Finite Group Databasebeta

← C2×#10618673 #13007549

Subgroups — C2×#10618673 #13007549

Order 1280.

7854 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#550C211yesmaximal, characteristic, complemented
2C2×#66168C211yesmaximal, characteristic, complemented
3C2×#66168C211yesmaximal, characteristic, complemented
4C2×#66161C211yesmaximal, characteristic, complemented
5C2×#41×Dic5C211yesmaximal, characteristic, complemented
6#10618673C2132yesmaximal, direct product factor
7C2×#66053C213yesmaximal, complemented
8C2×#66052C213yesmaximal, complemented
9C2×#65948C213yesmaximal, complemented
10C2×#65945C213yesmaximal, complemented
11C2×#65953C213yesmaximal, complemented
12C2×#65930C213yesmaximal, complemented
13C2×#65903C211yesmaximal, characteristic, complemented
14C2×#65908C211yesmaximal, characteristic, complemented
15C2×#65899C213yesmaximal, complemented
16C2×#65872C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×#41C2211yescharacteristic
19C22×#713C2211yescharacteristic
20C22×#711C2216yes—
21C5×#550C22116yescomplemented
22C2×C5×#127C2213yes—
23C2×C5×#121C2213yes—
24C2×C5×#121C2213yes—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4C2213yes—
27#66168C22116yescomplemented
28#66168C22116yescomplemented
29#66161C22116yescomplemented
30#41×Dic5C22116yescomplemented
31C2×Q8×Dic5C2211yescharacteristic
32C2×Q8×Dic5C2211yescharacteristic
33C2×Q8×Dic5C2211yescharacteristic
34C2×#4086C2213yes—
35C2×#4086C2213yes—
36C2×#4085C2213yes—
37C2×#4085C2216yes—
38C2×#4085C2216yes—
39C2×#4084C2213yes—
40C2×#4084C2213yes—
41C2×#4084C2216yes—
42C2×#4081C2213yes—
43C2×#4081C2216yes—
44C2×D4×Dic5C2213yes—
45C2×D4×Dic5C2213yes—
46C2×D4×Dic5C2213yes—
47C2×D4×Dic5C2213yes—
48C2×#4076C2213yes—
49C2×#4076C2213yes—
50C2×C4×C22⋊D5C2213yes—
51C2×C4×C22⋊D5C2213yes—
52C2×#4072C2213yes—
53C2×#4072C2213yes—
54C22×C4⋊Dic5C2213yes—
55C22×C4×Dic5C2213yes—
56#66053C22148yescomplemented
57#66052C22148yescomplemented
58#65953C22148yescomplemented
59#65948C22148yescomplemented
60#65945C22148yescomplemented
61#65930C22148yescomplemented
62#65908C22116yescomplemented
63#65903C22116yescomplemented
64#65899C22148yescomplemented
65#65872C22148yescomplemented
66C2×#4044C2213yes—
67C2×#4039C2213yes—
68C2×D5×C4⋊C4C2213yes—
69C2×#4036C2213yes—
70C2×#4035C2211yescharacteristic
71C2×#4034C2213yes—
72C2×#4032C2213yes—
73C2×#4031C2213yes—
74C2×#4029C2216yes—
75C2×#4027C2216yes—
76C2×#4025C2213yes—
77C2×#4024C2213yes—
78C2×C4×D20C2213yes—
79C2×#4018C2213yes—
80C2×#4016C2213yes—
81C2×C4×Dic10C2213yes—
82C2×#3517—51nomaximal, Sylow
83C2×C5×#41—28no—
84C2×C5×#41—28no—
85C2×C5×#41C2318yes—
86C2×C5×#41C2318yes—
87C22×C5×Q8C2311yescharacteristic
88C22×C5×D4C2313yes—
89C22×C5×D4C2313yes—
90C22×C5×D4C2316yes—
