Finite Group Databasebeta

← #14424155

Subgroups — #14424155

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91360C211yesmaximal, characteristic, complemented
4C2×#91313C211yesmaximal, characteristic, complemented
5C5×#5232C211yesmaximal, characteristic, complemented
6#11749295C212yesmaximal, complemented
7#11749291C212yesmaximal, complemented
8#11749049C212yesmaximal, complemented
9#11749045C212yesmaximal, complemented
10#11748368C211yesmaximal, characteristic, complemented
11#11748341C211yesmaximal, characteristic, complemented
12#10610616—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic, complemented
15C3×D5×#41—24no—
16C3×D5×#41—24no—
17C2×C3×#713C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic
19C2×C3×#711—21no—
20C2×C3×#711C2211yescharacteristic
21C2×C3×D4×D5—21no—
22C2×C3×D4×D5C2211yescharacteristic
23C2×C3×#709—21no—
24C2×C3×#709C2211yescharacteristic
25C22×C3×C4×D5—21no—
26C22×C3×C4×D5C2211yescharacteristic
27#91840—24no—
28C2×#6718C2212yescomplemented
29C2×#6716C2212yescomplemented
30C2×#6710C2211yescharacteristic, complemented
31C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
32C2×C5×#208C2211yescharacteristic, complemented
33C2×Dic3⋊Dic5—21no—
34C2×#6665—21no—
35#91360—21no—
36#91360—21no—
37#91360C2212yes—
38#91360C2212yescomplemented
39C2×#6662C2212yescomplemented
40#91313—24no—
41C2×#6657C2212yescomplemented
42C5×#835C2212yescomplemented
43C5×#832C2212yescomplemented
44#90970C2212yescomplemented
45#90964C2212yescomplemented
46#90955C2212yes—
47#90955C2212yescomplemented
48#84084—51nomaximal, Hall
49C2×D5×#41D311yescharacteristic
50C2×#4097—31no—
51C2×#4055—31no—
52C2×#4043—31no—
53C5×#417—31no—
54#65415—31no—
55#65255—31no—
56#65099—32no—
57#65097—32no—
58#65072—32no—
59#65065—32no—
60C23×C3×D5—21no—
61C23×C3×D5D411yescharacteristic
62C3×C5×#41—22no—
63C3×C5×#41D414yes—
64C2×C3×C5×Q8C2311yescharacteristic
65C2×C3×C5×D4—21no—
66C2×C3×C5×D4C2311yescharacteristic
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5C2311yescharacteristic
69C22×Dic15—21no—
70C2×Dic30—22no—
71C2×Dic30—22no—
72C2×Dic30—21no—
73C2×Dic30C2312yes—
74C22×C5×Dic3—21no—
75C2×C3×C22⋊D5—21no—
76C2×C3×C22⋊D5—21no—
77C2×C3×C22⋊D5—21no—
78C22×C3×Dic5—21no—
79C22×C3×Dic5D411yescharacteristic
80C3×#713—22no—
81C3×#713—22no—
82C3×Q8×D5—22no—
83C3×Q8×D5—22no—
84C3×#711—28no—
85C3×#711—22no—
86C3×#711—22no—
87C3×D4×D5—28no—
88C3×D4×D5—22no—
89C3×D4×D5—22no—
90C3×#709—28no—
91C3×#709—22no—
92C3×#709D414yes—
93C2×C3×D20—21no—
94C2×C3×D20C2311yescharacteristic
95C2×C3×C4×D5—28no—
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5D411yescharacteristic
102C2×C3×C4×D5D411yescharacteristic
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×Dic10—21no—
106C2×C3×Dic10C2311yescharacteristic
107#6718—24no—
108#6716—24no—
109#6710—22no—
