4×Q8—153no—
360C2×C4×Q8—153no—
361C2×C4×Q8—151no—
362C2×#117—153no—
363C2×#117—153no—
364C22×C3×C5C2511yescharacteristic
365C2×D15—21no—
366C2×D15—21no—
367C2×D15C23×C412yes—
368C2×C5×D3—21no—
369C2×C5×D3—21no—
370C2×C5×D3C23×C412yes—
371C2×C3×D5C23×C412yes—
372C2×C3×D52−1+412yes—
373C2×C3×D52−1+412yes—
374D3×D5—28no—
375C3×C4×C5—21no—
376C3×C4×C5—23no—
377C3×C4×C5C23×C416yes—
378Dic15—23no—
379Dic15—21no—
380Dic15C23×C416yes—
381C3×Dic5—21no—
382C3×Dic5—23no—
383C3×Dic5C23×C416yes—
384C5×Dic3—23no—
385C5×Dic3—21no—
386C5×Dic3C23×C416yes—
387C23×D3—51no—
388C2×C3×Q8—58no—
389C2×C3×Q8—53no—
390C2×C3×Q8C22×D511yescharacteristic
391C22×C3×C4—53no—
392C22×C3×C4—53no—
393C22×C3×C4—51no—
394C22×Dic3—53no—
395C22×Dic3—51no—
396C22×Dic3—53no—
397D3×Q8—58no—
398D3×Q8—524no—
399D3×Q8—524no—
400D3×Q8C4×D518yescomplemented
401C2×C4×D3—53no—
402C2×C4×D3—53no—
403C2×C4×D3—53no—
404C2×C4×D3—524no—
405C2×C4×D3C22×D513yes—
406C2×Dic6—53no—
407C2×Dic6—56no—
408C2×Dic6—524no—
409C2×Dic6C22×D513yes—
410C3×C4⋊C4—56no—
411C3×C4⋊C4—53no—
412C3×C4⋊C4C22×D513yes—
413C3×C42—53no—
414C3×C42—53no—
415C3×C42—53no—
416C3×C42C22×D513yes—
417(C2×D3)⋊C4—51no—
418(C2×D3)⋊C4—53no—
419(C2×D3)⋊C4—51no—
420(C2×D3)⋊C4—53no—
421(C2×D3)⋊C4—51no—
422(C2×D3)⋊C4—53no—
423(C2×D3)⋊C4C22×D511yescharacteristic
424(C2×D3)⋊C4C22×D513yes—
425C4⋊Dic3—53no—
426C4⋊Dic3—56no—
427C4⋊Dic3C22×D513yes—
428Dic3⋊C4—53no—
429Dic3⋊C4—53no—
430Dic3⋊C4—53no—
431Dic3⋊C4—53no—
432Dic3⋊C4—53no—
433Dic3⋊C4—53no—
434Dic3⋊C4C22×D513yes—
435Dic3⋊C4C22×D513yes—
436C4×Dic3—56no—
437C4×Dic3—53no—
438C4×Dic3—56no—
439C4×Dic3—56no—
440C4×Dic3—53no—
441C4×Dic3—53no—
442C4×Dic3C22×D516yes—
443C4×Dic3C22×D513yes—
444C23×C5—31no—
445C22×D5—31no—
446C22×D5—34no—
447C22×D5—62no—
448C22×D5—62no—
449C22×D5C23×D311yescharacteristic
450C5×Q8—312no—
451C5×Q8C2×C4×D314yes—
452C2×C4×C5—33no—
453C2×C4×C5—312no—
454C2×C4×C5—33no—
455C2×C4×C5—31no—
456C2×C4×C5C23×D313yes—
457C2×C4×C5C23×D311yescharacteristic
458C2×C4×C5C23×D313yes—
459C2×Dic5—33no—
460C2×Dic5—312no—
461C2×Dic5—33no—
462C2×Dic5—31no—
463C2×Dic5C23×D313yes—
464C2×Dic5C23×D311yescharacteristic
465C2×Dic5C23×D313yes—
466C4×D5—22no—
467C4×D5—26no—
468C4×D5—312no—
469C4×D5—312no—
470C4×D5—312no—
471C4×D5—66no—
472C4×D5—62no—
473C4×D5C2×C4×D3112yes—
474Dic10—312no—
475Dic10—324no—
476Dic10C2×C4×D3112yes—
477C22×Q8—31no—
478C22×Q8—51no—
479C22×Q8—153no—
480C22×Q8—153no—
481C22×Q8—153no—
482C22×Q8—1516no—
483C22×Q8—151no—
484C23×C4—153no—
485C4×Q8—31no—
486C4×Q8—33no—
487C4×Q8—33no—
488C4×Q8—51no—
489C4×Q8—53no—
490C4×Q8—53no—
491C4×Q8—156no—
492C4×Q8—156no—
493C4×Q8—153no—
494C4×Q8—153no—
495C4×Q8—156no—
496C4×Q8—153no—
497C4×Q8—153no—
498C4×Q8—156no—
499C4×Q8—153no—
500C4×Q8—153no—
501C4×Q8—151no—
502C4×Q8—153no—
503C4×Q8—153no—
504C4×Q8D3×D511yescharacteristic, complemented
505#117—33no—
506#117—33no—
507#117—153no—
508#117—156no—
509#117—153no—
510#117—153no—
511#117—153no—
512#117—153no—
513#117—153no—
514#117—156no—
515#117—153no—
516#117—153no—
517#117—153no—
