Finite Group Databasebeta

← C2×#10618670 #13007612

Subgroups — C2×#10618670 #13007612

Order 1280.

12366 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×#4149C211yesmaximal, characteristic, complemented
2C22×D5×#41C211yesmaximal, characteristic, complemented
3C2×C5×#550C211yesmaximal, characteristic, complemented
4C2×#66168C211yesmaximal, characteristic, complemented
5C2×#66165C211yesmaximal, characteristic, complemented
6#10618670C2132yesmaximal, direct product factor
7C2×#66051C213yesmaximal, complemented
8C2×#66049C213yesmaximal, complemented
9C2×#65946C213yesmaximal, complemented
10C2×#65943C213yesmaximal, complemented
11C2×#65942C213yesmaximal, complemented
12C2×D5×#121C213yesmaximal, complemented
13C2×#65910C211yesmaximal, characteristic, complemented
14C2×#65908C211yesmaximal, characteristic, complemented
15C2×#65884C213yesmaximal, complemented
16C2×#65881C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic, complemented
18C22×C5×#41C2211yescharacteristic, complemented
19C2×#4149—216no—
20C2×#4149C22116yescomplemented
21C2×D5×#41—216no—
22C2×D5×#41C22116yescomplemented
23C22×#713C2211yescharacteristic
24C22×#713C2211yescharacteristic, complemented
25C22×Q8×D5C2211yescharacteristic, complemented
26C22×#711C2213yescomplemented
27C22×D4×D5C2213yescomplemented
28C22×D4×D5C2213yescomplemented
29C22×D4×D5C2213yescomplemented
30C22×D4×D5C2216yescomplemented
31C22×#709C2213yescomplemented
32C22×#709C2213yescomplemented
33C23×D20C2213yescomplemented
34C23×C4×D5C2213yescomplemented
35C5×#550C22116yescomplemented
36C2×C5×#127C2213yescomplemented
37C2×C5×#121C2213yescomplemented
38C2×C5×#121C2213yescomplemented
39C2×C4×C5×Q8C2211yescharacteristic, complemented
40C2×C4×C5×D4C2213yescomplemented
41#66168C22116yescomplemented
42#66165C22116yescomplemented
43C2×Q8×Dic5C2211yescharacteristic, complemented
44C2×#4086C2213yescomplemented
45C2×#4085C2213yescomplemented
46C2×#4085C2216yescomplemented
47C2×#4084C2213yescomplemented
48C2×#4084C2213yescomplemented
49C2×#4084C2216yescomplemented
50C2×#4083C2213yescomplemented
51C2×#4083C2216yescomplemented
52C2×#4083C2216yescomplemented
53C2×#4082C2213yescomplemented
54C2×#4076C2213yescomplemented
55C2×C4×C22⋊D5C2213yescomplemented
56C2×C4×C22⋊D5C2213yescomplemented
57C2×#4070C2213yescomplemented
58#66051C22148yescomplemented
59#66049C22148yescomplemented
60#65946C22148yescomplemented
61#65943C22148yescomplemented
62#65942C22148yescomplemented
63D5×#121C22148yescomplemented
64#65910C22116yescomplemented
65#65908C22116yescomplemented
66#65884C22148yescomplemented
67#65881C22148yescomplemented
68C2×#4043C2213yescomplemented
69C2×#4042C2211yescharacteristic, complemented
70C2×#4041C2213yescomplemented
71C2×#4040C2213yescomplemented
72C2×#4039C2213yescomplemented
73C2×D5×C4⋊C4C2213yescomplemented
74C2×#4030C2213yescomplemented
75C2×#4030C2216yescomplemented
