Finite Group Databasebeta

← C2×#10617807 #13007491

Subgroups — C2×#10617807 #13007491

Order 1280.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#520C211yesmaximal, characteristic, complemented
2C2×#66165C211yesmaximal, characteristic, complemented
3C2×#66165C211yesmaximal, characteristic, complemented
4#10617807C2132yesmaximal, direct product factor
5C2×Q8×D20C211yesmaximal, characteristic, complemented
6C2×#65906C211yesmaximal, characteristic, complemented
7C2×C4×Q8×D5C211yesmaximal, characteristic, complemented
8C2×#65903C211yesmaximal, characteristic, complemented
9C2×#65892C213yesmaximal, complemented
10C2×#65895C213yesmaximal, complemented
11C2×#65891C213yesmaximal, complemented
12C2×#65876C213yesmaximal, complemented
13C2×#65862C213yesmaximal, complemented
14C2×#65852C213yesmaximal, complemented
15C2×#65845C213yesmaximal, complemented
16C2×#65847C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic
18C22×Q8×D5C2211yescharacteristic
19C22×Q8×D5C2211yescharacteristic
20C5×#520C22116yescomplemented
21C2×C4×C5×Q8C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×D4C2213yes—
24C2×C4×C5×D4C2213yes—
25C2×C5×#117C2213yes—
26C22×C5×C4⋊C4C2213yes—
27#66165C22116yescomplemented
28#66165C22116yescomplemented
29C2×Q8×Dic5C2211yescharacteristic
30C2×Q8×Dic5C2211yescharacteristic
31C2×#4084C2213yes—
32C2×#4084C2213yes—
33C2×#4082C2213yes—
34C2×#4082C2213yes—
35C2×#4075C2216yes—
36C2×C4×C22⋊D5C2213yes—
37C2×C4×C22⋊D5C2213yes—
38C2×C4×C22⋊D5C2216yes—
39C2×#4072C2216yes—
40C2×#4070C2213yes—
41C2×#4070C2213yes—
42C2×#4070C2216yes—
43Q8×D20C22116yescomplemented
44#65906C22116yescomplemented
45C4×Q8×D5C22116yescomplemented
46#65903C22116yescomplemented
47#65895C22148yescomplemented
48#65892C22148yescomplemented
49#65891C22148yescomplemented
50#65876C22148yescomplemented
51#65862C22148yescomplemented
52#65852C22148yescomplemented
53#65847C22148yescomplemented
54C2×#4044C2213yes—
55#65845C22148yescomplemented
56C2×#4043C2213yes—
57C2×#4043C2213yes—
58C2×#4042C2213yes—
59C2×#4040C2211yescharacteristic
60C2×#4038C2213yes—
61C2×D5×C4⋊C4C2213yes—
62C2×#4036C2213yes—
63C2×#4035C2216yes—
64C2×#4035C2213yes—
65C2×#4034C2213yes—
66C2×#4033C2213yes—
67C2×#4033C2213yes—
68C2×#4031C2213yes—
69C2×#4030C2213yes—
70C2×#4029C2213yes—
71C2×#4025C2216yes—
72C2×#4025C2216yes—
73C2×#4025C2213yes—
74C2×C4×D20C2213yes—
75C2×#4018C2213yes—
76C2×C42×D5C2213yes—
77C2×#4016C2213yes—
78C2×#4015C2213yes—
79C2×C4×Dic10C2213yes—
80C2×C4×Dic10C2213yes—
81C2×C4×Dic10C2213yes—
82C2×#3516—51nomaximal, Sylow
83C2×C5×#41—28no—
84C2×C5×#41C2318yes—
85C22×C5×Q8C2311yescharacteristic
