Finite Group Databasebeta

← C2×#10611330 #12969063

Subgroups — C2×#10611330 #12969063

Order 1280.

2266 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65882C211yesmaximal, characteristic, complemented
2C2×#65891C211yesmaximal, characteristic, complemented
3C2×C4×C5×D8C211yesmaximal, characteristic, complemented
4C2×#65448C211yesmaximal, characteristic, complemented
5C2×#65443C211yesmaximal, characteristic, complemented
6C2×C4×#687C211yesmaximal, characteristic, complemented
7C2×C4×#686C211yesmaximal, characteristic, complemented
8#10611330C2116yesmaximal, direct product factor
9C2×#65175C211yesmaximal, characteristic, complemented
10C2×#65165C211yesmaximal, characteristic, complemented
11C2×#65071C211yesmaximal, characteristic, complemented
12C2×#65069C211yesmaximal, characteristic, complemented
13C2×#65053C211yesmaximal, characteristic, complemented
14C2×#65054C211yesmaximal, characteristic, complemented
15C2×C4×#677C211yesmaximal, characteristic, complemented
16C2×C4×#676C211yesmaximal, characteristic, complemented
17C22×#709—21no—
18C22×C5×D8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×#4086C2211yescharacteristic
22C2×#4084C2211yescharacteristic
23C2×#4084C2211yescharacteristic
24C2×#4082C2211yescharacteristic
25C22×#687C2211yescharacteristic
26C22×#686C2211yescharacteristic
27C2×C4×C22⋊D5—21no—
28C2×C4×C22⋊D5—21no—
29C2×#4072—21no—
30C22×#677C2211yescharacteristic
31C22×#676C2211yescharacteristic
32C22×#676C2211yescharacteristic
33#65891—24no—
34#65891C2218yescomplemented
35#65882—24no—
36#65882C2218yescomplemented
37C2×#4043C2211yescharacteristic
38C2×#4041C2211yescharacteristic
39C2×#4036C2211yescharacteristic
40C2×#4034C2211yescharacteristic
41C2×#4031—21no—
42C2×#4030—21no—
43C2×#4029—21no—
44C2×#4025—21no—
45C2×C4×D20C2211yescharacteristic
46C2×C42×D5C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C4×C5×D8C2218yescomplemented
49C2×C5×#107C2211yescharacteristic
50C2×C5×#102C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52C2×C4×C5×C8C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55#65448C2218yescomplemented
56#65443C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3947C2211yescharacteristic
61C2×#3947C2211yescharacteristic
62C4×#687C2218yescomplemented
63C4×#686C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×C4×#168C2211yescharacteristic
69#65175C2218yescomplemented
70#65165C2218yescomplemented
71#65071C2218yescomplemented
72#65069C2218yescomplemented
73#65054C2218yescomplemented
74#65053C2218yescomplemented
75C4×#677C2218yescomplemented
76C4×#676C2218yescomplemented
77C2×#3171—51nomaximal, Sylow
78C22×C5×D4C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C2×#709—28no—
87C2×#709—48no—
88C22×D20—21no—
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5D411yescharacteristic
92C22×C4×D5D411yescharacteristic
93C22×C4×D5C2311yescharacteristic
94C22×Dic10—21no—
95C22×Dic10C2311yescharacteristic
96C2×C5×D8—24no—
97C2×C5×D8C2314yes—
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C4×C5×D4—22no—
101C4×C5×D4—22no—
102C4×C5×D4C2314yes—
103C4×C5×D4C2314yes—
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C42×C5C2311yescharacteristic
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112C2×C22⋊Dic5—21no—