76C2×#4029C2213yescomplemented
77C2×#4028C2213yescomplemented
78C2×D5×C22⋊C4C2216yescomplemented
79C2×#4024C2213yescomplemented
80C2×#4021C2213yescomplemented
81C2×C4×D20C2213yescomplemented
82C2×C4×D20C2213yescomplemented
83C2×#4018C2213yescomplemented
84C2×#3488—51nomaximal, Sylow
85C24×D5C2313yes—
86C24×D5C2316yes—
87C2×C5×#41—28no—
88C2×C5×#41—28no—
89C2×C5×#41C2318yescomplemented
90C2×C5×#41C2318yescomplemented
91C22×C5×Q8C2311yescharacteristic
92C22×C5×D4C2313yes—
93C22×C5×D4C2313yes—
94C22×C5×D4C2313yes—
95C22×C5×D4C2316yes—
96C23×C4×C5C2313yes—
97C23×C4×C5C2313yes—
98C22×C22⋊D5C2313yes—
99C22×C22⋊D5C2313yes—
100C22×C22⋊D5C2316yes—
101C22×C22⋊D5C2313yes—
102C22×C22⋊D5C2313yes—
103C22×C22⋊D5C2316yes—
104C23×Dic5C2313yes—
105#4149—2128no—
106D5×#41—2128no—
107C2×#713—28no—
108C2×#713D4116yescomplemented
109C2×#713C2318yes—
110C2×#713C2318yescomplemented
111C2×Q8×D5—28no—
112C2×Q8×D5C2318yescomplemented
113C2×#711—224no—
114C2×#711C23124yescomplemented
115C2×D4×D5—224no—
116C2×D4×D5—224no—
117C2×D4×D5—224no—
118C2×D4×D5—424no—
119C2×D4×D5C23124yescomplemented
120C2×D4×D5C23124yescomplemented
121C2×D4×D5C23124yescomplemented
122C2×D4×D5C23148yescomplemented
123C2×#709—224no—
124C2×#709—224no—
125C2×#709C23124yescomplemented
126C2×#709C23124yescomplemented
127C22×D20—224no—
128C22×D20C2313yes—
129C22×D20C2313yes—
130C22×D20C2313yes—
131C22×D20C2313yes—
132C22×D20C23124yescomplemented
133C22×C4×D5—224no—
134C22×C4×D5C2313yes—
135C22×C4×D5C2313yes—
136C22×C4×D5C2313yes—
137C22×C4×D5C2311yescharacteristic
138C22×C4×D5C2316yes—
139C22×C4×D5C2313yes—
140C22×C4×D5C23124yescomplemented
141C22×Dic10C2313yes—
142C22×Dic10C2311yescharacteristic
143C5×#127C23124yescomplemented
144C5×#121C23124yescomplemented
145C5×#121C23124yescomplemented
146C4×C5×Q8C2318yescomplemented
147C4×C5×D4C23124yescomplemented
148C2×C5×C4⋊C4C2313yes—
149C2×C5×C4⋊C4C2311yescharacteristic
150C2×C5×C22⋊C4C2313yes—
151C2×C5×C22⋊C4C2313yes—
152C2×C42×C5C2313yes—
153C2×C22⋊Dic5C2313yes—
154C2×C22⋊Dic5C2316yes—
155C2×C22⋊Dic5C2313yes—
156Q8×Dic5C2318yescomplemented
157#4086C23124yescomplemented
158#4085C23124yescomplemented
159#4085C23148yescomplemented
160#4084C23124yescomplemented
161#4084C23124yescomplemented
162#4084C23148yescomplemented
163#4083C23148yescomplemented
164#4083C23148yescomplemented
165#4083C23124yescomplemented
166#4082C23124yescomplemented
167#4076C23124yescomplemented
168C4×C22⋊D5C23124yescomplemented
169C4×C22⋊D5C23124yescomplemented
170C2×#685C2313yes—
171C2×#685C2313yes—
172C2×#685C2311yescharacteristic
173C2×#685C2313yes—
174C2×#685C2316yes—
175C2×#685C2313yes—
176C2×#685C2311yescharacteristic
177C2×C4⋊Dic5C2313yes—
178C2×C4⋊Dic5C2313yes—
179#4070C23124yescomplemented
180C2×#683C2311yescharacteristic
181C2×#683C2313yes—
182C2×#683C2313yes—
183C2×#683C2311yescharacteristic
184C2×C4×Dic5C2313yes—
185#4043C23124yescomplemented