86C22×C5×D4C2313yes—
87C23×C4×C5C2313yes—
88C23×C4×C5C2316yes—
89C22×C22⋊D5C2313yes—
90C22×C22⋊D5C2313yes—
91C2×Q8×D5—28no—
92C2×Q8×D5—28no—
93C2×Q8×D5C2318yes—
94C2×Q8×D5C2318yes—
95C22×D20C2311yescharacteristic
96C22×C4×D5C2311yescharacteristic
97C22×C4×D5C2313yes—
98C22×C4×D5C2313yes—
99C22×C4×D5C2313yes—
100C22×Dic10C2313yes—
101C22×Dic10C2313yes—
102C22×Dic10C2313yes—
103C4×C5×Q8C2318yes—
104C4×C5×Q8C2318yes—
105C4×C5×D4C23124yes—
106C4×C5×D4C23124yes—
107C5×#117C23124yes—
108C2×C5×C4⋊C4C2313yes—
109C2×C5×C4⋊C4C2313yes—
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2313yes—
112C2×C5×C4⋊C4C23124yes—
113C2×C5×C22⋊C4C2313yes—
114C2×C5×C22⋊C4C2313yes—
115C2×C42×C5C2313yes—
116C2×C42×C5C2313yes—
117C2×C22⋊Dic5C2316yes—
118C2×C22⋊Dic5C2316yes—
119C2×C22⋊Dic5C2313yes—
120C2×C22⋊Dic5C2313yes—
121Q8×Dic5C2318yes—
122Q8×Dic5C2318yes—
123#4084C23124yes—
124#4084C23124yes—
125#4082C23124yes—
126#4082C23124yes—
127#4075C23148yes—
128C4×C22⋊D5C23124yes—
129C4×C22⋊D5C23148yes—
130C4×C22⋊D5C23124yes—
131C2×#685C2311yescharacteristic
132C2×#685C2313yes—
133C2×#685C2313yes—
134C2×#685C2313yes—
135C2×#685C2311yescharacteristic
136C2×#685C2311yescharacteristic
137#4072C23148yes—
138C2×C4⋊Dic5C2313yes—
139C2×C4⋊Dic5C2313yes—
140C2×C4⋊Dic5C2313yes—
141C2×C4⋊Dic5C2313yes—
142C2×C4⋊Dic5C2316yes—
143#4070C23124yes—
144#4070C23148yes—
145#4070C23124yes—
146C2×#683C2311yescharacteristic
147C2×#683C2313yes—
148C2×#683C2313yes—
149C2×#683C2316yes—
150C2×#683C2316yes—
151C2×#683C2313yes—
152C2×#683C2313yes—
153C2×#683C2313yes—
154C2×C4×Dic5C2313yes—
155C2×C4×Dic5C2313yes—
156C2×C4×Dic5C2313yes—
157C2×C4×Dic5C2316yes—
158C2×C4×Dic5C2313yes—
159#4044C23124yes—
160#4043C23124yes—
161#4043C23124yes—
162#4042C23124yes—
163#4040C2318yes—
164#4038C23124yes—
165D5×C4⋊C4C23124yes—
166#4036C23124yes—
167#4035C23148yes—
168#4035C23124yes—
169#4034C23124yes—
170#4033C23124yes—
171#4033C23124yes—
172#4031C23124yes—
173#4030C23124yes—
174#4029C23124yes—
175#4025C23148yes—
176#4025C23148yes—
177#4025C23124yes—
178C4×D20C23124yes—
179#4018C23124yes—
180C42×D5C23124yes—
181#4016C23124yes—
182#4015C23124yes—
183C4×Dic10C23124yes—
184C4×Dic10C23124yes—
185C4×Dic10C23124yes—
186#3516—532no—
187C2×#557—51no—
188C2×#556—53no—
189C2×#554—53no—
190C2×#553—53no—
191C2×#552—53no—
192C2×D4×Q8—51no—
193C2×#548—51no—
194C2×#548—51no—
195C2×#542—53no—
196C2×#541—53no—
197C2×#529—53no—
198C2×#529—53no—
199C2×#520D511yescharacteristic, complemented
200C2×#519—51no—
201C22×C4×Q8—51no—
202C24×C5C2413yes—
203C23×D5C2411yescharacteristic
204C23×D5C2411yescharacteristic
205C5×#41—232no—
206C2×C5×Q8#4118yes—