91C22×C5×D4C2313yes—
92C23×C4×C5C2313yes—
93C23×C4×C5C2313yes—
94C22×C22⋊D5C2313yes—
95C22×C22⋊D5C2316yes—
96C22×C22⋊D5C2316yes—
97C22×C22⋊D5C2313yes—
98C23×Dic5C2313yes—
99C23×Dic5C2316yes—
100C23×Dic5C2313yes—
101C2×#713—28no—
102C2×#713C2318yes—
103C2×#711—424no—
104C2×#711C23148yes—
105C22×D20C2313yes—
106C22×C4×D5C2313yes—
107C22×C4×D5C2316yes—
108C22×Dic10C2313yes—
109C5×#127C23124yes—
110C5×#121C23124yes—
111C5×#121C23124yes—
112C4×C5×Q8C2318yes—
113C4×C5×D4C23124yes—
114C2×C5×C4⋊C4C2313yes—
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4C2313yes—
117C2×C5×C22⋊C4C2313yes—
118C2×C42×C5C2313yes—
119C2×C22⋊Dic5C2313yes—
120C2×C22⋊Dic5C2313yes—
121C2×C22⋊Dic5C2313yes—
122C2×C22⋊Dic5C2316yes—
123C2×C22⋊Dic5C2313yes—
124Q8×Dic5C2318yes—
125Q8×Dic5C2318yes—
126Q8×Dic5C2318yes—
127#4086C23124yes—
128#4086C23124yes—
129#4085C23124yes—
130#4085C23148yes—
131#4085C23148yes—
132#4084C23148yes—
133#4084C23124yes—
134#4084C23124yes—
135#4081C23124yes—
136#4081C23148yes—
137D4×Dic5C23124yes—
138D4×Dic5C23124yes—
139D4×Dic5C23124yes—
140D4×Dic5C23124yes—
141#4076C23124yes—
142#4076C23124yes—
143C4×C22⋊D5C23124yes—
144C4×C22⋊D5C23124yes—
145C2×#685C2313yes—
146C2×#685C2313yes—
147C2×#685C2313yes—
148C2×#685C2313yes—
149#4072C23124yes—
150#4072C23124yes—
151C2×C4⋊Dic5C2313yes—
152C2×C4⋊Dic5C2313yes—
153C2×C4⋊Dic5C2313yes—
154C2×C4⋊Dic5C2313yes—
155C2×C4⋊Dic5C2313yes—
156C2×C4⋊Dic5C2311yescharacteristic
157C2×C4⋊Dic5C23124yes—
158C2×#683C2311yescharacteristic
159C2×#683C2313yes—
160C2×#683C2316yes—
161C2×#683C2311yescharacteristic
162C2×#683C2313yes—
163C2×#683C2311yescharacteristic
164C2×#683C2311yescharacteristic
165C2×C4×Dic5C2313yes—
166C2×C4×Dic5C2313yes—
167C2×C4×Dic5C2313yes—
168C2×C4×Dic5C2313yes—
169C2×C4×Dic5C2311yescharacteristic
170C2×C4×Dic5C23124yes—
171#4044C23124yes—
172#4039C23124yes—
173D5×C4⋊C4C23124yes—
174#4036C23124yes—
175#4035C2318yes—
176#4034C23124yes—
177#4032C23124yes—
178#4031C23124yes—
179#4029C23148yes—
180#4027C23148yes—
181#4025C23124yes—
182#4024C23124yes—
183C4×D20C23124yes—
184#4018C23124yes—
185#4016C23124yes—
186C4×Dic10C23124yes—
187#3517—532no—
188C2×#557—51no—
189C2×#553—53no—
190C2×#553—53no—
191C2×#550—51no—
192C2×#550—51no—
193C2×#550—53no—
194C2×#550D511yescharacteristic, complemented
195C2×#547—53no—
196C2×#540—53no—
197C2×#540—53no—
198C2×#532—53no—
199C2×#529—53no—
200C2×#520—51no—
201C2×#520—51no—
202C2×C4×#41—51no—
203C24×C5C2413yes—
204C24×C5C2413yes—
205C23×D5C2413yes—
206C5×#41—232no—
207C5×#41—232no—
208C2×C5×Q8#4118yescomplemented
209C2×C5×Q8C2414yes—
210C2×C5×D4—212no—
211C2×C5×D4—212no—
212C2×C5×D4—412no—
213C2×C5×D4—46no—
214C2×C5×D4C24112yes—
215C2×C5×D4C24112yes—
216C2×C5×D4C24112yes—
217C2×C5×D4C24124yes—