110C2×C3⋊#168C2312yes—
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2312yes—
113C5×#208—22no—
114C2×C5×C3⋊C8C2312yes—
115Dic3⋊Dic5—22no—
116Dic3⋊Dic5—22no—
117#6665—22no—
118#6665—22no—
119#6662—24no—
120#6657—24no—
121C22×C3×#41—51no—
122C2×#951—51no—
123C2×#951—51no—
124C2×#924—51no—
125#5239—52no—
126#5239—52no—
127#5232—51no—
128#5232D511yescharacteristic, complemented
129#5228—52no—
130#5218—52no—
131#5207—51no—
132C2×C5×#41C2×D311yescharacteristic
133D5×#41—24no—
134D5×#41—24no—
135C2×#713C2×D311yescharacteristic
136C2×Q8×D5C2×D311yescharacteristic
137C2×#711—21no—
138C2×#711C2×D311yescharacteristic
139C2×D4×D5—21no—
140C2×D4×D5C2×D311yescharacteristic
141C2×#709—21no—
142C2×#709C2×D311yescharacteristic
143C22×C4×D5—21no—
144C22×C4×D5C2×D311yescharacteristic
145C22×Dic10—31no—
146C2×C5×M16—31no—
147C2×C5×C4⋊C4—31no—
148#4097—64no—
149C2×#689—32no—
150C2×#687—32no—
151C2×#685—61no—
152C2×C4⋊Dic5—61no—
153C2×#681—31no—
154#4055—64no—
155C2×Dic20—32no—
156C2×#677—32no—
157#4043—32no—
158#4043—32no—
159#4043—61no—
160#4043—61no—
161C5×#103—32no—
162C5×#102—32no—
163#3952—32no—
164#3952—32no—
165#3942—32no—
166#3941—32no—
167#3007—151noSylow
168C23×C3×C5—21no—
169C23×C3×C5C2×D411yescharacteristic
170C22×C3×D5—24no—
171C22×C3×D5—22no—
172C22×C3×D5—21no—
173C22×C3×D5—22no—
174C22×C3×D5—41no—
175C22×C3×D5—42no—
176C22×C3×D5—42no—
177C22×C3×D5C2×D411yescharacteristic
178C22×C3×D5C2×D411yescharacteristic
179C3×C5×Q8—21no—
180C3×C5×Q8C2×D412yes—
181C3×C5×D4—24no—
182C3×C5×D4—21no—
183C3×C5×D4C2×D412yes—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—24no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D412yes—
188C2×C3×C4×C5C2×D412yes—
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—22no—
191C2×Dic15—42no—
192Dic30—22no—
193Dic30—22no—
194Dic30—42no—
195C2×C5×Dic3—22no—
196C2×C5×Dic3—42no—
197C3×C22⋊D5—24no—
198C3×C22⋊D5—24no—
199C3×C22⋊D5—24no—
200C2×C3×Dic5—24no—
201C2×C3×Dic5—22no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C3×D20—24no—
206C3×D20—21no—
207C3×D20C2×D412yes—
208C3×C4×D5—24no—
209C3×C4×D5—24no—
210C3×C4×D5—22no—
211C3×C4×D5—24no—
212C3×C4×D5—22no—
213C3×C4×D5—21no—
214C3×C4×D5—21no—
215C3×C4×D5—21no—
216C3×C4×D5—21no—
217C3×Dic10—24no—
218C3×Dic10—21no—
219C3×Dic10C2×D412yes—
220C3⋊#168—22no—
221C5×C3⋊C8—22no—
222C2×C3×#41—51no—
223C2×C3×#41—51no—
224C2×C3×#41—51no—
225C2×C3×#41—101no—
226C2×C3×#41—101no—
227C2×C3×#41—104no—
228C2×C3×#41—104no—
229C2×C3×#41C2×D511yescharacteristic
230C22×C3×Q8—51no—
231C22×C3×D4—51no—
232C22×C3×D4—101no—
233C23×C3×C4—51no—
234C23×C3×C4—101no—
235C22×Dic6—51no—
236C2×#217—101no—
237#951—104no—
238#951—104no—
239C2×#216—52no—
240C2×#216—52no—
241C2×#214—52no—
242C2×#214—52no—
243C2×C4⋊Dic3C2×D511yescharacteristic, complemented
244#924—52no—
245#924—52no—
246#924—101no—