207C2×C5×Q8C2414yes—
208C2×C5×D4—212no—
209C2×C5×D4C24112yes—
210C22×C4×C5—212no—
211C22×C4×C5—412no—
212C22×C4×C5C2411yescharacteristic
213C22×C4×C5C2411yescharacteristic
214C22×C4×C5C2413yes—
215C22×C4×C5C2413yes—
216C22×C4×C5C2411yescharacteristic
217C22×C4×C5C24112yes—
218C22×C4×C5C24124yes—
219C22×C4×C5C2413yes—
220C2×C22⋊D5—212no—
221C2×C22⋊D5—46no—
222C2×C22⋊D5C24112yes—
223C2×C22⋊D5C24112yes—
224C22×Dic5C2411yescharacteristic
225C22×Dic5C2413yes—
226C22×Dic5C2413yes—
227C22×Dic5C2411yescharacteristic
228C22×Dic5C2413yes—
229C22×Dic5C2413yes—
230Q8×D5—232no—
231Q8×D5—232no—
232C2×D20—24no—
233C2×D20C2414yes—
234C2×C4×D5—24no—
235C2×C4×D5—212no—
236C2×C4×D5—212no—
237C2×C4×D5—46no—
238C2×C4×D5C24112yes—
239C2×C4×D5C24112yes—
240C2×C4×D5C2414yes—
241C2×C4×D5C24112yes—
242C2×Dic10—212no—
243C2×Dic10—212no—
244C2×Dic10—46no—
245C2×Dic10C24112yes—
246C2×Dic10C24112yes—
247C2×Dic10C24112yes—
248C5×C4⋊C4C24112yes—
249C5×C4⋊C4C24112yes—
250C5×C4⋊C4C24112yes—
251C5×C4⋊C4C2414yes—
252C5×C22⋊C4C24112yes—
253C5×C22⋊C4C24112yes—
254C42×C5C24112yes—
255C42×C5C24112yes—
256C22⋊Dic5C24124yes—
257C22⋊Dic5C24124yes—
258C22⋊Dic5C24112yes—
259C22⋊Dic5C24112yes—
260#685C2414yes—
261#685C24112yes—
262#685C24112yes—
263#685C24112yes—
264#685C2414yes—
265#685C2414yes—
266C4⋊Dic5C24112yes—
267C4⋊Dic5C24112yes—
268C4⋊Dic5C24112yes—
269C4⋊Dic5C24112yes—
270C4⋊Dic5C24124yes—
271#683C2414yes—
272#683C24112yes—
273#683C24112yes—
274#683C24124yes—
275#683C24124yes—
276#683C24112yes—
277#683C24112yes—
278#683C24112yes—
279C4×Dic5C24112yes—
280C4×Dic5C24112yes—
281C4×Dic5C24112yes—
282C4×Dic5C24124yes—
283C4×Dic5C24112yes—
284C22×#41C2×D511yescharacteristic
285C23×Q8—51no—
286C23×Q8—51no—
287#557—516no—
288#556—548no—
289#554—548no—
290#553—548no—
291#552—548no—
292D4×Q8—516no—
293#548—516no—
294#548—516no—
295#542—548no—
296#541—548no—
297C2×C4⋊Q8—53no—
298C2×C4⋊Q8—53no—
299#529—548no—
300#529—548no—
301C2×#126—53no—
302C2×#126—56no—
303C2×#126—53no—
304C2×#126—56no—
305C2×#125—53no—
306C2×#125—56no—
307C2×#125—53no—
308C2×#125—53no—
309C2×#124—53no—
310C2×#124—53no—
311C2×#124—53no—
312C2×#123—56no—
313C2×#123—51no—
314C2×#123—53no—
315C2×C22⋊Q8—53no—
316C2×C22⋊Q8—53no—
317C2×C22⋊Q8—56no—
318C2×C22⋊Q8—53no—
319C2×C22⋊Q8—53no—
320C2×C22⋊Q8—53no—
321C2×#121—53no—
322C2×#121—53no—
323C2×#121—53no—
324#520C2×D5116yescomplemented
325#519—516no—
326C2×C4×Q8—51no—
327C2×C4×Q8—51no—
328C2×C4×Q8—516no—
329C2×C4×Q8—53no—
330C2×C4×Q8—53no—
331C2×C4×Q8—53no—
332C2×C4×Q8—53no—
333C2×C4×Q8—53no—
334C2×C4×Q8C2×D511yescharacteristic
335C2×C4×Q8C2×D511yescharacteristic
336C2×C4×D4—53no—
337C2×C4×D4—53no—