186#4042C2318yescomplemented
187#4041C23124yescomplemented
188#4040C23124yescomplemented
189#4039C23124yescomplemented
190D5×C4⋊C4C23124yescomplemented
191#4030C23124yescomplemented
192#4030C23148yescomplemented
193#4029C23124yescomplemented
194#4028C23124yescomplemented
195D5×C22⋊C4C23148yescomplemented
196#4024C23124yescomplemented
197#4021C23124yescomplemented
198C4×D20C23124yescomplemented
199C4×D20C23124yescomplemented
200#4018C23124yescomplemented
201C22×H(5,𝔽2)—51no—
202C23×#41—51no—
203#3488—532no—
204C2×#550—51no—
205C2×#550D511yescharacteristic, complemented
206C2×#548—51no—
207C2×#548—51no—
208C2×#546—53no—
209C2×#546—53no—
210C2×D42—53no—
211C2×D42—53no—
212C2×#537—53no—
213C2×#535—53no—
214C2×#525—53no—
215C22×#121—53no—
216C2×#520—51no—
217C24×C5C2413yes—
218C24×C5C2413yes—
219C23×D5—212no—
220C23×D5—212no—
221C23×D5—224no—
222C23×D5—46no—
223C23×D5—412no—
224C23×D5—412no—
225C23×D5C2413yes—
226C23×D5C24112yes—
227C23×D5C2413yes—
228C23×D5C2411yescharacteristic
229C23×D5C24124yes—
230C5×#41—232no—
231C5×#41—232no—
232C2×C5×Q8C2×D418yescomplemented
233C2×C5×Q8C2414yes—
234C2×C5×D4—212no—
235C2×C5×D4—212no—
236C2×C5×D4—412no—
237C2×C5×D4—46no—
238C2×C5×D4C24112yes—
239C2×C5×D4C24112yes—
240C2×C5×D4C24112yes—
241C2×C5×D4C24124yes—
242C22×C4×C5—212no—
243C22×C4×C5—212no—
244C22×C4×C5C2411yescharacteristic
245C22×C4×C5C2413yes—
246C22×C4×C5C2411yescharacteristic
247C22×C4×C5C2411yescharacteristic
248C22×C4×C5C24112yes—
249C22×C4×C5C24112yes—
250C22×C4×C5C2413yes—
251C2×C22⋊D5—212no—
252C2×C22⋊D5—224no—
253C2×C22⋊D5—212no—
254C2×C22⋊D5—212no—
255C2×C22⋊D5—412no—
256C2×C22⋊D5—46no—
257C2×C22⋊D5C24112yes—
258C2×C22⋊D5C24112yes—
259C2×C22⋊D5C24124yes—
260C2×C22⋊D5C24112yes—
261C2×C22⋊D5C24124yes—
262C2×C22⋊D5C24112yes—
263C22×Dic5—212no—
264C22×Dic5C2413yes—
265C22×Dic5C2411yescharacteristic
266C22×Dic5C2413yes—
267C22×Dic5C2411yescharacteristic
268C22×Dic5C24112yes—
269C22×Dic5C2411yescharacteristic
270#713—232no—
271#713C2×D4164yescomplemented
272Q8×D5—232no—
273#711—296no—
274D4×D5—296no—
275D4×D5—296no—
276D4×D5—296no—
277D4×D5—496no—
278#709—296no—
279#709—296no—
280C2×D20—212no—
281C2×D20—212no—
282C2×D20—212no—
283C2×D20—296no—
284C2×D20C2×D4124yescomplemented
285C2×D20C24112yes—
286C2×D20C24112yes—
287C2×D20C24112yes—
288C2×D20C24112yes—
289C2×C4×D5—212no—
290C2×C4×D5—212no—
291C2×C4×D5—212no—
292C2×C4×D5—24no—
293C2×C4×D5—296no—
294C2×C4×D5—412no—
295C2×C4×D5C2×D4124yescomplemented
296C2×C4×D5C2414yes—
297C2×C4×D5C24112yes—
298C2×C4×D5C24112yes—
299C2×C4×D5C24112yes—
300C2×C4×D5C24124yes—
301C2×C4×D5C24112yes—
302C2×Dic10—212no—
303C2×Dic10—24no—
304C2×Dic10C2414yes—
305C2×Dic10C24112yes—
306C5×C4⋊C4C2414yes—
307C5×C4⋊C4C24112yes—
308C5×C22⋊C4C24112yes—
309C5×C22⋊C4C24112yes—
310C42×C5C24112yes—
311C22⋊Dic5C24112yes—
312C22⋊Dic5C24124yes—
313C22⋊Dic5C24112yes—
314#685C24112yes—
315#685C24112yes—