247#924—101no—
248C2×Dic3⋊C4—101no—
249C2×#208—51no—
250C2×#208C2×D511yescharacteristic, complemented
251#835—52no—
252#835C2×D512yescomplemented
253#832—52no—
254#832C2×D512yescomplemented
255#830—52no—
256#830—52no—
257C23×D5—21no—
258C23×D5#6711yescharacteristic
259C5×#41—22no—
260C5×#41#6714yes—
261C2×C5×Q8C22×D311yescharacteristic
262C2×C5×D4—21no—
263C2×C5×D4C22×D311yescharacteristic
264C22×C4×C5—21no—
265C22×C4×C5—61no—
266C22×C4×C5C22×D311yescharacteristic
267C2×C22⋊D5—21no—
268C2×C22⋊D5—21no—
269C2×C22⋊D5—21no—
270C22×Dic5—21no—
271C22×Dic5—61no—
272C22×Dic5#6711yescharacteristic
273#713—22no—
274#713—22no—
275Q8×D5—22no—
276Q8×D5—22no—
277#711—28no—
278#711—22no—
279#711—22no—
280D4×D5—28no—
281D4×D5—22no—
282D4×D5—22no—
283#709—28no—
284#709—22no—
285#709#6714yes—
286C2×D20—21no—
287C2×D20C22×D311yescharacteristic
288C2×C4×D5—28no—
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—22no—
292C2×C4×D5—22no—
293C2×C4×D5—21no—
294C2×C4×D5#6711yescharacteristic
295C2×C4×D5#6711yescharacteristic
296C2×C4×D5C22×D311yescharacteristic
297C2×C4×D5C22×D311yescharacteristic
298C2×Dic10—21no—
299C2×Dic10—32no—
300C2×Dic10—62no—
301C2×Dic10—62no—
302C2×Dic10—61no—
303C2×Dic10C22×D311yescharacteristic
304C5×M16—62no—
305C2×C5×C8—32no—
306C5×C4⋊C4—32no—
307C5×C4⋊C4—61no—
308#689—64no—
309#687—64no—
310#685—62no—
311#685—62no—
312C4⋊Dic5—62no—
313C4⋊Dic5—62no—
314#681—62no—
315C2×#168—32no—
316Dic20—64no—
317#677—64no—
318C22×#41—51no—
319C2×#137—151no—
320C2×#137—151no—
321C2×C22⋊Q8—151no—
322#452—152no—
323#452—152no—
324#451—152no—
325#450—152no—
326#417—31no—
327#417—151no—
328#407—151no—
329C22×C3×C5—21no—
330C22×C3×C5—21no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5#12012yes—
335C22×C3×C5C22×D411yescharacteristic
336C2×C3×D5—21no—
337C2×C3×D5—21no—
338C2×C3×D5—21no—
339C2×C3×D5—22no—
340C2×C3×D5—21no—
341C2×C3×D5—21no—
342C2×C3×D5—44no—
343C2×C3×D5—48no—
344C2×C3×D5—41no—
345C2×C3×D5—41no—
346C2×C3×D5#13712yescomplemented
347C3×C4×C5—22no—
348C3×C4×C5#12012yes—
349C3×C4×C5C22×D411yescharacteristic
350C3×C4×C5C22×D411yescharacteristic
351Dic15—42no—
352C3×Dic5—21no—
353C3×Dic5—22no—
354C3×Dic5—21no—
355C5×Dic3—42no—
356C24×C3—51no—
357C24×C3—101no—
358C3×#41—22no—
359C3×#41—54no—
360C3×#41—108no—
361C3×#41—102no—
362C3×#41—108no—
363C3×#41—102no—
364C3×#41—102no—
365C3×#41—102no—
366C3×#41—102no—
367C3×#41D2014yes—
368C2×C3×Q8—51no—
369C2×C3×Q8—101no—
370C2×C3×Q8—102no—
371C2×C3×Q8—102no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—21no—
374C2×C3×D4—51no—
375C2×C3×D4—101no—
376C2×C3×D4—101no—
377C2×C3×D4—102no—
378C2×C3×D4—108no—
379C2×C3×D4—101no—
380C2×C3×D4—101no—
381C2×C3×D4—102no—
382C2×C3×D4C22×D511yescharacteristic
383C22×C3×C4—21no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—51no—
389C22×C3×C4—101no—