218C22×C4×C5—212no—
219C22×C4×C5—212no—
220C22×C4×C5C2411yescharacteristic
221C22×C4×C5C2413yes—
222C22×C4×C5C2411yescharacteristic
223C22×C4×C5C2411yescharacteristic
224C22×C4×C5C24112yes—
225C22×C4×C5C24112yes—
226C22×C4×C5C2413yes—
227C2×C22⋊D5—212no—
228C2×C22⋊D5—412no—
229C2×C22⋊D5—412no—
230C2×C22⋊D5—46no—
231C2×C22⋊D5C24112yes—
232C2×C22⋊D5C24124yes—
233C2×C22⋊D5C24124yes—
234C2×C22⋊D5C24112yes—
235C22×Dic5—212no—
236C22×Dic5—412no—
237C22×Dic5—46no—
238C22×Dic5C2411yescharacteristic
239C22×Dic5C2413yes—
240C22×Dic5C2411yescharacteristic
241C22×Dic5C2413yes—
242C22×Dic5C2411yescharacteristic
243C22×Dic5C2413yes—
244C22×Dic5C24112yes—
245C22×Dic5C24124yes—
246C22×Dic5C24112yes—
247C22×Dic5C2411yescharacteristic
248#713—232no—
249#711—496no—
250C2×D20—212no—
251C2×D20C24112yes—
252C2×C4×D5—212no—
253C2×C4×D5—412no—
254C2×C4×D5C24112yes—
255C2×C4×D5C24124yes—
256C2×Dic10—212no—
257C2×Dic10C24112yes—
258C5×C4⋊C4C2414yes—
259C5×C4⋊C4C24112yes—
260C5×C22⋊C4C24112yes—
261C5×C22⋊C4C24112yes—
262C42×C5C24112yes—
263C22⋊Dic5C24112yes—
264C22⋊Dic5C24112yes—
265C22⋊Dic5C24112yes—
266C22⋊Dic5C24124yes—
267C22⋊Dic5C24112yes—
268#685C24112yes—
269#685C24112yes—
270#685C24112yes—
271#685C24112yes—
272C4⋊Dic5C24112yes—
273C4⋊Dic5C24112yes—
274C4⋊Dic5C24112yes—
275C4⋊Dic5C24112yes—
276C4⋊Dic5C24112yes—
277C4⋊Dic5C2414yes—
278#683C2414yes—
279#683C24112yes—
280#683C24124yes—
281#683C2414yes—
282#683C24112yes—
283#683C2414yes—
284#683C2414yes—
285C4×Dic5C24112yes—
286C4×Dic5C24112yes—
287C4×Dic5C24112yes—
288C4×Dic5C24112yes—
289C4×Dic5C2414yes—
290C22×#41—51no—
291C22×#41—56no—
292C22×#41C2×D511yescharacteristic
293C22×#41C2×D511yescharacteristic
294#557—516no—
295#553—548no—
296#553—548no—
297#550—516no—
298#550—516no—
299#550—548no—
300#550C2×D5116yescomplemented
301#547—548no—
302#540—548no—
303#540—548no—
304#532—548no—
305C2×C4⋊Q8—53no—
306C2×#127—53no—
307C2×#127—53no—
308C2×#127C2×D513yes—
309#529—548no—
310C2×#126—53no—
311C2×#126—53no—
312C2×#125—51no—
313C2×#125—53no—
314C2×#125—53no—
315C2×#124—53no—
316C2×#123—53no—
317C2×#123—56no—
318C2×#123—56no—
319C2×#123—53no—
320C2×C22⋊Q8—53no—
321C2×#121—53no—
322C2×#121—56no—
323C2×#121—53no—
324C2×#121—53no—
325C2×#121—56no—
326C2×#121—56no—
327C2×#121—53no—
328C2×#121—53no—
329C2×#121C2×D513yes—
330C2×#121C2×D513yes—
331#520—516no—
332#520—516no—
333C4×#41—516no—
334C2×C4×Q8—51no—
335C2×C4×Q8—51no—
336C2×C4×Q8—51no—
337C2×C4×Q8—53no—
338C2×C4×Q8C2×D511yescharacteristic
339C2×C4×D4—53no—
340C2×C4×D4—53no—
341C2×C4×D4—53no—
342C2×C4×D4—53no—
343C2×C4×D4—53no—
344C2×C4×D4—53no—
345C2×C4×D4—53no—
346C2×C4×D4—56no—
347C2×C4×D4—53no—
348C2×C4×D4C2×D513yes—
349C2×#117—53no—
350C2×#117—53no—
351C2×#117—53no—