316#685C2414yes—
317#685C24112yes—
318#685C24124yes—
319#685C24112yes—
320#685C2414yes—
321C4⋊Dic5C24112yes—
322C4⋊Dic5C24112yes—
323#683C2414yes—
324#683C24112yes—
325#683C24112yes—
326#683C2414yes—
327C4×Dic5C24112yes—
328C2×H(5,𝔽2)—516no—
329C2×H(5,𝔽2)—1016no—
330C22×#41—516no—
331C22×#41—51no—
332C22×#41—51no—
333C22×#41—53no—
334C22×#41—53no—
335C22×#41—53no—
336C22×#41—1016no—
337C22×#41C2×D511yescharacteristic, complemented
338C22×#41C2×D511yescharacteristic, complemented
339C23×Q8—51no—
340C23×D4—53no—
341C23×D4—53no—
342C23×D4—53no—
343C23×D4—56no—
344C23×D4—53no—
345C24×C4—53no—
346#550—516no—
347#550C2×D5116yescomplemented
348#548—516no—
349#548—516no—
350#546—548no—
351#546—548no—
352D42—548no—
353D42—548no—
354#537—548no—
355#535—548no—
356C2×#127—53no—
357C2×#127C2×D513yescomplemented
358C2×#124—53no—
359C2×#124—53no—
360#525—548no—
361C2×#123—53no—
362C2×#123—53no—
363C2×C22⋊Q8—53no—
364C2×C22⋊Q8—51no—
365C2×C22⋊Q8—53no—
366C2×C22⋊Q8—53no—
367C2×#121—53no—
368C2×#121—56no—
369C2×#121—53no—
370C2×#121—56no—
371C2×#121—53no—
372C2×#121—53no—
373C2×#121—548no—
374C2×#121—53no—
375C2×#121—53no—
376C2×#121—56no—
377C2×#121C2×D513yescomplemented
378C2×#121C2×D513yescomplemented
379C2×#120—53no—
380C2×#120—56no—
381C2×#120—56no—
382C2×#120—53no—
383#520—516no—
384C2×C4×Q8—51no—
385C2×C4×Q8C2×D511yescharacteristic, complemented
386C2×C4×D4—53no—
387C2×C4×D4—53no—
388C2×C4×D4—53no—
389C2×C4×D4—53no—
390C2×C4×D4—53no—
391C2×C4×D4C2×D513yescomplemented
392C2×#117—53no—
393C22×C4⋊C4—53no—
394C22×C22⋊C4—56no—
395C23×C5—26no—
396C23×C5—26no—
397C23×C5—26no—
398C23×C5—26no—
399C23×C5—26no—
400C23×C5—26no—
401C23×C5C2516yes—
402C23×C5C2516yes—
403C23×C5C2511yescharacteristic
404C22×D5—22no—
405C22×D5—26no—
406C22×D5—22no—
407C22×D5—26no—
408C22×D5—26no—
409C22×D5—26no—
410C22×D5—26no—
411C22×D5—224no—
412C22×D5—224no—
413C22×D5—248no—
414C22×D5—412no—
415C22×D5—448no—
416C22×D5—424no—
417C22×D5—424no—
418C22×D5—848no—
419C22×D5C22×D4112yes—
420C22×D5H(5,𝔽2)14yescomplemented
421C22×D5C2516yes—
422C22×D5C2516yes—
423C22×D5C2512yes—
424C5×Q8C22×D4116yescomplemented
425C5×D4—224no—
426C5×D4—224no—
427C5×D4—424no—
428C5×D4—412no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—26no—
432C2×C4×C5—22no—
433C2×C4×C5—224no—
434C2×C4×C5—224no—
435C2×C4×C5C22×D4112yes—
436C2×C4×C5C2512yes—
437C2×C4×C5C2516yes—
438C2×C4×C5C2512yes—
439C2×C4×C5C2512yes—
440C2×C4×C5C2516yes—
441C22⋊D5—224no—
442C22⋊D5—248no—
443C22⋊D5—224no—
444C22⋊D5—224no—
445C22⋊D5—424no—
446C22⋊D5—412no—
447C2×Dic5—26no—
448C2×Dic5—22no—
449C2×Dic5—26no—
450C2×Dic5—22no—
451C2×Dic5—224no—
452C2×Dic5C22×D414yes—
453C2×Dic5C2512yes—
454C2×Dic5C2516yes—
455C2×Dic5C2512yes—
456C2×Dic5C2516yes—
457C2×Dic5C2512yes—
458D20—224no—
459D20—224no—
460D20—224no—
461D20C22×D4148yescomplemented
462C4×D5—224no—
463C4×D5—224no—
464C4×D5—224no—
465C4×D5—28no—