113#4086—22no—
114#4086C2314yes—
115#4084—22no—
116#4084—22no—
117#4084C2314yes—
118#4084C2314yes—
119#4082—22no—
120#4082C2314yes—
121C2×#687—24no—
122C2×#687C2314yes—
123C2×#686—24no—
124C2×#686C2314yes—
125C4×C22⋊D5—28no—
126C4×C22⋊D5—28no—
127C2×#685—21no—
128C2×#685—21no—
129C2×#685—21no—
130#4072—28no—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5D411yescharacteristic
140C2×C4×Dic5D411yescharacteristic
141C2×C4×Dic5C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C2×#677—24no—
145C2×#677C2314yes—
146C2×#676—24no—
147C2×#676—24no—
148C2×#676C2314yes—
149C2×#676C2314yes—
150#4043—22no—
151#4043C2314yes—
152#4041—22no—
153#4041C2314yes—
154#4036—22no—
155#4036C2314yes—
156#4034—22no—
157#4034C2314yes—
158#4031—28no—
159#4030—28no—
160#4029—28no—
161#4025—28no—
162C4×D20—22no—
163C4×D20C2314yes—
164C42×D5D414yes—
165C42×D5C2314yes—
166C4×Dic10—22no—
167C4×Dic10C2314yes—
168C5×#107C2314yes—
169C5×#102C2314yes—
170C5×#102C2314yes—
171C4×C5×C8C2314yes—
172#3964C2314yes—
173#3964C2314yes—
174#3953C2314yes—
175#3949C2314yes—
176#3948C2314yes—
177#3947C2314yes—
178#3947C2314yes—
179#3942C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3939C2314yes—
183C4×#168C2314yes—
184C2×#532—51no—
185C2×#529—51no—
186#3171—516no—
187C2×#501—51no—
188C2×#496—51no—
189C2×#490—51no—
190C2×#489—51no—
191C2×#469—51no—
192C2×#469—51no—
193C2×#468—51no—
194C2×#468—51no—
195C2×C4×SD16—51no—
196C2×C4×SD16—51no—
197C2×C4×D8—51no—
198C2×C4×D8D511yescharacteristic, complemented
199C2×C4×M16—51no—
200C24×C5—21no—
201C24×C5—21no—
202C23×D5—21no—
203C23×D5C2×D411yescharacteristic
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—22no—
207C2×C5×D4—22no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4C2412yes—
211C2×C5×D4C2412yes—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—24no—
216C22×C4×C5—44no—
217C22×C4×C5—44no—
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2411yescharacteristic
221C2×C22⋊D5—24no—
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—24no—
225C2×C22⋊D5—44no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—44no—
228C2×C22⋊D5—44no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5C2×D411yescharacteristic
233C22×Dic5C2×D411yescharacteristic
234C22×Dic5C2×D411yescharacteristic
235#709—432no—
236C2×D20—22no—
237C2×D20—22no—
238C2×D20—24no—
239C2×D20—21no—
240C2×D20—44no—
241C2×D20C2412yes—
242C2×C4×D5—24no—
243C2×C4×D5—22no—
244C2×C4×D5—22no—
245C2×C4×D5—24no—
246C2×C4×D5—42no—
247C2×C4×D5—44no—
248C2×C4×D5C2×D414yes—
249C2×C4×D5C2×D412yes—
250C2×C4×D5C2×D414yes—
251C2×C4×D5C2412yes—
252C2×Dic10—22no—
253C2×Dic10—22no—
254C2×Dic10—21no—
255C2×Dic10—24no—
256C2×Dic10—44no—
257C2×Dic10C2412yes—
258C5×D8—28no—
259C2×C5×C8—22no—
260C2×C5×C8#4114yescomplemented
261C2×C5×C8C2412yes—
262C2×C5×C8C2412yes—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4C2412yes—
266C5×C4⋊C4C2412yes—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C42×C5C2×D412yes—
270C42×C5C2412yes—
271C22⋊Dic5—24no—
272C22⋊Dic5—24no—
273C22⋊Dic5—24no—
274C22⋊Dic5—24no—
275#687—28no—
276#686—28no—
277#685—24no—
278#685—24no—
279#685—24no—
280C4⋊Dic5—21no—
281C4⋊Dic5—21no—
282C4⋊Dic5—24no—
283C4⋊Dic5—24no—
284C4⋊Dic5C2412yes—
285C4⋊Dic5C2412yes—
286#683—24no—
