Finite Group Databasebeta

← C2×#10611244 #12975892

Subgroups — C2×#10611244 #12975892

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65877C211yesmaximal, characteristic, complemented
2C2×#65886C211yesmaximal, characteristic
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65426C211yesmaximal, characteristic, complemented
5C2×#65422C211yesmaximal, characteristic, complemented
6C22×#3948C211yesmaximal, characteristic, complemented
7C2×#65403C211yesmaximal, characteristic, complemented
8#10611244C2116yesmaximal, direct product factor
9C2×#65140C211yesmaximal, characteristic, complemented
10C2×#65134C211yesmaximal, characteristic, complemented
11C2×#65028C211yesmaximal, characteristic, complemented
12C2×#65022C211yesmaximal, characteristic, complemented
13C2×#65024C211yesmaximal, characteristic, complemented
14C2×#65010C211yesmaximal, characteristic, complemented
15C2×#65005C211yesmaximal, characteristic, complemented
16C2×#65003C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4085—21no—
23C2×D4×Dic5—21no—
24C2×#4076C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C2×#4070C2211yescharacteristic
28C2×#4070C2211yescharacteristic
29C2×#4070C2211yescharacteristic
30C22×Dic20C2211yescharacteristic
31C22×Dic20C2211yescharacteristic
32C22×#677C2211yescharacteristic
33#65886—24no—
34#65886C2218yes—
35#65877—24no—
36#65877C2218yescomplemented
37C2×#4042—21no—
38C2×#4036—21no—
39C2×#4031—21no—
40C2×#4027—21no—
41C2×#4024—21no—
42C2×#4024—21no—
43C2×#4021C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#435C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×C5×#97C2211yescharacteristic
52#65426C2218yescomplemented
53#65422C2218yescomplemented
54#65403C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3948C2211yescharacteristic
67C2×#3948C2211yescharacteristic
68C2×#3948C2218yescomplemented
69#65140C2218yescomplemented
70#65134C2218yescomplemented
71#65028C2218yescomplemented
72#65024C2218yescomplemented
73#65022C2218yescomplemented
74#65010C2218yescomplemented
75#65005C2218yescomplemented
76#65003C2218yescomplemented
77C2×#3316—51nomaximal, Sylow
78C22×C5×D4D411yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C23×Dic5—21no—
85C23×Dic5—21no—
86C2×#709—22no—
87C2×#709—24no—
88C2×#709—42no—
89C2×#709C2314yes—
90C22×D20C2311yescharacteristic
91C22×C4×D5—21no—
92C22×Dic10—24no—
93C22×Dic10—21no—
94C22×Dic10—22no—
95C22×Dic10—21no—
96C22×Dic10—42no—
97C22×Dic10C2311yescharacteristic
98C22×Dic10C2311yescharacteristic
99C22×Dic10C2314yes—
100C22×Dic10C2311yescharacteristic
101C2×C5×M16—42no—
102C2×C5×M16C2314yes—
103C22×C5×C8—42no—
104C22×C5×C8C2311yescharacteristic
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2314yes—
109C4×C5×D4D414yes—
110C4×C5×D4C2314yes—
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C5×C22⋊C4D411yescharacteristic
114C2×C42×C5C2311yescharacteristic
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118#4085—28no—
119D4×Dic5—28no—
120#4076—22no—
121#4076C2314yes—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—22no—