466C4×D5—424no—
467C4×D5C22×D4148yescomplemented
468Dic10—224no—
469Dic10—28no—
470C25—53no—
471C25—56no—
472H(5,𝔽2)—10128no—
473C2×#41—28no—
474C2×#41—28no—
475C2×#41—516no—
476C2×#41—58no—
477C2×#41—58no—
478C2×#41—524no—
479C2×#41—524no—
480C2×#41—524no—
481C2×#41—1024no—
482C2×#41—1024no—
483C2×#41—1024no—
484C2×#41—10128no—
485C2×#41—108no—
486C2×#41C22×D518yescomplemented
487C2×#41C22×D518yescomplemented
488C22×Q8—58no—
489C22×Q8—51no—
490C22×Q8—53no—
491C22×Q8—108no—
492C22×Q8C22×D511yescharacteristic
493C22×D4—53no—
494C22×D4—56no—
495C22×D4—53no—
496C22×D4—53no—
497C22×D4—53no—
498C22×D4—56no—
499C22×D4—524no—
500C22×D4—524no—
501C22×D4—524no—
502C22×D4—548no—
503C22×D4—53no—
504C22×D4—53no—
505C22×D4—53no—
506C22×D4—53no—
507C22×D4—524no—
508C22×D4—1024no—
509C22×D4—1024no—
510C22×D4—1024no—
511C22×D4—1024no—
512C22×D4—2024no—
513C22×D4C22×D513yes—
514C22×D4C22×D513yes—
515C22×D4C22×D513yes—
516C22×D4C22×D516yes—
517C23×C4—53no—
518C23×C4—53no—
519C23×C4—53no—
520C23×C4—53no—
521C23×C4—53no—
522C23×C4—51no—
523C23×C4—524no—
524C23×C4—56no—
525C23×C4—1024no—
526C23×C4C22×D513yes—
527C23×C4C22×D513yes—
528#127—524no—
529#127C22×D5124yescomplemented
530#124—524no—
531#124—524no—
532#123—524no—
533#123—524no—
534C22⋊Q8—524no—
535C22⋊Q8—58no—
536C22⋊Q8—524no—
537C22⋊Q8—524no—
538#121—548no—
539#121—524no—
540#121—524no—
541#121—548no—
542#121—524no—
543#121—524no—
544#121—524no—
545#121—524no—
546#121—548no—
547#121C22×D5124yescomplemented
548#121C22×D5124yescomplemented
549#120—524no—
550#120—548no—
551#120—548no—
552#120—524no—
553C4×Q8—58no—
554C4×Q8C22×D518yescomplemented
555C4×D4—524no—
556C4×D4—524no—
557C4×D4—524no—
558C4×D4—524no—
559C4×D4—524no—
560C4×D4C22×D5124yescomplemented
561#117—524no—
562C2×C4⋊C4—53no—
563C2×C4⋊C4—53no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—53no—
567C2×C4⋊C4—53no—
568C2×C4⋊C4—524no—
569C2×C4⋊C4C22×D513yes—
570C2×C4⋊C4C22×D511yescharacteristic
571C2×C22⋊C4—56no—
572C2×C22⋊C4—53no—
573C2×C22⋊C4—53no—
574C2×C22⋊C4—53no—
575C2×C22⋊C4—56no—
576C2×C22⋊C4—53no—
577C2×C22⋊C4—53no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—51no—
580C2×C22⋊C4—53no—
581C2×C22⋊C4—548no—
582C2×C22⋊C4C22×D513yes—
583C2×C22⋊C4C22×D513yes—
584C2×C42—53no—
585C2×C42C22×D513yes—
586C22×C5—26no—
587C22×C5—26no—
588C22×C5—26no—
589C22×C5—26no—
590C22×C5—26no—
591C22×C5—26no—
592C22×C5—412no—
593C22×C5—412no—
594C22×C5C23×D412yes—
595C22×C5C2×H(5,𝔽2)12yes—
596C22×C5#58512yes—
597C22×C5C2611yescharacteristic
598C2×D5—22no—
599C2×D5—26no—
600C2×D5—22no—
601C2×D5—26no—
602C2×D5—28no—
603C2×D5—224no—
604C2×D5—26no—
605C2×D5—26no—
606C2×D5—26no—
607C2×D5—448no—
608C2×D5—412no—
609C2×D5—848no—
610C2×D5C23×D4112yes—
611C2×D5C2×H(5,𝔽2)14yescomplemented
612C4×C5—22no—
613C4×C5—22no—
614C4×C5—26no—
615C4×C5—22no—
616C4×C5C23×D4112yes—
617Dic5—26no—
618Dic5—22no—
619Dic5—26no—
620Dic5—22no—