352C22×C4⋊C4—53no—
353C22×C4⋊C4—53no—
354C22×C42—53no—
355C23×C5—26no—
356C23×C5—26no—
357C23×C5—26no—
358C23×C5—26no—
359C23×C5—26no—
360C23×C5—26no—
361C23×C5C2516yes—
362C23×C5C2516yes—
363C23×C5C2511yescharacteristic
364C22×D5—26no—
365C22×D5—26no—
366C22×D5—26no—
367C22×D5C2516yes—
368C5×Q8C2×#41116yescomplemented
369C5×D4—224no—
370C5×D4—224no—
371C5×D4—424no—
372C5×D4—412no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—26no—
376C2×C4×C5—22no—
377C2×C4×C5—224no—
378C2×C4×C5—224no—
379C2×C4×C5C2×#41112yes—
380C2×C4×C5C2512yes—
381C2×C4×C5C2512yes—
382C2×C4×C5C2516yes—
383C2×C4×C5C2512yes—
384C2×C4×C5C2516yes—
385C22⋊D5—224no—
386C22⋊D5—424no—
387C22⋊D5—424no—
388C22⋊D5—412no—
389C2×Dic5—22no—
390C2×Dic5—26no—
391C2×Dic5—26no—
392C2×Dic5—22no—
393C2×Dic5—26no—
394C2×Dic5—22no—
395C2×Dic5—224no—
396C2×Dic5—424no—
397C2×Dic5—412no—
398C2×Dic5H(5,𝔽2)14yes—
399C2×Dic5C2512yes—
400C2×Dic5C2512yes—
401C2×Dic5C2516yes—
402C2×Dic5C2516yes—
403C2×Dic5C2516yes—
404C2×Dic5C2512yes—
405C2×Dic5C2512yes—
406D20—224no—
407C4×D5—224no—
408C4×D5—424no—
409Dic10—224no—
410C2×#41—28no—
411C2×#41—28no—
412C2×#41—58no—
413C2×#41—548no—
414C2×#41—108no—
415C2×#41—2024no—
416C2×#41C22×D518yes—
417C2×#41C22×D518yes—
418C22×Q8—53no—
419C22×Q8C22×D511yescharacteristic
420C22×D4—53no—
421C22×D4—56no—
422C22×D4—53no—
423C22×D4—56no—
424C22×D4—53no—
425C22×D4C22×D513yes—
426C22×D4C22×D513yes—
427C22×D4C22×D513yes—
428C22×D4C22×D516yes—
429C23×C4—53no—
430C23×C4—56no—
431C23×C4—53no—
432C23×C4—53no—
433C23×C4—56no—
434C23×C4C22×D513yes—
435C23×C4C22×D513yes—
436C4⋊Q8—524no—
437#127—524no—
438#127—524no—
439#127C22×D5124yes—
440#126—524no—
441#126—524no—
442#125—58no—
443#125—524no—
444#125—524no—
445#124—524no—
446#123—524no—
447#123—548no—
448#123—524no—
449#123—548no—
450C22⋊Q8—524no—
451#121—524no—
452#121—548no—
453#121—524no—
454#121—548no—
455#121—524no—
456#121—548no—
457#121—524no—
458#121—524no—
459#121C22×D5124yes—
460#121C22×D5124yes—
461C4×Q8—58no—
462C4×Q8—58no—
463C4×Q8—58no—
464C4×Q8—524no—
465C4×Q8C22×D518yes—
466C4×D4—524no—
467C4×D4—524no—
468C4×D4—524no—
469C4×D4—524no—
470C4×D4—524no—
471C4×D4—524no—
472C4×D4—524no—
473C4×D4—548no—
474C4×D4—524no—
475C4×D4C22×D5124yes—
476#117—524no—
477#117—524no—
478#117—524no—
479C2×C4⋊C4—53no—
480C2×C4⋊C4—53no—
481C2×C4⋊C4—53no—
482C2×C4⋊C4—53no—
483C2×C4⋊C4—524no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—53no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4—56no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—53no—
492C2×C4⋊C4—53no—
493C2×C4⋊C4—524no—
494C2×C4⋊C4C22×D513yes—
495C2×C4⋊C4C22×D511yescharacteristic
496C2×C22⋊C4—53no—
497C2×C22⋊C4—56no—
498C2×C22⋊C4—53no—
499C2×C22⋊C4—53no—
500C2×C22⋊C4—53no—