518#117—153no—
519C2×C4⋊C4—53no—
520C2×C4⋊C4—153no—
521C2×C4⋊C4—153no—
522C2×C4⋊C4—153no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—153no—
525C2×C42—53no—
526C2×C42—153no—
527C2×C42—156no—
528C2×C3×C5C24×C411yescharacteristic
529C2×C3×C5C2×2−1+411yescharacteristic
530C2×C3×C5C2×2−1+411yescharacteristic
531D15—22no—
532C3×D5#51914yescomplemented
533C5×D3—22no—
534C23×C3—51no—
535C22×D3—51no—
536C22×D3—54no—
537C22×D3—102no—
538C22×D3—102no—
539C22×D3C23×D511yescharacteristic
540C3×Q8—512no—
541C3×Q8C2×C4×D514yes—
542C2×C3×C4—53no—
543C2×C3×C4—512no—
544C2×C3×C4—53no—
545C2×C3×C4—51no—
546C2×C3×C4—102no—
547C2×C3×C4—106no—
548C2×C3×C4C23×D513yes—
549C2×C3×C4C23×D511yescharacteristic
550C2×C3×C4C23×D513yes—
551C2×Dic3—53no—
552C2×Dic3—512no—
553C2×Dic3—51no—
554C2×Dic3—53no—
555C2×Dic3—106no—
556C2×Dic3—102no—
557C2×Dic3C23×D511yescharacteristic
558C2×Dic3C23×D513yes—
559C2×Dic3C23×D513yes—
560C4×D3—512no—
561C4×D3—512no—
562C4×D3—512no—
563C4×D3C2×C4×D5112yes—
564Dic6—512no—
565Dic6—524no—
566Dic6C2×C4×D5112yes—
567C22×C5—32no—
568C22×C5—61no—
569C22×C5—61no—
570C22×C5C24×D311yescharacteristic
571C2×D5—32no—
572C2×D5—61no—
573C2×D5—61no—
574C2×D5—68no—
575C2×D5C22×C4×D312yes—
576C2×D5#100712yes—
577C2×D5#101012yes—
578C4×C5—21no—
579C4×C5—23no—
580C4×C5—36no—
581C4×C5—63no—
582C4×C5—61no—
583C4×C5C22×C4×D316yes—
584Dic5—21no—
585Dic5—23no—
586Dic5—36no—
587Dic5—63no—
588Dic5—61no—
589Dic5C22×C4×D316yes—
590C24—151no—
591C2×Q8—38no—
592C2×Q8—33no—
593C2×Q8—58no—
594C2×Q8—53no—
595C2×Q8—156no—
596C2×Q8—1524no—
597C2×Q8—1524no—
598C2×Q8—1524no—
599C2×Q8—158no—
600C2×Q8—153no—
601C2×Q8C2×D3×D511yescharacteristic
602C22×C4—33no—
603C22×C4—53no—
604C22×C4—51no—
605C22×C4—53no—
606C22×C4—153no—
607C22×C4—1524no—
608C22×C4—153no—
609C22×C4—151no—
610C22×C4—153no—
611C22×C4—153no—
612C22×C4—153no—
613C4⋊C4—33no—
614C4⋊C4—33no—
615C4⋊C4—33no—
616C4⋊C4—56no—
617C4⋊C4—53no—
618C4⋊C4—153no—
619C4⋊C4—153no—
620C4⋊C4—156no—
621C4⋊C4—153no—
622C4⋊C4—153no—
623C4⋊C4—153no—
624C4⋊C4—153no—
625C4⋊C4—153no—
626C4⋊C4C2×D3×D513yes—
627C22⋊C4—33no—
628C22⋊C4—31no—
629C22⋊C4—151no—
630C22⋊C4—153no—
631C22⋊C4—151no—
632C22⋊C4—153no—
633C22⋊C4—153no—
634C22⋊C4—151no—
635C42—36no—
636C42—33no—
637C42—53no—
638C42—53no—
639C42—53no—
640C42—156no—
641C42—153no—
642C42—153no—
643C42—156no—
644C42—156no—
645C42—153no—
646C42C2×D3×D513yes—
647C3×C5C2×#51911yescharacteristic, complemented, Hall
648C22×C3—52no—
649C22×C3—52no—
650C22×C3—52no—
651C22×C3C24×D511yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—52no—
655C2×D3—108no—
656C2×D3—101no—
657C2×D3—101no—
658C2×D3C22×C4×D512yes—
659C3×C4—21no—
660C3×C4—23no—
661C3×C4—56no—
662C3×C4—101no—
663C3×C4—103no—
664C3×C4C22×C4×D516yes—
665Dic3—23no—
666Dic3—21no—
667Dic3—56no—
668Dic3—103no—
669Dic3—101no—
670Dic3C22×C4×D516yes—
671C2×C5—62no—
672C2×C5C23×C4×D311yescharacteristic
673C2×C5C2×#100711yescharacteristic
674C2×C5C2×#101011yescharacteristic
675D5—62no—
676D5#557214yesdirect product factor