621Dic5C23×D414yes—
622C24—53no—
623C24—51no—
624C24—53no—
625C24—512no—
626C24—524no—
627C24—1012no—
628C24—1012no—
629C24—1024no—
630C24—206no—
631C24—2012no—
632C24—2012no—
633C24C23×D513yes—
634C24C23×D513yes—
635#41—232no—
636#41—232no—
637#41—564no—
638#41—1096no—
639#41—1096no—
640#41—1096no—
641#41—1032no—
642C2×Q8—54no—
643C2×Q8—512no—
644C2×Q8—104no—
645C2×Q8—1032no—
646C2×Q8—1012no—
647C2×Q8D4×D518yescomplemented
648C2×Q8C23×D514yes—
649C2×D4—212no—
650C2×D4—212no—
651C2×D4—412no—
652C2×D4—46no—
653C2×D4—512no—
654C2×D4—524no—
655C2×D4—512no—
656C2×D4—512no—
657C2×D4—512no—
658C2×D4—524no—
659C2×D4—524no—
660C2×D4—512no—
661C2×D4—512no—
662C2×D4—512no—
663C2×D4—512no—
664C2×D4—1096no—
665C2×D4—1012no—
666C2×D4—1012no—
667C2×D4—1096no—
668C2×D4—1012no—
669C2×D4—1096no—
670C2×D4—1096no—
671C2×D4—1012no—
672C2×D4—1024no—
673C2×D4—1012no—
674C2×D4—1012no—
675C2×D4—2012no—
676C2×D4—206no—
677C2×D4—2096no—
678C2×D4C23×D5112yes—
679C2×D4C23×D5112yes—
680C2×D4C23×D5112yes—
681C2×D4C23×D5124yes—
682C22×C4—212no—
683C22×C4—212no—
684C22×C4—51no—
685C22×C4—524no—
686C22×C4—512no—
687C22×C4—512no—
688C22×C4—51no—
689C22×C4—53no—
690C22×C4—53no—
691C22×C4—51no—
692C22×C4—512no—
693C22×C4—512no—
694C22×C4—512no—
695C22×C4—54no—
696C22×C4—524no—
697C22×C4—104no—
698C22×C4—1096no—
699C22×C4—1012no—
700C22×C4—1012no—
701C22×C4—1012no—
702C22×C4—1012no—
703C22×C4—2012no—
704C22×C4C23×D5112yes—
705C22×C4C23×D5112yes—
706C22×C4C23×D511yescharacteristic
707C22×C4C23×D513yes—
708C22×C4C23×D511yescharacteristic
709C22×C4C23×D511yescharacteristic
710C22×C4C23×D513yes—
711C4⋊C4—512no—
712C4⋊C4—512no—
713C4⋊C4—54no—
714C4⋊C4—54no—
715C4⋊C4—512no—
716C4⋊C4—512no—
717C4⋊C4C23×D5112yes—
718C4⋊C4C23×D514yes—
719C22⋊C4—524no—
720C22⋊C4—512no—
721C22⋊C4—512no—
722C22⋊C4—512no—
723C22⋊C4—524no—
724C22⋊C4—512no—
725C22⋊C4—512no—
726C22⋊C4—54no—
727C22⋊C4—54no—
728C22⋊C4—512no—
729C22⋊C4C23×D5112yes—
730C22⋊C4C23×D5112yes—
731C42—512no—
732C42C23×D5112yes—
733C2×C5—46no—
734C2×C5—46no—
735C2×C5#348814yescomplemented
736C2×C5C24×D411yescharacteristic
737C2×C5C22×H(5,𝔽2)11yescharacteristic
738C2×C5C2×#58511yescharacteristic
739D5—24no—
740D5—212no—
741D5—46no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—512no—
749C23—54no—
750C23—56no—
751C23—52no—
752C23—56no—
753C23—1024no—
754C23—1024no—
755C23—1048no—
756C23—102no—
757C23—102no—
758C23—106no—
759C23—106no—
760C23—106no—
761C23—106no—
762C23—106no—
763C23—2012no—
764C23—2024no—
765C23—2024no—
766C23—2048no—
767C23—4048no—
768C23C24×D516yes—
769C23C24×D516yes—
770C23C24×D511yescharacteristic
771Q8—108no—
772Q8—1024no—
773Q8C2×D4×D5116yescomplemented
774D4—224no—
775D4—224no—
776D4—424no—
777D4—412no—
778D4—548no—
779D4—1024no—
780D4—1024no—
781D4—1024no—
782D4—1024no—
783D4—1048no—
784D4—1024no—
785D4—1024no—
786D4—2024no—
787D4—2012no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—224no—