129C2×C4⋊Dic5—22no—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2314yes—
136#4070—22no—
137#4070—22no—
138#4070—22no—
139#4070C2314yes—
140#4070C2314yes—
141#4070C2314yes—
142C2×#683—21no—
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C2×Dic20—24no—
150C2×Dic20—42no—
151C2×Dic20C2314yes—
152C2×Dic20C2314yes—
153C2×#677—42no—
154C2×#677C2314yes—
155#4042—28no—
156#4036—28no—
157#4031—28no—
158#4027—28no—
159#4024—28no—
160#4024—28no—
161#4021—22no—
162#4021C2314yes—
163#4015—22no—
164#4015C2314yes—
165C4×Dic10—22no—
166C4×Dic10—22no—
167C4×Dic10C2314yes—
168C4×Dic10C2314yes—
169C5×C4⋊C8C2314yes—
170C5×C22⋊C8C2314yes—
171C5×C22⋊C8C2314yes—
172C5×#97C2314yes—
173#3953C2314yes—
174#3953C2314yes—
175#3953C2314yes—
176#3949C2314yes—
177#3949C2314yes—
178#3949C2314yes—
179#3948C2314yes—
180#3948C2314yes—
181#3948C2314yes—
182#3948C2314yes—
183#3948C2314yes—
184#3948C2314yes—
185#3948C2314yes—
186C2×#554—51no—
187C2×#548—51no—
188#3316—516no—
189C2×#489—51no—
190C2×#481—51no—
191C2×#483—51no—
192C2×#475—51no—
193C2×#470—51no—
194C2×#465—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#451—51no—
198C2×#441—51no—
199C2×#435D511yescharacteristic, complemented
200C2×#417—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C2×C5×D4—24no—
206C2×C5×D4C2×D414yes—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2411yescharacteristic
220C2×C22⋊D5—24no—
221C2×C22⋊D5—24no—
222C2×C22⋊D5—44no—
223C2×C22⋊D5—44no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—24no—
231C22×Dic5—21no—
232C22×Dic5—24no—
233C22×Dic5—24no—
234C22×Dic5—44no—
235C22×Dic5—82no—
236C22×Dic5—82no—
237#709—28no—
238#709—44no—
239#709—48no—
240C2×D20—22no—
241C2×D20—22no—
242C2×D20—21no—
243C2×D20C2412yes—
244C2×C4×D5—24no—
245C2×C4×D5—44no—
246C2×Dic10—21no—
247C2×Dic10—22no—
248C2×Dic10—22no—
249C2×Dic10—22no—
250C2×Dic10—22no—
251C2×Dic10—22no—
252C2×Dic10—28no—
253C2×Dic10—21no—
254C2×Dic10—24no—
255C2×Dic10—21no—
256C2×Dic10—24no—
257C2×Dic10—44no—
258C2×Dic10—48no—
259C2×Dic10—44no—
260C2×Dic10—82no—
261C2×Dic10#4114yes—
262C2×Dic10C2412yes—
263C2×Dic10C2412yes—
264C2×Dic10C2412yes—
265C5×M16—44no—
266C2×C5×C8—22no—
267C2×C5×C8—22no—
268C2×C5×C8—22no—
269C2×C5×C8—22no—
270C2×C5×C8—44no—
271C2×C5×C8C2412yes—
272C2×C5×C8C2412yes—
273C2×C5×C8C2412yes—
274C2×C5×C8C2412yes—
275C5×C4⋊C4C2×D414yes—
276C5×C22⋊C4C2×D414yes—
277C5×C22⋊C4C2×D414yes—
278C42×C5C2×D412yes—
279C42×C5C2412yes—
280C22⋊Dic5—24no—
281C22⋊Dic5—24no—
282C22⋊Dic5—24no—
283#685—24no—
284#685—24no—
285#685—24no—
286C4⋊Dic5—21no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—24no—
291C4⋊Dic5—24no—
292C4⋊Dic5—24no—
293C4⋊Dic5C2412yes—
294C4⋊Dic5C2412yes—
295C4⋊Dic5C2412yes—
296C4⋊Dic5C2412yes—
297#683—24no—
298#683—24no—
299#683—24no—
300#683—24no—
301#683—24no—
302C4×Dic5—24no—
303C4×Dic5—24no—
304Dic20—28no—
305Dic20—44no—
306#677—44no—
307C22×#41—51no—
308C23×Q8—51no—
309C22×Q16—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×M16C2×D511yescharacteristic
313C23×C8C2×D511yescharacteristic
314#554—58no—
315#554—104no—
316#548—58no—
317#548—104no—
318C2×C4⋊Q8—51no—