390C22×C3×C4—101no—
391C22×C3×C4—108no—
392C22×C3×C4—101no—
393C22×C3×C4—102no—
394C22×C3×C4—102no—
395C22×C3×C4—101no—
396C22×C3×C4C22×D511yescharacteristic
397C22×Dic3—21no—
398C22×Dic3—101no—
399C2×Dic6—52no—
400C2×Dic6—102no—
401C2×Dic6—102no—
402C2×Dic6—101no—
403#217—102no—
404#217—102no—
405#216—104no—
406#216—104no—
407#214—104no—
408#214—104no—
409C4⋊Dic3—21no—
410C4⋊Dic3C22×D512yes—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413#208—22no—
414#208—102no—
415C2×C3⋊C8—52no—
416C2×C3⋊C8C22×D512yes—
417C23×C5—21no—
418C23×C5C2×#6711yescharacteristic
419C22×D5—24no—
420C22×D5—22no—
421C22×D5—21no—
422C22×D5—22no—
423C22×D5—41no—
424C22×D5—42no—
425C22×D5—42no—
426C22×D5C2×#6711yescharacteristic
427C22×D5C2×#6711yescharacteristic
428C5×Q8—21no—
429C5×Q8C2×#6712yes—
430C5×D4—24no—
431C5×D4—21no—
432C5×D4C2×#6712yes—
433C2×C4×C5—21no—
434C2×C4×C5—24no—
435C2×C4×C5—62no—
436C2×C4×C5—122no—
437C2×C4×C5C2×#6712yes—
438C2×C4×C5C2×#6711yescharacteristic
439C2×C4×C5C2×#6712yes—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—24no—
442C22⋊D5—24no—
443C22⋊D5—24no—
444C2×Dic5—24no—
445C2×Dic5—22no—
446C2×Dic5—21no—
447C2×Dic5—62no—
448C2×Dic5—122no—
449C2×Dic5C2×#6711yescharacteristic
450C2×Dic5C2×#6711yescharacteristic
451D20—24no—
452D20—21no—
453D20C2×#6712yes—
454C4×D5—24no—
455C4×D5—24no—
456C4×D5—22no—
457C4×D5—24no—
458C4×D5—22no—
459C4×D5—21no—
460C4×D5—21no—
461C4×D5—21no—
462C4×D5—21no—
463Dic10—24no—
464Dic10—21no—
465Dic10—62no—
466Dic10—62no—
467Dic10—122no—
468Dic10C2×#6712yes—
469C5×C8—62no—
470#168—62no—
471C2×#41—51no—
472C2×#41—51no—
473C2×#41—51no—
474C2×#41—101no—
475C2×#41—101no—
476C2×#41—104no—
477C2×#41—104no—
478C2×#41D3×D511yescharacteristic
479C22×Q8—51no—
480C22×Q8—151no—
481C22×D4—51no—
482C22×D4—101no—
483C23×C4—51no—
484C23×C4—101no—
485#137—304no—
486#137—304no—
487C2×Q16—152no—
488C2×Q16—152no—
489C2×SD16—152no—
490C2×SD16—152no—
491C2×M16—31no—
492C2×M16—151no—
493C22⋊Q8—152no—
494C22⋊Q8—152no—
495C22⋊Q8—301no—
496C22⋊Q8—301no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—301no—
499C2×C22⋊C4—301no—
500#103—32no—
501#103—152no—
502#102—32no—
503#102—152no—
504C22⋊C8—152no—
505C22⋊C8—152no—
506C2×C3×C5—22no—
507C2×C3×C5—42no—
508C2×C3×C5C2×#12011yescharacteristic
509C2×C3×C5C2×#13711yescharacteristic
510C2×C3×C5#57511yescharacteristic
511C3×D5—22no—
512C3×D5—41no—
513C3×D5—42no—
514C23×C3—21no—
515C23×C3—51no—
516C23×C3—51no—
517C23×C3—102no—
518C23×C3—104no—
519C23×C3—101no—
520C23×C3—102no—
521C23×C3—201no—
522C23×C3—202no—
523C23×C3—202no—
524C23×C3D4×D511yescharacteristic
525C3×Q8—21no—
526C3×Q8—52no—
527C3×Q8—104no—
528C3×Q8—101no—
529C3×Q8C2×D2012yes—
530C3×D4—24no—
531C3×D4—21no—
532C3×D4—52no—
533C3×D4—104no—
534C3×D4—104no—
535C3×D4—104no—
536C3×D4—104no—
537C3×D4—101no—
538C3×D4C2×D2012yes—