793C2×C4—224no—
794C2×C4—54no—
795C2×C4—52no—
796C2×C4—548no—
797C2×C4—52no—
798C2×C4—56no—
799C2×C4—56no—
800C2×C4—52no—
801C2×C4—108no—
802C2×C4—1024no—
803C2×C4—1024no—
804C2×C4—102no—
805C2×C4—106no—
806C2×C4—102no—
807C2×C4—106no—
808C2×C4—1024no—
809C2×C4—1024no—
810C2×C4—2024no—
811C2×C4C2×D4×D5112yes—
812C2×C4C24×D512yes—
813C2×C4C24×D516yes—
814C2×C4C24×D512yes—
815C2×C4C24×D512yes—
816C2×C4C24×D516yes—
817C5C2×#348811yescharacteristic, complemented, Sylow
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—512no—
827C22—54no—
828C22—102no—
829C22—102no—
830C22—106no—
831C22—106no—
832C22—108no—
833C22—1024no—
834C22—106no—
835C22—106no—
836C22—106no—
837C22—2048no—
838C22—2012no—
839C22—4048no—
840C22C22×D4×D512yes—
841C22#6628312yes—
842C22D5×H(5,𝔽2)12yes—
843C22C25×D511yescharacteristic
844C4—22no—
845C4—22no—
846C4—22no—
847C4—26no—
848C4—54no—
849C4—102no—
850C4—106no—
851C4—102no—
852C4—106no—
853C4C22×D4×D5112yes—
854C2—46no—
855C2—46no—
856C2—104no—
857C2—1012no—
858C2—206no—
859C2#1061867014yesdirect product factor
860C2C23×D4×D511yescharacteristic
861C2C2×#6628311yescharacteristic
862C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#550C2
socleC23×C5C25
hypercenterC2×#550D5
hypocenterC5C2×#3488
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#4149C2semidirect
2. C22×D5×#41C2semidirect
3. C2×C5×#550C2semidirect
4. C2×#66168C2semidirect
5. C2×#66165C2semidirect
6. #10618670C2direct (N × H)
7. C2×#66051C2semidirect
8. C2×#66049C2semidirect
9. C2×#65946C2semidirect
10. C2×#65943C2semidirect
11. C2×#65942C2semidirect
12. C2×D5×#121C2semidirect
13. C2×#65910C2semidirect
14. C2×#65908C2semidirect
15. C2×#65884C2semidirect
16. C2×#65881C2semidirect
17. C22×C5×#41C22semidirect
18. C22×C5×#41C22semidirect
20. C2×#4149C22semidirect
22. C2×D5×#41C22semidirect
24. C22×#713C22semidirect
25. C22×Q8×D5C22semidirect
26. C22×#711C22semidirect
27. C22×D4×D5C22semidirect
28. C22×D4×D5C22semidirect
29. C22×D4×D5C22semidirect
30. C22×D4×D5C22semidirect
31. C22×#709C22semidirect
32. C22×#709C22semidirect
33. C23×D20C22semidirect
34. C23×C4×D5C22semidirect
35. C5×#550C22semidirect
36. C2×C5×#127C22semidirect
37. C2×C5×#121C22semidirect
38. C2×C5×#121C22semidirect
39. C2×C4×C5×Q8C22semidirect
40. C2×C4×C5×D4C22semidirect
41. #66168C22semidirect
42. #66165C22semidirect
43. C2×Q8×Dic5C22semidirect
44. C2×#4086C22semidirect
45. C2×#4085C22semidirect
46. C2×#4085C22semidirect
47. C2×#4084C22semidirect
48. C2×#4084C22semidirect
49. C2×#4084C22semidirect
50. C2×#4083C22semidirect
51. C2×#4083C22semidirect
52. C2×#4083C22semidirect
53. C2×#4082C22semidirect
54. C2×#4076C22semidirect
55. C2×C4×C22⋊D5C22semidirect
56. C2×C4×C22⋊D5C22semidirect
57. C2×#4070C22semidirect
58. #66051C22semidirect
59. #66049C22semidirect
60. #65946C22semidirect
61. #65943C22semidirect
62. #65942C22semidirect