338C2×C4×D4—56no—
339C2×C4×D4—53no—
340C2×C4×D4C2×D513yes—
341C2×C4×D4C2×D513yes—
342C2×#117—56no—
343C2×#117—53no—
344C2×#117—53no—
345C2×#117C2×D513yes—
346C22×C4⋊C4—53no—
347C22×C4⋊C4C2×D513yes—
348C22×C42—53no—
349C23×C5—26no—
350C23×C5—26no—
351C23×C5—26no—
352C23×C5C2516yes—
353C23×C5C2511yescharacteristic
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D52−1+414yes—
360C22×D5C2512yes—
361C22×D5C2512yes—
362C5×Q8C2×#41116yes—
363C5×D4—224no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—26no—
368C2×C4×C5—26no—
369C2×C4×C5—224no—
370C2×C4×C5—424no—
371C2×C4×C5C2×#41112yes—
372C2×C4×C5C2512yes—
373C2×C4×C5C2516yes—
374C2×C4×C5C2512yes—
375C2×C4×C5C2512yes—
376C2×C4×C5C2516yes—
377C2×C4×C5C2516yes—
378C22⋊D5—224no—
379C22⋊D5—412no—
380C2×Dic5—26no—
381C2×Dic5—26no—
382C2×Dic5—22no—
383C2×Dic5—26no—
384C2×Dic5—22no—
385C2×Dic5—26no—
386C2×Dic5C2512yes—
387C2×Dic5C2516yes—
388C2×Dic5C2512yes—
389C2×Dic5C2516yes—
390C2×Dic5C2516yes—
391C2×Dic5C2516yes—
392D20—28no—
393C4×D5—28no—
394C4×D5—224no—
395C4×D5—224no—
396C4×D5—412no—
397Dic10—224no—
398Dic10—224no—
399Dic10—412no—
400C2×#41—28no—
401C2×#41C22×D518yes—
402C22×Q8—58no—
403C22×Q8—58no—
404C22×Q8—53no—
405C22×Q8—53no—
406C22×Q8—53no—
407C22×Q8—108no—
408C22×Q8—108no—
409C22×Q8C22×D511yescharacteristic
410C22×D4—53no—
411C22×D4—53no—
412C22×D4—51no—
413C22×D4C22×D513yes—
414C23×C4—53no—
415C23×C4—53no—
416C23×C4—51no—
417C23×C4—53no—
418C23×C4C22×D513yes—
419C23×C4C22×D516yes—
420C4⋊Q8—524no—
421C4⋊Q8—524no—
422#126—524no—
423#126—548no—
424#126—524no—
425#126—548no—
426#125—524no—
427#125—524no—
428#125—548no—
429#125—524no—
430#124—524no—
431#124—524no—
432#124—524no—
433#123—548no—
434#123—58no—
435#123—524no—
436C22⋊Q8—524no—
437C22⋊Q8—524no—
438C22⋊Q8—548no—
439C22⋊Q8—524no—
440C22⋊Q8—524no—
441C22⋊Q8—524no—
442#121—524no—
443#121—524no—
444#121—524no—
445C4×Q8—58no—
446C4×Q8—58no—
447C4×Q8—524no—
448C4×Q8—524no—
449C4×Q8—524no—
450C4×Q8—524no—
451C4×Q8—524no—
452C4×Q8C22×D518yes—
453C4×Q8C22×D518yes—
454C4×D4—524no—
455C4×D4—524no—
456C4×D4—548no—
457C4×D4—524no—
458C4×D4C22×D5124yes—
459C4×D4C22×D5124yes—
460#117—548no—
461#117—524no—
462#117—524no—
463#117C22×D5124yes—
464C2×C4⋊C4—53no—
465C2×C4⋊C4—56no—
466C2×C4⋊C4—53no—
467C2×C4⋊C4—53no—
468C2×C4⋊C4—53no—
469C2×C4⋊C4—53no—
470C2×C4⋊C4—56no—
471C2×C4⋊C4—53no—
472C2×C4⋊C4—53no—
473C2×C4⋊C4—56no—
474C2×C4⋊C4—53no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—53no—
477C2×C4⋊C4—524no—
478C2×C4⋊C4C22×D513yes—
479C2×C4⋊C4C22×D513yes—
480C2×C4⋊C4C22×D513yes—
481C2×C4⋊C4C22×D5124yes—
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C22⋊C4—53no—