501C2×C22⋊C4—53no—
502C2×C22⋊C4—53no—
503C2×C22⋊C4—53no—
504C2×C22⋊C4—53no—
505C2×C22⋊C4C22×D513yes—
506C2×C22⋊C4C22×D513yes—
507C2×C42—53no—
508C2×C42—53no—
509C2×C42—53no—
510C2×C42—53no—
511C2×C42—524no—
512C2×C42—51no—
513C2×C42C22×D513yes—
514C22×C5—26no—
515C22×C5—26no—
516C22×C5—26no—
517C22×C5—26no—
518C22×C5—26no—
519C22×C5—26no—
520C22×C5—412no—
521C22×C5—412no—
522C22×C5C22×#4112yes—
523C22×C5C2×H(5,𝔽2)12yes—
524C22×C5#58512yes—
525C22×C5C2611yescharacteristic
526C2×D5—26no—
527C2×D5—26no—
528C2×D5—26no—
529C2×D5—412no—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5—26no—
533C4×C5—22no—
534C4×C5C22×#41112yes—
535Dic5—22no—
536Dic5—26no—
537Dic5—26no—
538Dic5—22no—
539Dic5—26no—
540Dic5—22no—
541Dic5C2×H(5,𝔽2)14yes—
542C24—53no—
543C24C23×D513yes—
544C24C23×D513yes—
545#41—232no—
546#41—232no—
547#41—1032no—
548#41—2096no—
549C2×Q8—512no—
550C2×Q8—1012no—
551C2×Q8#71118yescomplemented
552C2×Q8C23×D514yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—412no—
556C2×D4—46no—
557C2×D4—512no—
558C2×D4—524no—
559C2×D4—512no—
560C2×D4—524no—
561C2×D4—512no—
562C2×D4—1012no—
563C2×D4—1012no—
564C2×D4—2012no—
565C2×D4—2012no—
566C2×D4—206no—
567C2×D4C23×D5112yes—
568C2×D4C23×D5112yes—
569C2×D4C23×D5112yes—
570C2×D4C23×D5124yes—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—51no—
574C22×C4—512no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—53no—
578C22×C4—53no—
579C22×C4—53no—
580C22×C4—51no—
581C22×C4—512no—
582C22×C4—524no—
583C22×C4—512no—
584C22×C4—524no—
585C22×C4—1012no—
586C22×C4—1012no—
587C22×C4—2012no—
588C22×C4—2012no—
589C22×C4—206no—
590C22×C4C23×D5112yes—
591C22×C4C23×D5112yes—
592C22×C4C23×D511yescharacteristic
593C22×C4C23×D511yescharacteristic
594C22×C4C23×D513yes—
595C22×C4C23×D511yescharacteristic
596C22×C4C23×D513yes—
597C4⋊C4—512no—
598C4⋊C4—512no—
599C4⋊C4—512no—
600C4⋊C4—512no—
601C4⋊C4—54no—
602C4⋊C4—54no—
603C4⋊C4—512no—
604C4⋊C4—54no—
605C4⋊C4—54no—
606C4⋊C4—524no—
607C4⋊C4—54no—
608C4⋊C4—512no—
609C4⋊C4—512no—
610C4⋊C4C23×D5112yes—
611C4⋊C4C23×D514yes—
612C22⋊C4—512no—
613C22⋊C4—524no—
614C22⋊C4—512no—
615C22⋊C4—512no—
616C22⋊C4—512no—
617C22⋊C4—512no—
618C22⋊C4—512no—
619C22⋊C4—512no—
620C22⋊C4—512no—
621C22⋊C4C23×D5112yes—
622C22⋊C4C23×D5112yes—
623C42—54no—
624C42—512no—
625C42—512no—
626C42—512no—
627C42—512no—
628C42C23×D5112yes—
629C2×C5—46no—
630C2×C5—46no—
631C2×C5#351714yescomplemented
632C2×C5C23×#4111yescharacteristic
633C2×C5C22×H(5,𝔽2)11yescharacteristic
634C2×C5C2×#58511yescharacteristic
635D5—46no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—56no—
643C23—106no—
644C23—106no—
645C23—106no—
646C23C24×D516yes—
647C23C24×D516yes—
648C23C24×D511yescharacteristic
649Q8—1024no—