287#683—24no—
288#683—24no—
289C4×Dic5—24no—
290C4×Dic5C2×D412yes—
291C4×Dic5C2×D414yes—
292C4×Dic5C2×D414yes—
293C4×Dic5C2412yes—
294C2×#168—22no—
295C2×#168#4114yescomplemented
296C2×#168C2412yes—
297C2×#168C2412yes—
298#677—28no—
299#676—28no—
300#676—28no—
301C22×#41—101no—
302C22×SD16—51no—
303C22×SD16—51no—
304C22×D8—51no—
305C22×D8C2×D511yescharacteristic
306C22×M16—51no—
307C22×M16—51no—
308#532—58no—
309#532—104no—
310C2×C4⋊Q8—51no—
311C2×#127—51no—
312#529—58no—
313#529—104no—
314C2×#126—101no—
315C2×#125—51no—
316C2×#124—51no—
317C2×#124—101no—
318C2×#123—101no—
319C2×C22⋊Q8—51no—
320C2×#121—51no—
321C2×#121—51no—
322C2×#121—51no—
323C2×#121—101no—
324C2×C4×Q8—51no—
325C2×C4×D4—51no—
326C2×C4×D4—101no—
327C2×C4×D4—101no—
328C2×C4×D4C2×D511yescharacteristic
329C2×C4×D4C2×D511yescharacteristic
330C2×#117—101no—
331C22×C42—51no—
332#501—58no—
333#496—58no—
334#490—58no—
335#489—58no—
336#469—58no—
337#469—58no—
338#468—58no—
339#468—58no—
340C4×SD16—58no—
341C4×SD16—58no—
342C4×D8—58no—
343C4×D8C2×D518yescomplemented
344C2×#107—51no—
345C2×#107C2×D511yescharacteristic
346C2×#106—51no—
347C2×#106—51no—
348C2×#103—51no—
349C2×#103—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×#102—51no—
354C2×#102C2×D511yescharacteristic
355C2×#102C2×D511yescharacteristic
356C4×M16—58no—
357C2×#97—51no—
358C2×#97—51no—
359C2×C4×C8—51no—
360C2×C4×C8C2×D511yescharacteristic
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—42no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5—42no—
368C23×C5—42no—
369C23×C5C22×D411yescharacteristic
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—42no—
375C22×D5—42no—
376C22×D5—42no—
377C22×D5C22×D412yes—
378C5×D4—22no—
379C5×D4—22no—
380C5×D4—22no—
381C5×D4—22no—
382C5×D4—42no—
383C5×D4—42no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—48no—
390C2×C4×C5—48no—
391C2×C4×C5AGL(1,ℤ/8)14yes—
392C2×C4×C5C22×D412yes—
393C2×C4×C5C22×D411yescharacteristic
394C2×C4×C5C22×D412yes—
395C2×C4×C5C2×#4112yes—
396C2×C4×C5C2×#4112yes—
397C2×C4×C5C2511yescharacteristic
398C22⋊D5—48no—
399C22⋊D5—48no—
400C22⋊D5—48no—
401C22⋊D5—48no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—42no—
409C2×Dic5—42no—
410C2×Dic5—42no—
411C2×Dic5C22×D412yes—
412C2×Dic5C22×D412yes—
413C2×Dic5C22×D412yes—
414D20—22no—
415D20—22no—
416D20—48no—
417D20—42no—
418C4×D5—24no—
419C4×D5—28no—
420C4×D5—22no—
421C4×D5—22no—
422C4×D5—44no—
423C4×D5—48no—
424Dic10—22no—
425Dic10—22no—
426Dic10—48no—
427Dic10—42no—
428C5×C8—22no—
429C5×C8C2×#4114yescomplemented
430#168—22no—
431#168C2×#4114yescomplemented
432C2×#41—108no—
433C2×#41—208no—
434C22×Q8—51no—
435C22×Q8—101no—
436C22×D4—51no—
437C22×D4—101no—
438C22×D4—101no—
439C22×D4—101no—
440C22×D4—101no—
441C22×D4—101no—
442C22×D4C22×D511yescharacteristic
443C22×D4C22×D511yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—51no—
447C23×C4—51no—
448C23×C4—51no—
449C23×C4—101no—
450C2×SD16—54no—
451C2×SD16—54no—
452C2×SD16—104no—
453C2×SD16—104no—
454C2×D8—24no—
455C2×D8—54no—
456C2×D8—104no—
457C2×D8C22×D514yes—
458C2×M16—54no—
459C2×M16—54no—
460C2×M16—104no—
461C2×M16—104no—
462C22×C8—51no—
463C22×C8—51no—
464C22×C8C22×D511yescharacteristic
465C22×C8C22×D511yescharacteristic
466C4⋊Q8—54no—
467C4⋊Q8—102no—