484C2×C22⋊C4—56no—
485C2×C22⋊C4—56no—
486C2×C22⋊C4—53no—
487C2×C22⋊C4—53no—
488C2×C22⋊C4—51no—
489C2×C22⋊C4—51no—
490C2×C22⋊C4—53no—
491C2×C22⋊C4—51no—
492C2×C22⋊C4—53no—
493C2×C22⋊C4C22×D513yes—
494C2×C22⋊C4C22×D513yes—
495C2×C42—56no—
496C2×C42—53no—
497C2×C42—53no—
498C2×C42—53no—
499C2×C42—53no—
500C2×C42—524no—
501C2×C42C22×D513yes—
502C2×C42C22×D513yes—
503C22×C5—26no—
504C22×C5—26no—
505C22×C5—26no—
506C22×C5—412no—
507C22×C5C22×#4112yes—
508C22×C5C2×2−1+412yes—
509C22×C5#58512yes—
510C22×C5C2611yescharacteristic
511C2×D5—22no—
512C2×D5—22no—
513C2×D5—28no—
514C2×D5—22no—
515C2×D5—22no—
516C2×D5—22no—
517C2×D5—44no—
518C2×D5C2×2−1+414yes—
519C4×C5—22no—
520C4×C5—22no—
521C4×C5—22no—
522C4×C5—26no—
523C4×C5—26no—
524C4×C5C22×#41112yes—
525Dic5—26no—
526Dic5—26no—
527Dic5—22no—
528Dic5—26no—
529Dic5—22no—
530Dic5—26no—
531C24—51no—
532C24—51no—
533C24C23×D513yes—
534#41—232no—
535C2×Q8—512no—
536C2×Q8—512no—
537C2×Q8—512no—
538C2×Q8—1032no—
539C2×Q8—1032no—
540C2×Q8—1012no—
541C2×Q8—1012no—
542C2×Q8—206no—
543C2×Q8#70918yes—
544C2×Q8C23×D514yes—
545C2×D4—212no—
546C2×D4—512no—
547C2×D4—512no—
548C2×D4—54no—
549C2×D4—104no—
550C2×D4—1012no—
551C2×D4—206no—
552C2×D4C23×D5112yes—
553C22×C4—212no—
554C22×C4—412no—
555C22×C4—51no—
556C22×C4—51no—
557C22×C4—53no—
558C22×C4—53no—
559C22×C4—53no—
560C22×C4—53no—
561C22×C4—54no—
562C22×C4—512no—
563C22×C4—512no—
564C22×C4—512no—
565C22×C4—104no—
566C22×C4—1012no—
567C22×C4—1012no—
568C22×C4—206no—
569C22×C4C23×D5112yes—
570C22×C4C23×D511yescharacteristic
571C22×C4C23×D513yes—
572C22×C4C23×D511yescharacteristic
573C22×C4C23×D513yes—
574C22×C4C23×D511yescharacteristic
575C22×C4C23×D5124yes—
576C22×C4C23×D513yes—
577C4⋊C4—512no—
578C4⋊C4—524no—
579C4⋊C4—512no—
580C4⋊C4—512no—
581C4⋊C4—512no—
582C4⋊C4—512no—
583C4⋊C4—524no—
584C4⋊C4—512no—
585C4⋊C4—512no—
586C4⋊C4—524no—
587C4⋊C4—512no—
588C4⋊C4—54no—
589C4⋊C4—512no—
590C4⋊C4C23×D5112yes—
591C4⋊C4C23×D5112yes—
592C4⋊C4C23×D5112yes—
593C4⋊C4C23×D514yes—
594C22⋊C4—512no—
595C22⋊C4—524no—
596C22⋊C4—524no—
597C22⋊C4—512no—
598C22⋊C4—512no—
599C22⋊C4—54no—
600C22⋊C4—54no—
601C22⋊C4—512no—
602C22⋊C4—54no—
603C22⋊C4—512no—
604C22⋊C4C23×D5112yes—
605C22⋊C4C23×D5112yes—
606C42—512no—
607C42—512no—
608C42—512no—
609C42—524no—
610C42—512no—
611C42C23×D5112yes—
612C42C23×D5112yes—
613C2×C5—46no—
614C2×C5#351614yescomplemented
615C2×C5C23×#4111yescharacteristic
616C2×C5C22×2−1+411yescharacteristic
617C2×C5C2×#58511yescharacteristic
618D5—24no—
619D5—42no—
620C23—26no—
621C23—26no—
622C23—26no—
623C23—54no—
624C23—52no—