319C2×#125—101no—
320C2×#124—51no—
321C2×#124—101no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—51no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C22⋊Q8—101no—
328C2×#121—51no—
329C2×#121—101no—
330C2×C4×Q8—51no—
331C2×C4×Q8—51no—
332C2×C4×D4—101no—
333C2×C4×D4—101no—
334C2×C4×D4C2×D511yescharacteristic
335C22×C4⋊C4—51no—
336C22×C4⋊C4—51no—
337#489—58no—
338#483—58no—
339#481—58no—
340#475—58no—
341#470—58no—
342#465—58no—
343#464—58no—
344#452—58no—
345#451—58no—
346#441—58no—
347#435C2×D518yescomplemented
348C2×#106—51no—
349C2×#106—51no—
350C2×#106—51no—
351C2×C4⋊C8C2×D511yescharacteristic
352#417—58no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—58no—
360C2×#103—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×C22⋊C8C2×D511yescharacteristic
365C2×C22⋊C8C2×D511yescharacteristic
366C2×#97C2×D511yescharacteristic
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5#13714yes—
373C23×C5C22×D412yes—
374C23×C5C22×D412yes—
375C23×C5C22×D411yescharacteristic
376C22×D5—22no—
377C22×D5—42no—
378C22×D5—42no—
379C22×D5—42no—
380C5×D4—28no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—24no—
386C2×C4×C5—24no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D412yes—
393C2×C4×C5C22×D412yes—
394C2×C4×C5C22×D412yes—
395C2×C4×C5C22×D411yescharacteristic
396C2×C4×C5C2×#4112yes—
397C2×C4×C5H(5,𝔽2)12yes—
398C2×C4×C5C2511yescharacteristic
399C22⋊D5—48no—
400C22⋊D5—48no—
401C2×Dic5—24no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—48no—
410C2×Dic5—42no—
411C2×Dic5—42no—
412C2×Dic5—42no—
413C2×Dic5—42no—
414C2×Dic5—42no—
415C2×Dic5—42no—
416C2×Dic5—84no—
417C2×Dic5—84no—
418D20—22no—
419D20—22no—
420D20—42no—
421C4×D5—48no—
422Dic10—24no—
423Dic10—22no—
424Dic10—22no—
425Dic10—22no—
426Dic10—22no—
427Dic10—22no—
428Dic10—48no—
429Dic10—42no—
430Dic10—42no—
431Dic10—84no—
432Dic10C2×#4114yes—
433C5×C8—22no—
434C5×C8—22no—
435C5×C8—22no—
436C5×C8—22no—
437C2×#41—54no—
438C2×#41—104no—
439C2×#41—102no—
440C2×#41—202no—
441C22×Q8—51no—
442C22×Q8—51no—
443C22×Q8—51no—
444C22×Q8—54no—
445C22×Q8—104no—
446C22×Q8—101no—
447C22×Q8—102no—
448C22×Q8—101no—
449C22×Q8—202no—
450C22×D4—51no—
451C22×D4—101no—
452C22×D4—101no—
453C22×D4D2011yescharacteristic
454C23×C4—101no—
455C23×C4—101no—
456C23×C4—101no—
457C23×C4—101no—
458C23×C4C22×D511yescharacteristic
459C23×C4C22×D511yescharacteristic
460C2×Q16—54no—
461C2×Q16—54no—
462C2×Q16—104no—
463C2×Q16—202no—
464C2×SD16—54no—
465C2×SD16—202no—
466C2×M16—42no—
467C2×M16C22×D514yes—
468C22×C8—42no—
469C22×C8C22×D511yescharacteristic
470C22×C8C22×D511yescharacteristic
471C22×C8C22×D511yescharacteristic
472C22×C8C22×D511yescharacteristic
473C22×C8C22×D514yes—
474C4⋊Q8—54no—
475C4⋊Q8—102no—
476#125—108no—
477#124—54no—
478#124—108no—
479#124—102no—
480C22⋊Q8—54no—
481C22⋊Q8—54no—
482C22⋊Q8—54no—
483C22⋊Q8—102no—
484C22⋊Q8—102no—
485C22⋊Q8—102no—
486C22⋊Q8—108no—
487C22⋊Q8—108no—
488C22⋊Q8—108no—
489#121—54no—
490#121—108no—
491#121—102no—
492C4×Q8—54no—
493C4×Q8—54no—
494C4×Q8—102no—
495C4×Q8—102no—
496C4×D4—108no—
497C4×D4—108no—