468#127—54no—
469#127—102no—
470#126—108no—
471#125—54no—
472#125—102no—
473#124—54no—
474#124—108no—
475#124—102no—
476#123—108no—
477C22⋊Q8—54no—
478C22⋊Q8—102no—
479#121—54no—
480#121—54no—
481#121—54no—
482#121—108no—
483#121—102no—
484#121—102no—
485#121—102no—
486C4×Q8—54no—
487C4×Q8—102no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—54no—
491C4×D4—108no—
492C4×D4—108no—
493C4×D4—102no—
494C4×D4C22×D514yes—
495C4×D4C22×D514yes—
496#117—108no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4C22×D511yescharacteristic
505C2×C4⋊C4C22×D511yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4—101no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C42—51no—
516C2×C42—51no—
517C2×C42—51no—
518C2×C42—54no—
519C2×C42—54no—
520C2×C42—101no—
521C2×C42C22×D511yescharacteristic
522#107—54no—
523#107C22×D514yes—
524#106—54no—
525#106—54no—
526#103—54no—
527#103—54no—
528#102—54no—
529#102—54no—
530#102—54no—
531#102—54no—
532#102C22×D514yes—
533#102C22×D514yes—
534#97—54no—
535#97—54no—
536C4×C8—54no—
537C4×C8C22×D514yes—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—84no—
545C22×C5—84no—
546C22×C5#53212yes—
547C22×C5C2×AGL(1,ℤ/8)12yes—
548C22×C5#57512yes—
549C22×C5C23×D411yescharacteristic
550C2×D5—22no—
551C2×D5—22no—
552C2×D5—22no—
553C2×D5—44no—
554C2×D5—42no—
555C2×D5—42no—
556C2×D5—42no—
557C2×D5—84no—
558C4×C5—22no—
559C4×C5—42no—
560C4×C5—42no—
561C4×C5#53212yes—
562C4×C5C2×AGL(1,ℤ/8)14yes—
563C4×C5C22×#4111yescharacteristic
564C4×C5C22×#4111yescharacteristic
565Dic5—22no—
566Dic5—22no—
567Dic5—22no—
568Dic5—42no—
569Dic5—42no—
570Dic5—42no—
571C24—21no—
572C24—21no—
573C24—51no—
574C24—101no—
575#41—2032no—
576C2×Q8—52no—
577C2×Q8—104no—
578C2×Q8—101no—
579C2×Q8—102no—
580C2×Q8—102no—
581C2×Q8—204no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—52no—
589C2×D4—104no—
590C2×D4—104no—
591C2×D4—104no—
592C2×D4—104no—
593C2×D4—104no—
594C2×D4—102no—
595C2×D4—101no—
596C2×D4—102no—
597C2×D4—204no—
598C2×D4—204no—
599C2×D4—204no—
600C2×D4—204no—
601C2×D4—204no—
602C2×D4C23×D512yes—
603C2×D4C23×D512yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—54no—
614C22×C4—52no—
615C22×C4—52no—
616C22×C4—54no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—104no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—104no—
624C22×C4—202no—
625C22×C4—204no—
626C22×C4D4×D511yescharacteristic
627C22×C4D4×D511yescharacteristic
628C22×C4C23×D511yescharacteristic
629SD16—108no—
630SD16—108no—
631D8—28no—
632D8—108no—
633M16—108no—
634M16—108no—
635C2×C8—22no—
636C2×C8—54no—
637C2×C8—52no—
638C2×C8—52no—
639C2×C8—102no—
640C2×C8#70914yescomplemented
641C2×C8C23×D512yes—
642C2×C8C23×D512yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—52no—
646C4⋊C4—52no—
647C4⋊C4—104no—
648C4⋊C4—104no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—101no—
652C4⋊C4—101no—
653C4⋊C4—104no—
654C4⋊C4C23×D512yes—
655C4⋊C4C23×D512yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—104no—
659C22⋊C4—104no—
660C22⋊C4—104no—
661C22⋊C4—104no—
662C22⋊C4—104no—
663C22⋊C4—104no—
664C22⋊C4—104no—
665C42—54no—
666C42—54no—
667C42—52no—
668C42—52no—
669C42—104no—
670C42D4×D512yes—
671C42C23×D512yes—
672C2×C5—82no—
673C2×C5—82no—
674C2×C5#317114yescomplemented