677C23—31no—
678C23—51no—
679C23—154no—
680C23—151no—
681C23—302no—
682C23—302no—
683Q8—312no—
684Q8—512no—
685Q8—1524no—
686Q8—1512no—
687Q8C4×D3×D514yes—
688C2×C4—33no—
689C2×C4—312no—
690C2×C4—33no—
691C2×C4—31no—
692C2×C4—53no—
693C2×C4—512no—
694C2×C4—51no—
695C2×C4—53no—
696C2×C4—102no—
697C2×C4—106no—
698C2×C4—1512no—
699C2×C4—1512no—
700C2×C4—1512no—
701C2×C4—153no—
702C2×C4—1512no—
703C2×C4—153no—
704C2×C4—151no—
705C2×C4—306no—
706C2×C4—302no—
707C2×C4C22×D3×D513yes—
708C2×C4C22×D3×D511yescharacteristic
709C2×C4C22×D3×D513yes—
710C2×C3—54no—
711C2×C3C23×C4×D511yescharacteristic
712C2×C3D5×2−1+411yescharacteristic
713C2×C3D5×2−1+411yescharacteristic
714D3—22no—
715D3—102no—
716C5C2×#557211yescharacteristic, complemented, Sylow
717C22—32no—
718C22—52no—
719C22—52no—
720C22—52no—
721C22—61no—
722C22—61no—
723C22—152no—
724C22—308no—
725C22—301no—
726C22—301no—
727C22C23×D3×D511yescharacteristic
728C4—21no—
729C4—23no—
730C4—36no—
731C4—56no—
732C4—63no—
733C4—61no—
734C4—101no—
735C4—103no—
736C4—156no—
737C4—303no—
738C4—301no—
739C4C2×C4×D3×D516yes—
740C3D5×#51911yescharacteristic, complemented, Sylow
741C2—54no—
742C2—62no—
743C2—302no—
744C2C22×C4×D3×D511yescharacteristic
745C2D5×#100711yescharacteristic
746C2D5×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC22×D3×D5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11756331C2semidirect
3. C5×#5572C2semidirect
4. C3×C4×Q8×D5C2semidirect
5. Q8×D5×Dic3C2semidirect
6. #11755144C2semidirect
7. #11755124C2semidirect
9. #11753405C2semidirect
10. D5×#887C2semidirect
11. #11753381C2semidirect
13. #11752523C2semidirect
14. C4×D5×Dic6C2semidirect
15. #11752460C2semidirect
20. D3×Q8×D5C4semidirect
25. C3×C4×C5×Q8C22semidirect
26. Q8×Dic15C22semidirect
28. #91776C22semidirect
30. C4×Dic30C22semidirect
31. C5×Q8×Dic3C22semidirect
33. C5×#887C22semidirect
35. C4×C5×Dic6C22semidirect
36. C3×Q8×Dic5C22semidirect
38. C3×#4033C22semidirect
40. C3×C4×Dic10C22semidirect
43. C4×#1204C22semidirect
58. #91344C22semidirect
59. #91340C22semidirect
61. #91333C22semidirect
62. Dic5×Dic6C22semidirect
63. #91331C22semidirect
64. Dic3×Dic10C22semidirect
65. #91325C22semidirect
66. #91324C22semidirect
67. #91323C22semidirect
79. C4×Q8×D5D3semidirect
86. Q8×D15C2×C4semidirect
89. C5×D3×Q8C2×C4semidirect
104. D15⋊Q8C2×C4semidirect
105. D3×Dic10C2×C4semidirect
151. #5572D5direct (N × H)
167. C4×C5×Q8C2×D3semidirect
173. Q8×Dic5C2×D3semidirect
189. #4033C2×D3semidirect
206. C4×Dic10C2×D3semidirect
252. C3×C4×Q8C2×D5semidirect
258. Q8×Dic3C2×D5semidirect
277. #887C2×D5semidirect
291. C4×Dic6C2×D5semidirect
400. D3×Q8C4×D5semidirect
504. C4×Q8D3×D5semidirect
532. C3×D5#519semidirect
647. C3×C5C2×#519semidirect
676. D5#5572direct (N × H)
716. C5C2×#5572semidirect
740. C3D5×#519semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q8×D52
#117563312
C5×#55722
C3×C4×Q8×D52
Q8×D5×Dic32
#117551442
#117551242
D5×#8922
#117534052
D5×#8872
#117533812
D5×#8722
#117525232
C4×D5×Dic62
#117524602
D5×#5193
C2×#55725