Finite Group Databasebeta

← C2×#10612924 #12976110

Subgroups — C2×#10612924 #12976110

Order 1280.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66028C211yesmaximal, characteristic, complemented
2C2×#65888C211yesmaximal, characteristic
3C2×C5×#478C211yesmaximal, characteristic, complemented
4C2×#65357C211yesmaximal, characteristic, complemented
5C2×C4×#687C211yesmaximal, characteristic, complemented
6#10612924C2116yesmaximal, direct product factor
7C2×#65177C211yesmaximal, characteristic, complemented
8C2×#65175C211yesmaximal, characteristic, complemented
9C2×#65152C211yesmaximal, characteristic, complemented
10C2×#65157C211yesmaximal, characteristic, complemented
11C2×#65134C211yesmaximal, characteristic, complemented
12C2×#65127C211yesmaximal, characteristic, complemented
13C2×#65072C211yesmaximal, characteristic, complemented
14C2×#65065C211yesmaximal, characteristic, complemented
15C2×#65060C211yesmaximal, characteristic, complemented
16C2×#65059C211yesmaximal, characteristic, complemented
17C22×#711C2211yescharacteristic
18C22×D4×D5C2211yescharacteristic
19C2×C5×#125C2211yescharacteristic, complemented
20C2×C4×C5×D4C2211yescharacteristic
21C22×#687C2211yescharacteristic
22C2×#4076—21no—
23C22×#685—21no—
24C22×Dic20C2211yescharacteristic, complemented
25C22×#677C2211yescharacteristic
26C22×#676C2211yescharacteristic
27C22×#676C2211yescharacteristic, complemented
28#66028—24no—
29#66028C2218yescomplemented
30#65888—24no—
31#65888C2218yes—
32C2×#4044—21no—
33C2×#4043C2211yescharacteristic
34C2×#4043C2211yescharacteristic
35C2×#4043C2211yescharacteristic, complemented
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4038—21no—
39C2×#4038C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic, complemented
41C2×#4036—21no—
42C2×#4032—21no—
43C2×#4028—21no—
44C2×#4021C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic, complemented
47C5×#478C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#106C2211yescharacteristic, complemented
50C2×C5×C4⋊C8C2211yescharacteristic, complemented
51C2×C5×#102C2211yescharacteristic
52C2×C5×#102C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3953C2211yescharacteristic
55C2×#3952C2211yescharacteristic
56C2×#3952C2211yescharacteristic, complemented
57C2×#3948C2211yescharacteristic, complemented
58#65357C2218yescomplemented
59C4×#687C2218yescomplemented
60C2×#3942C2211yescharacteristic, complemented
61C2×#3942C2211yescharacteristic, complemented
62C2×#3942C2211yescharacteristic, complemented
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic, complemented
66C2×C4×#168C2211yescharacteristic, complemented
67#65177C2218yescomplemented
68#65175C2218yescomplemented
69#65157C2218yescomplemented
70#65152C2218yescomplemented
71#65134C2218yescomplemented
72#65127C2218yescomplemented
73#65072C2218yescomplemented
74#65065C2218yescomplemented
75#65060C2218yescomplemented
76#65059C2218yescomplemented
77C2×#3323—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C2×#711—24no—
85C2×#711—22no—
86C2×#711—42no—
87C2×#711C2314yes—
88C2×D4×D5—24no—
89C2×D4×D5—22no—
90C2×D4×D5—42no—
91C2×D4×D5C2314yes—
92C22×D20—21no—
93C22×D20D411yescharacteristic
94C22×D20C2311yescharacteristic
95C22×C4×D5—21no—
96C22×C4×D5C2311yescharacteristic