675C2×C5C2×#53211yescharacteristic
676C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
677C2×C5C2×#57511yescharacteristic
678D5—42no—
679D5—82no—
680C23—22no—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—52no—
689C23—102no—
690C23—102no—
691C23—102no—
692C23—102no—
693C23—202no—
694C23—202no—
695C23—202no—
696C23C2×D4×D511yescharacteristic
697Q8—102no—
698Q8—102no—
699Q8—208no—
700Q8—202no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—42no—
706D4—42no—
707D4—102no—
708D4—102no—
709D4—208no—
710D4—208no—
711D4—208no—
712D4—208no—
713D4—208no—
714D4—202no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—108no—
729C2×C4—104no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—204no—
736C2×C4—202no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—208no—
740C2×C4#405714yes—
741C2×C4C2×#70912yes—
742C2×C4C2×D4×D512yes—
743C2×C4C2×D4×D512yes—
744C2×C4C2×D4×D511yescharacteristic
745C2×C4D5×#4112yes—
746C2×C4C24×D511yescharacteristic
747C8—22no—
748C8—54no—
749C8—102no—
750C8C2×#70914yescomplemented
751C5C2×#317111yescharacteristic, complemented, Sylow
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—84no—
759C22—84no—
760C22—102no—
761C22—102no—
762C22—102no—
763C22—204no—
764C22—202no—
765C22—202no—
766C22—202no—
767C22—404no—
768C22#6588212yes—
769C22C2×#405712yes—
770C22#6610212yes—
771C22C22×D4×D511yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—102no—
776C4—102no—
777C4—102no—
778C4—202no—
779C4—202no—
780C4—202no—
781C4#6588212yes—
782C4C2×#405714yes—
783C4C22×#70911yescharacteristic
784C4C2×D5×#4111yescharacteristic
785C2—82no—
786C2—82no—
787C2—202no—
788C2—402no—
789C2#1061133014yesdirect product factor
790C2C2×#6588211yescharacteristic
791C2C22×#405711yescharacteristic
792C2C2×#6610211yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×D8C2
socleC23×C5C22×D4
hypercenterC2×C4×D8D5
hypocenterC5C2×#3171
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#65882C2semidirect
2. C2×#65891C2semidirect
3. C2×C4×C5×D8C2semidirect
4. C2×#65448C2semidirect
5. C2×#65443C2semidirect
6. C2×C4×#687C2semidirect
7. C2×C4×#686C2semidirect
8. #10611330C2direct (N × H)
9. C2×#65175C2semidirect
10. C2×#65165C2semidirect
11. C2×#65071C2semidirect
12. C2×#65069C2semidirect
13. C2×#65053C2semidirect
14. C2×#65054C2semidirect
15. C2×C4×#677C2semidirect
16. C2×C4×#676C2semidirect
34. #65891C22semidirect
36. #65882C22semidirect
48. C4×C5×D8C22semidirect
55. #65448C22semidirect
56. #65443C22semidirect
62. C4×#687C22semidirect
63. C4×#686C22semidirect
69. #65175C22semidirect
70. #65165C22semidirect
71. #65071C22semidirect
72. #65069C22semidirect
73. #65054C22semidirect
74. #65053C22semidirect
75. C4×#677C22semidirect
76. C4×#676C22semidirect
198. C2×C4×D8D5semidirect
260. C2×C5×C8#41semidirect
295. C2×#168#41semidirect
343. C4×D8C2×D5semidirect
429. C5×C8C2×#41semidirect
431. #168C2×#41semidirect
640. C2×C8#709semidirect
674. C2×C5#3171semidirect
750. C8C2×#709semidirect
751. C5C2×#3171semidirect
789. C2#10611330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658822
C2×#658912
C2×C4×C5×D82
C2×#654482
C2×#654432
C2×C4×#6872
C2×C4×#6862
#106113302
C2×#651752
C2×#651652
C2×#650712
C2×#650692
C2×#650532
C2×#650542
C2×C4×#6772
C2×C4×#6762
C2×#31715