539C2×C3×C4—21no—
540C2×C3×C4—24no—
541C2×C3×C4—51no—
542C2×C3×C4—51no—
543C2×C3×C4—104no—
544C2×C3×C4—104no—
545C2×C3×C4—104no—
546C2×C3×C4—101no—
547C2×C3×C4—102no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—102no—
553C2×C3×C4—102no—
554C2×C3×C4—104no—
555C2×C3×C4C2×D2012yes—
556C2×C3×C4D4×D512yes—
557C2×C3×C4D4×D511yescharacteristic
558C2×C3×C4C23×D511yescharacteristic
559C2×Dic3—22no—
560C2×Dic3—42no—
561C2×Dic3—102no—
562C2×Dic3—202no—
563Dic6—102no—
564Dic6—102no—
565Dic6—202no—
566C3⋊C8—22no—
567C3⋊C8—102no—
568C22×C5—21no—
569C22×C5—21no—
570C22×C5—22no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5#95312yes—
574C22×C5C22×#6711yescharacteristic
575C2×D5—21no—
576C2×D5—21no—
577C2×D5—21no—
578C2×D5—21no—
579C2×D5—21no—
580C2×D5—22no—
581C2×D5—44no—
582C2×D5—48no—
583C2×D5—41no—
584C2×D5—41no—
585C2×D5#95112yescomplemented
586C4×C5—22no—
587C4×C5—122no—
588C4×C5#95312yes—
589C4×C5C22×#6711yescharacteristic
590C4×C5C22×#6711yescharacteristic
591Dic5—21no—
592Dic5—22no—
593Dic5—21no—
594Dic5—122no—
595C24—51no—
596C24—101no—
597#41—22no—
598#41—54no—
599#41—108no—
600#41—102no—
601#41—108no—
602#41—102no—
603#41—102no—
604#41—102no—
605#41—102no—
606#41#120214yes—
607C2×Q8—51no—
608C2×Q8—101no—
609C2×Q8—102no—
610C2×Q8—102no—
611C2×Q8—152no—
612C2×Q8—301no—
613C2×Q8—302no—
614C2×Q8—302no—
615C2×Q8C2×D3×D511yescharacteristic
616C2×D4—21no—
617C2×D4—51no—
618C2×D4—101no—
619C2×D4—101no—
620C2×D4—102no—
621C2×D4—108no—
622C2×D4—101no—
623C2×D4—101no—
624C2×D4—102no—
625C2×D4C2×D3×D511yescharacteristic
626C22×C4—21no—
627C22×C4—51no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—61no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—108no—
636C22×C4—101no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—101no—
640C22×C4—301no—
641C22×C4C2×D3×D511yescharacteristic
642Q16—304no—
643Q16—304no—
644SD16—304no—
645SD16—304no—
646M16—62no—
647M16—302no—
648C2×C8—32no—
649C2×C8—152no—
650C4⋊C4—32no—
651C4⋊C4—61no—
652C4⋊C4—302no—
653C4⋊C4—302no—
654C22⋊C4—302no—
655C22⋊C4—302no—
656C3×C5#300711yescharacteristic, complemented, Hall
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—52no—
663C22×C3—101no—
664C22×C3—101no—
665C22×C3—102no—
666C22×C3—101no—
667C22×C3—101no—
668C22×C3—101no—
669C22×C3—204no—
670C22×C3—208no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3#402812yes—
674C22×C3C2×D4×D511yescharacteristic
675C3×C4—22no—
676C3×C4—101no—
677C3×C4—101no—
678C3×C4—102no—
679C3×C4#402812yes—
680C3×C4C22×D2011yescharacteristic
681C3×C4C2×D4×D511yescharacteristic
682Dic3—42no—
683Dic3—202no—
684C2×C5—22no—
685C2×C5—42no—
686C2×C5#582211yescharacteristic
687C2×C5C2×#95111yescharacteristic
688C2×C5C2×#95311yescharacteristic
689D5—22no—
690D5—41no—
691D5—42no—
692C23—21no—
693C23—51no—
694C23—51no—