97C22×C4×D5C2311yescharacteristic
98C22×Dic10C2311yescharacteristic
99C22×Dic10C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C22×C5×C8C2311yescharacteristic
102C5×#125—22no—
103C5×#125C2314yescomplemented
104C4×C5×D4—22no—
105C4×C5×D4C2314yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C22⋊C4—21no—
112C2×C42×C5C2311yescharacteristic
113C2×#687—24no—
114C2×#687C2314yes—
115#4076—28no—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685—21no—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—28no—
124C2×#685D411yescharacteristic
125C2×#685D411yescharacteristic
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5D411yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×#683—21no—
132C2×#683—21no—
133C2×C4×Dic5—21no—
134C2×C4×Dic5—21no—
135C22×#168C2311yescharacteristic
136C22×#168C2311yescharacteristic
137C2×Dic20—42no—
138C2×Dic20C2314yescomplemented
139C2×#677—42no—
140C2×#677C2314yes—
141C2×#676—42no—
142C2×#676—42no—
143C2×#676C2314yes—
144C2×#676C2314yescomplemented
145#4044—28no—
146#4043—22no—
147#4043—22no—
148#4043—22no—
149#4043C2314yes—
150#4043C2314yes—
151#4043C2314yescomplemented
152#4041—22no—
153#4041C2314yes—
154#4040—28no—
155#4038—22no—
156#4038—28no—
157#4038C2314yes—
158D5×C4⋊C4—22no—
159D5×C4⋊C4C2314yescomplemented
160#4036—28no—
161#4032—28no—
162#4028—28no—
163#4021—22no—
164#4021C2314yes—
165C4×D20D414yes—
166C4×D20C2314yes—
167C4×Dic10—22no—
168C4×Dic10C2314yescomplemented
169C5×#107C2314yescomplemented
170C5×#106C2314yescomplemented
171C5×C4⋊C8C2314yescomplemented
172C5×#102C2314yes—
173C5×#102C2314yes—
174#3964C2314yes—
175#3953C2314yes—
176#3952C2314yes—
177#3952C2314yescomplemented
178#3948C2314yescomplemented
179#3942C2314yescomplemented
180#3942C2314yescomplemented
181#3942C2314yescomplemented
182#3941C2314yes—
183#3941C2314yes—
184#3940C2314yescomplemented
185C4×#168C2314yescomplemented
186C2×#552—51no—
187C2×#546—51no—
188#3323—516no—
189C2×#488—51no—
190C2×#481—51no—
191C2×#485—51no—
192C2×#478D511yescharacteristic, complemented
193C2×#470—51no—
194C2×#468—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#450—51no—
198C2×C4×SD16—51no—
199C2×#436—51no—
200C2×#417—51no—
201C2×#418—51no—
202C24×C5—21no—
203C23×D5—21no—
204C23×D5—24no—
205C23×D5—44no—
206C23×D5—44no—
207C23×D5—82no—
208C23×D5C2×D411yescharacteristic
209C23×D5C2×D411yescharacteristic
210C2×C5×D4—21no—
211C2×C5×D4—22no—
212C2×C5×D4#4114yes—
213C2×C5×D4C2412yes—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—24no—
218C22×C4×C5—82no—
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2411yescharacteristic
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—44no—
225C2×C22⋊D5—44no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—24no—
230C22×Dic5—44no—
231C22×Dic5C2×D411yescharacteristic
232C22×Dic5C2×D411yescharacteristic
233#711—28no—
234#711—44no—
235#711—48no—
236D4×D5—28no—
237D4×D5—44no—
238D4×D5—48no—
239C2×D20—22no—
240C2×D20—22no—
241C2×D20—21no—
242C2×D20—24no—
243C2×D20—42no—
244C2×D20—82no—
245C2×D20C2×D414yes—
246C2×D20C2412yes—
247C2×C4×D5—22no—
248C2×C4×D5—22no—
249C2×C4×D5—22no—
250C2×C4×D5—22no—
251C2×C4×D5—24no—
252C2×C4×D5—44no—
253C2×C4×D5C2×D412yes—
254C2×C4×D5C2×D412yes—
255C2×C4×D5C2412yes—
256C2×C4×D5C2412yes—
257C2×Dic10—22no—