625C23—52no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23C24×D516yes—
632C23C24×D511yescharacteristic
633Q8—1024no—
634Q8—1024no—
635Q8—2012no—
636Q8C2×#709116yes—
637D4—224no—
638D4—108no—
639D4—1024no—
640D4—2012no—
641C2×C4—22no—
642C2×C4—26no—
643C2×C4—26no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—224no—
647C2×C4—424no—
648C2×C4—52no—
649C2×C4—52no—
650C2×C4—56no—
651C2×C4—56no—
652C2×C4—56no—
653C2×C4—56no—
654C2×C4—108no—
655C2×C4—106no—
656C2×C4—106no—
657C2×C4—106no—
658C2×C4—102no—
659C2×C4—102no—
660C2×C4—106no—
661C2×C4—1024no—
662C2×C4—1024no—
663C2×C4—2012no—
664C2×C4C2×#709112yes—
665C2×C4C24×D512yes—
666C2×C4C24×D516yes—
667C2×C4C24×D512yes—
668C2×C4C24×D516yes—
669C2×C4C24×D512yes—
670C2×C4C24×D516yes—
671C5C2×#351611yescharacteristic, complemented, Sylow
672C22—26no—
673C22—26no—
674C22—26no—
675C22—412no—
676C22—54no—
677C22—102no—
678C22—102no—
679C22—108no—
680C22—102no—
681C22—102no—
682C22—102no—
683C22—204no—
684C22C22×#70912yes—
685C22#6628512yes—
686C22D5×2−1+412yes—
687C22C25×D511yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—22no—
693C4—106no—
694C4—106no—
695C4—106no—
696C4—102no—
697C4—102no—
698C4—106no—
699C4C22×#709112yes—
700C2—46no—
701C2—104no—
702C2—202no—
703C2#1061780714yesdirect product factor
704C2C23×#70911yescharacteristic
705C2C2×#6628511yescharacteristic
706C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#520C2
socleC23×C5C25
hypercenterC2×#520D5
hypocenterC5C2×#3516
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C5×#520C2semidirect
2. C2×#66165C2semidirect
3. C2×#66165C2semidirect
4. #10617807C2direct (N × H)
5. C2×Q8×D20C2semidirect
6. C2×#65906C2semidirect
7. C2×C4×Q8×D5C2semidirect
8. C2×#65903C2semidirect
9. C2×#65892C2semidirect
10. C2×#65895C2semidirect
11. C2×#65891C2semidirect
12. C2×#65876C2semidirect
13. C2×#65862C2semidirect
14. C2×#65852C2semidirect
15. C2×#65845C2semidirect
16. C2×#65847C2semidirect
20. C5×#520C22semidirect
27. #66165C22semidirect
28. #66165C22semidirect
43. Q8×D20C22semidirect
44. #65906C22semidirect
45. C4×Q8×D5C22semidirect
46. #65903C22semidirect
47. #65895C22semidirect
48. #65892C22semidirect
49. #65891C22semidirect
50. #65876C22semidirect
51. #65862C22semidirect
52. #65852C22semidirect
53. #65847C22semidirect
55. #65845C22semidirect
199. C2×#520D5semidirect
324. #520C2×D5semidirect
614. C2×C5#3516semidirect
671. C5C2×#3516semidirect
703. C2#10617807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5202
C2×#661652
#106178072
C2×Q8×D202
C2×#659062
C2×C4×Q8×D52
C2×#659032
C2×#658922
C2×#658952
C2×#658912
C2×#658762
C2×#658622
C2×#658522
C2×#658452
C2×#658472
C2×#35165