498C4×D4D2014yes—
499C4×D4C22×D514yes—
500C2×C4⋊C4—51no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—51no—
503C2×C4⋊C4—54no—
504C2×C4⋊C4—54no—
505C2×C4⋊C4—51no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—102no—
509C2×C4⋊C4—102no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4D2011yescharacteristic
517C2×C22⋊C4—101no—
518C2×C22⋊C4—101no—
519C2×C22⋊C4—101no—
520C2×C22⋊C4—101no—
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4D2011yescharacteristic
524C2×C22⋊C4D2011yescharacteristic
525C2×C42—101no—
526C2×C42—101no—
527C2×C42C22×D511yescharacteristic
528#106—54no—
529#106—54no—
530#106—54no—
531C4⋊C8C22×D514yes—
532#103—54no—
533#103—54no—
534#103—54no—
535#103—54no—
536#103—54no—
537#103—54no—
538#103—54no—
539#102—54no—
540#102—54no—
541#102—54no—
542C22⋊C8C22×D514yes—
543C22⋊C8C22×D514yes—
544#97C22×D514yes—
545C22×C5—22no—
546C22×C5—28no—
547C22×C5—22no—
548C22×C5—22no—
549C22×C5—22no—
550C22×C5—22no—
551C22×C5—44no—
552C22×C5#54612yes—
553C22×C5C2×#13714yes—
554C22×C5C2×#13712yes—
555C22×C5#57712yes—
556C22×C5C23×D411yescharacteristic
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—84no—
561C4×C5—22no—
562C4×C5—22no—
563C4×C5—22no—
564C4×C5—22no—
565C4×C5#54612yes—
566C4×C5C22×#4111yescharacteristic
567C4×C5C2×H(5,𝔽2)11yescharacteristic
568Dic5—24no—
569Dic5—42no—
570Dic5—42no—
571Dic5—42no—
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575C24—101no—
576C24C2×D2011yescharacteristic
577C24C2×D2011yescharacteristic
578#41—108no—
579#41—204no—
580#41—208no—
581C2×Q8—54no—
582C2×Q8—52no—
583C2×Q8—52no—
584C2×Q8—52no—
585C2×Q8—108no—
586C2×Q8—101no—
587C2×Q8—101no—
588C2×Q8—104no—
589C2×Q8—101no—
590C2×Q8—104no—
591C2×Q8—102no—
592C2×Q8—102no—
593C2×Q8—102no—
594C2×Q8—102no—
595C2×Q8—102no—
596C2×Q8—204no—
597C2×Q8—204no—
598C2×Q8—208no—
599C2×Q8—402no—
600C2×D4—24no—
601C2×D4—52no—
602C2×D4—104no—
603C2×D4—104no—
604C2×D4—101no—
605C2×D4—102no—
606C2×D4—102no—
607C2×D4—204no—
608C2×D4—204no—
609C2×D4C2×D2014yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—101no—
615C22×C4—104no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—104no—
623C22×C4—104no—
624C22×C4—104no—
625C22×C4—204no—
626C22×C4—204no—
627C22×C4—402no—
628C22×C4—402no—
629C22×C4C2×D2012yes—
630C22×C4C2×D2012yes—
631C22×C4C2×D2011yescharacteristic
632C22×C4C2×D2011yescharacteristic
633C22×C4C2×D2011yescharacteristic
634C22×C4C2×D2011yescharacteristic
635C22×C4C23×D512yes—
636C22×C4C23×D512yes—
637C22×C4C23×D511yescharacteristic
638Q16—108no—
639Q16—204no—
640SD16—204no—
641M16—44no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—44no—
647C2×C8C23×D512yes—
648C2×C8C23×D512yes—
649C2×C8C23×D512yes—
650C2×C8C23×D512yes—
651C4⋊C4—52no—
652C4⋊C4—52no—
653C4⋊C4—52no—
654C4⋊C4—52no—
655C4⋊C4—101no—
656C4⋊C4—104no—
657C4⋊C4—104no—
658C4⋊C4—101no—
659C4⋊C4—101no—
660C4⋊C4—101no—
661C4⋊C4—104no—
662C4⋊C4—104no—
663C4⋊C4—104no—
664C4⋊C4—104no—
665C4⋊C4—104no—
666C4⋊C4—104no—
667C4⋊C4C2×D2014yes—
668C22⋊C4—104no—
669C22⋊C4—104no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C22⋊C4—104no—