695C23—102no—
696C23—104no—
697C23—101no—
698C23—102no—
699C23—201no—
700C23—202no—
701C23—202no—
702C23D5×#6711yescharacteristic
703Q8—21no—
704Q8—52no—
705Q8—104no—
706Q8—101no—
707Q8—302no—
708Q8—302no—
709Q8—602no—
710Q8C2×#120212yes—
711D4—24no—
712D4—21no—
713D4—52no—
714D4—104no—
715D4—104no—
716D4—104no—
717D4—104no—
718D4—101no—
719D4C2×#120212yes—
720C2×C4—21no—
721C2×C4—24no—
722C2×C4—51no—
723C2×C4—51no—
724C2×C4—62no—
725C2×C4—104no—
726C2×C4—104no—
727C2×C4—104no—
728C2×C4—101no—
729C2×C4—102no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—104no—
737C2×C4—122no—
738C2×C4—302no—
739C2×C4—602no—
740C2×C4C2×#120212yes—
741C2×C4D5×#6712yes—
742C2×C4D5×#6711yescharacteristic
743C2×C4C22×D3×D511yescharacteristic
744C8—62no—
745C8—302no—
746C2×C3—22no—
747C2×C3—42no—
748C2×C3—102no—
749C2×C3—201no—
750C2×C3—202no—
751C2×C3C2×#402811yescharacteristic
752C2×C3#6610711yescharacteristic
753C2×C3D5×#13711yescharacteristic
754C5#8408411yescharacteristic, complemented, Sylow
755C22—21no—
756C22—21no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—52no—
761C22—101no—
762C22—101no—
763C22—101no—
764C22—101no—
765C22—102no—
766C22—101no—
767C22—204no—
768C22—208no—
769C22—201no—
770C22—201no—
771C22#9156412yes—
772C22C2×D5×#6711yescharacteristic
773C4—22no—
774C4—101no—
775C4—101no—
776C4—102no—
777C4—122no—
778C4—602no—
779C4#9156412yes—
780C4C22×#120211yescharacteristic
781C4C2×D5×#6711yescharacteristic
782C3#1061061611yescharacteristic, complemented, Sylow
783C2—22no—
784C2—42no—
785C2—102no—
786C2—201no—
787C2—202no—
788C2D5×#95111yescharacteristic
789C2#1175534311yescharacteristic
790C2C2×#9156411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D5×#41C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91840C2semidirect
3. C2×#91360C2semidirect
4. C2×#91313C2semidirect
5. C5×#5232C2semidirect
6. #11749295C2semidirect
7. #11749291C2semidirect
8. #11749049C2semidirect
9. #11749045C2semidirect
10. #11748368C2semidirect
11. #11748341C2semidirect
14. C22×Dic30C22semidirect
28. C2×#6718C22semidirect
29. C2×#6716C22semidirect
30. C2×#6710C22semidirect
31. C2×C5×C4⋊Dic3C22semidirect
32. C2×C5×#208C22semidirect
38. #91360C22semidirect
39. C2×#6662C22semidirect
41. C2×#6657C22semidirect
42. C5×#835C22semidirect
43. C5×#832C22semidirect
44. #90970C22semidirect
45. #90964C22semidirect
47. #90955C22semidirect
128. #5232D5semidirect
243. C2×C4⋊Dic3C2×D5semidirect
250. C2×#208C2×D5semidirect
252. #835C2×D5semidirect
254. #832C2×D5semidirect
346. C2×C3×D5#137semidirect
585. C2×D5#951semidirect
656. C3×C5#3007semidirect
754. C5#84084semidirect
782. C3#10610616semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C2×#918402
C2×#913602
C2×#913132
C5×#52322
#117492952
#117492912
#117490492
#117490452
#117483682
#117483412
#106106163
#840845