650Q8C2×#711116yescomplemented
651D4—224no—
652D4—224no—
653D4—424no—
654D4—412no—
655D4—1024no—
656D4—1024no—
657D4—2024no—
658D4—2024no—
659D4—2012no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—26no—
664C2×C4—224no—
665C2×C4—224no—
666C2×C4—54no—
667C2×C4—52no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—56no—
671C2×C4—56no—
672C2×C4—56no—
673C2×C4—52no—
674C2×C4—1024no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—106no—
678C2×C4—102no—
679C2×C4—106no—
680C2×C4—106no—
681C2×C4—1024no—
682C2×C4—2024no—
683C2×C4—2024no—
684C2×C4—2012no—
685C2×C4C2×#711112yes—
686C2×C4C24×D512yes—
687C2×C4C24×D512yes—
688C2×C4C24×D516yes—
689C2×C4C24×D512yes—
690C2×C4C24×D516yes—
691C5C2×#351711yescharacteristic, complemented, Sylow
692C22—26no—
693C22—26no—
694C22—26no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—412no—
700C22—106no—
701C22—106no—
702C22—106no—
703C22—2012no—
704C22C22×#71112yes—
705C22#6628312yes—
706C22D5×H(5,𝔽2)12yes—
707C22C25×D511yescharacteristic
708C4—22no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—54no—
713C4—102no—
714C4—102no—
715C4—106no—
716C4—102no—
717C4—106no—
718C4—106no—
719C4C22×#711112yes—
720C2—46no—
721C2—46no—
722C2—206no—
723C2#1061867314yesdirect product factor
724C2C23×#71111yescharacteristic
725C2C2×#6628311yescharacteristic
726C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#550C2
socleC23×C5C25
hypercenterC2×#550D5
hypocenterC5C2×#3517
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C5×#550C2semidirect
2. C2×#66168C2semidirect
3. C2×#66168C2semidirect
4. C2×#66161C2semidirect
5. C2×#41×Dic5C2semidirect
6. #10618673C2direct (N × H)
7. C2×#66053C2semidirect
8. C2×#66052C2semidirect
9. C2×#65948C2semidirect
10. C2×#65945C2semidirect
11. C2×#65953C2semidirect
12. C2×#65930C2semidirect
13. C2×#65903C2semidirect
14. C2×#65908C2semidirect
15. C2×#65899C2semidirect
16. C2×#65872C2semidirect
21. C5×#550C22semidirect
27. #66168C22semidirect
28. #66168C22semidirect
29. #66161C22semidirect
30. #41×Dic5C22semidirect
56. #66053C22semidirect
57. #66052C22semidirect
58. #65953C22semidirect
59. #65948C22semidirect
60. #65945C22semidirect
61. #65930C22semidirect
62. #65908C22semidirect
63. #65903C22semidirect
64. #65899C22semidirect
65. #65872C22semidirect
194. C2×#550D5semidirect
208. C2×C5×Q8#41semidirect
300. #550C2×D5semidirect
368. C5×Q8C2×#41semidirect
551. C2×Q8#711semidirect
631. C2×C5#3517semidirect
650. Q8C2×#711semidirect
691. C5C2×#3517semidirect
723. C2#10618673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5502
C2×#661682
C2×#661612
C2×#41×Dic52
#106186732
C2×#660532
C2×#660522
C2×#659482
C2×#659452
C2×#659532
C2×#659302
C2×#659032
C2×#659082
C2×#658992
C2×#658722
C2×#35175