63. D5×#121C22semidirect
64. #65910C22semidirect
65. #65908C22semidirect
66. #65884C22semidirect
67. #65881C22semidirect
68. C2×#4043C22semidirect
69. C2×#4042C22semidirect
70. C2×#4041C22semidirect
71. C2×#4040C22semidirect
72. C2×#4039C22semidirect
73. C2×D5×C4⋊C4C22semidirect
74. C2×#4030C22semidirect
75. C2×#4030C22semidirect
76. C2×#4029C22semidirect
77. C2×#4028C22semidirect
78. C2×D5×C22⋊C4C22semidirect
79. C2×#4024C22semidirect
80. C2×#4021C22semidirect
81. C2×C4×D20C22semidirect
82. C2×C4×D20C22semidirect
83. C2×#4018C22semidirect
89. C2×C5×#41C23semidirect
90. C2×C5×#41C23semidirect
108. C2×#713D4semidirect
110. C2×#713C23semidirect
112. C2×Q8×D5C23semidirect
114. C2×#711C23semidirect
119. C2×D4×D5C23semidirect
120. C2×D4×D5C23semidirect
121. C2×D4×D5C23semidirect
122. C2×D4×D5C23semidirect
125. C2×#709C23semidirect
126. C2×#709C23semidirect
132. C22×D20C23semidirect
140. C22×C4×D5C23semidirect
143. C5×#127C23semidirect
144. C5×#121C23semidirect
145. C5×#121C23semidirect
146. C4×C5×Q8C23semidirect
147. C4×C5×D4C23semidirect
156. Q8×Dic5C23semidirect
157. #4086C23semidirect
158. #4085C23semidirect
159. #4085C23semidirect
160. #4084C23semidirect
161. #4084C23semidirect
162. #4084C23semidirect
163. #4083C23semidirect
164. #4083C23semidirect
165. #4083C23semidirect
166. #4082C23semidirect
167. #4076C23semidirect
168. C4×C22⋊D5C23semidirect
169. C4×C22⋊D5C23semidirect
179. #4070C23semidirect
185. #4043C23semidirect
186. #4042C23semidirect
187. #4041C23semidirect
188. #4040C23semidirect
189. #4039C23semidirect
190. D5×C4⋊C4C23semidirect
191. #4030C23semidirect
192. #4030C23semidirect
193. #4029C23semidirect
194. #4028C23semidirect
195. D5×C22⋊C4C23semidirect
196. #4024C23semidirect
197. #4021C23semidirect
198. C4×D20C23semidirect
199. C4×D20C23semidirect
200. #4018C23semidirect
205. C2×#550D5semidirect
232. C2×C5×Q8C2×D4semidirect
271. #713C2×D4semidirect
284. C2×D20C2×D4semidirect
295. C2×C4×D5C2×D4semidirect
337. C22×#41C2×D5semidirect
338. C22×#41C2×D5semidirect
347. #550C2×D5semidirect
357. C2×#127C2×D5semidirect
377. C2×#121C2×D5semidirect
378. C2×#121C2×D5semidirect
385. C2×C4×Q8C2×D5semidirect
391. C2×C4×D4C2×D5semidirect
420. C22×D5H(5,𝔽2)semidirect
424. C5×Q8C22×D4semidirect
461. D20C22×D4semidirect
467. C4×D5C22×D4semidirect
486. C2×#41C22×D5semidirect
487. C2×#41C22×D5semidirect
529. #127C22×D5semidirect
547. #121C22×D5semidirect
548. #121C22×D5semidirect
554. C4×Q8C22×D5semidirect
560. C4×D4C22×D5semidirect
611. C2×D5C2×H(5,𝔽2)semidirect
647. C2×Q8D4×D5semidirect
735. C2×C5#3488semidirect
773. Q8C2×D4×D5semidirect
817. C5C2×#3488semidirect
859. C2#10618670direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41492
C22×D5×#412
C2×C5×#5502
C2×#661682
C2×#661652
#106186702
C2×#660512
C2×#660492
C2×#659462
C2×#659432
C2×#659422
C2×D5×#1212
C2×#659102
C2×#659082
C2×#658842
C2×#658812
C2×#34885