674C22⋊C4C2×D2014yes—
675C22⋊C4C2×D2014yes—
676C42—104no—
677C42—104no—
678C42C2×D2012yes—
679C42C23×D512yes—
680C2×C5—24no—
681C2×C5—42no—
682C2×C5#331614yescomplemented
683C2×C5C2×#54611yescharacteristic
684C2×C5C22×#13711yescharacteristic
685C2×C5C2×#57711yescharacteristic
686D5—82no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—102no—
693C23—202no—
694C23—202no—
695C23—202no—
696C23#405514yes—
697C23C22×D2012yes—
698C23C22×D2012yes—
699C23C22×D2011yescharacteristic
700Q8—54no—
701Q8—104no—
702Q8—102no—
703Q8—102no—
704Q8—102no—
705Q8—102no—
706Q8—102no—
707Q8—208no—
708Q8—202no—
709Q8—202no—
710Q8—404no—
711D4—28no—
712D4—102no—
713D4—102no—
714D4—208no—
715D4—208no—
716D4—202no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—104no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—208no—
736C2×C4—208no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—404no—
744C2×C4—404no—
745C2×C4C22×D2012yes—
746C2×C4C22×D2012yes—
747C2×C4C22×D2012yes—
748C2×C4C22×D2012yes—
749C2×C4C22×D2011yescharacteristic
750C2×C4#414412yes—
751C2×C4D5×#4112yes—
752C2×C4C24×D511yescharacteristic
753C8—22no—
754C8—22no—
755C8—22no—
756C8—22no—
757C5C2×#331611yescharacteristic, complemented, Sylow
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—202no—
766C22—202no—
767C22—202no—
768C22—404no—
769C22#6588812yes—
770C22C2×#405514yes—
771C22C2×#405512yes—
772C22#6608512yes—
773C22C23×D2011yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—104no—
779C4—202no—
780C4—202no—
781C4—202no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4#6588812yes—
786C4C2×#414411yescharacteristic
787C4C2×D5×#4111yescharacteristic
788C2—24no—
789C2—42no—
790C2—402no—
791C2#1061124414yesdirect product factor
792C2C2×#6588811yescharacteristic
793C2C22×#405511yescharacteristic
794C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
prime radicalC2×#65886C2
hypercenterC2×#435D5
hypocenterC5C2×#3316
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#65877C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65426C2semidirect
5. C2×#65422C2semidirect
6. C22×#3948C2semidirect
7. C2×#65403C2semidirect
8. #10611244C2direct (N × H)
9. C2×#65140C2semidirect
10. C2×#65134C2semidirect
11. C2×#65028C2semidirect
12. C2×#65022C2semidirect
13. C2×#65024C2semidirect
14. C2×#65010C2semidirect
15. C2×#65005C2semidirect
16. C2×#65003C2semidirect
36. #65877C22semidirect
47. C5×#435C22semidirect
52. #65426C22semidirect
53. #65422C22semidirect
54. #65403C22semidirect
68. C2×#3948C22semidirect
69. #65140C22semidirect
70. #65134C22semidirect
71. #65028C22semidirect
72. #65024C22semidirect
73. #65022C22semidirect
74. #65010C22semidirect
75. #65005C22semidirect
76. #65003C22semidirect
199. C2×#435D5semidirect
347. #435C2×D5semidirect
682. C2×C5#3316semidirect
757. C5C2×#3316semidirect
791. C2#10611244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658772
C2×#658862
C2×C5×#4352
C2×#654262
C2×#654222
C22×#39482
C2×#654032
#106112442
C2×#651402
C2×#651342
C2×#650282
C2×#650222
C2×#650242
C2×#650102
C2×#650052
C2×#650032
C2×#33165