258C2×Dic10—22no—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—21no—
262C2×Dic10—21no—
263C2×Dic10C2412yes—
264C2×Dic10C2412yes—
265C2×C5×C8—22no—
266C2×C5×C8—22no—
267C2×C5×C8C2412yes—
268C2×C5×C8C2412yes—
269C5×C4⋊C4—24no—
270C5×C4⋊C4—24no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4C2412yes—
275C5×C4⋊C4C2412yes—
276C5×C4⋊C4C2412yes—
277C5×C22⋊C4—24no—
278C42×C5C2×D412yes—
279C42×C5C2412yes—
280#687—28no—
281#685—24no—
282#685—24no—
283#685—24no—
284#685—24no—
285#685—24no—
286#685—24no—
287#685—24no—
288#685C2×D414yes—
289#685C2×D414yes—
290C4⋊Dic5—21no—
291C4⋊Dic5—24no—
292C4⋊Dic5—24no—
293C4⋊Dic5—24no—
294C4⋊Dic5C2×D414yes—
295C4⋊Dic5C2412yes—
296#683—24no—
297#683—24no—
298C4×Dic5—24no—
299C4×Dic5—24no—
300C2×#168—22no—
301C2×#168—22no—
302C2×#168C2412yes—
303C2×#168C2412yes—
304Dic20—44no—
305#677—44no—
306#676—44no—
307#676—44no—
308C22×#41—51no—
309C23×D4—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×SD16—51no—
313C22×M16—51no—
314C22×M16—51no—
315#552—58no—
316#552—104no—
317#546—58no—
318#546—104no—
319C2×#126—101no—
320C2×#125—101no—
321C2×#125C2×D511yescharacteristic, complemented
322C2×#124—51no—
323C2×#123—101no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×C22⋊Q8—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×#120—101no—
331C2×C4×Q8—51no—
332C2×C4×D4—51no—
333C2×C4×D4C2×D511yescharacteristic
334C2×#117—51no—
335C2×#117—101no—
336C22×C4⋊C4—51no—
337C22×C22⋊C4—101no—
338#488—58no—
339#485—58no—
340#481—58no—
341#478C2×D518yescomplemented
342#470—58no—
343#468—58no—
344#464—58no—
345#452—58no—
346#450—58no—
347C4×SD16—58no—
348#436—58no—
349C2×#107C2×D511yescharacteristic, complemented
350C2×#106—51no—
351C2×#106C2×D511yescharacteristic, complemented
352C2×C4⋊C8C2×D511yescharacteristic, complemented
353#418—58no—
354#417—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102C2×D511yescharacteristic
364C2×#102C2×D511yescharacteristic
365C2×C22⋊C8—51no—
366C2×C22⋊C8—51no—
367C2×C4×C8—51no—
368C23×C5—24no—
369C23×C5—22no—
370C23×C5—42no—
371C23×C5—42no—
372C23×C5C22×D411yescharacteristic
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—48no—
381C22×D5—48no—
382C22×D5—42no—
383C22×D5—42no—
384C22×D5—42no—
385C22×D5—84no—
386C22×D5—816no—
387C22×D5C22×D412yes—
388C22×D5C22×D412yes—
389C5×D4—24no—
390C5×D4—22no—
391C5×D4C2×#4114yes—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—42no—
398C2×C4×C5—42no—
399C2×C4×C5—42no—
400C2×C4×C5—84no—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D411yescharacteristic
404C2×C4×C5C2×#4112yes—
405C2×C4×C5H(5,𝔽2)12yes—
406C2×C4×C5C2511yescharacteristic
407C22⋊D5—48no—
408C22⋊D5—48no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—48no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5—42no—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420D20—22no—
421D20—22no—
422D20—44no—
423D20—42no—
424D20—84no—
425C4×D5—24no—
426C4×D5—24no—
427C4×D5—22no—
428C4×D5—22no—
429C4×D5—22no—
430C4×D5—22no—
431C4×D5—48no—
432Dic10—22no—
433Dic10—22no—
434Dic10—22no—
435Dic10—22no—
436Dic10—42no—
437Dic10—42no—
438C5×C8—22no—
439C5×C8—22no—
440#168—22no—
441#168—22no—
442C25—101no—
443C2×#41—54no—
444C2×#41—102no—
445C2×#41—104no—
446C2×#41—202no—
447C22×Q8—51no—
448C22×Q8—51no—
449C22×D4—54no—
450C22×D4—51no—
451C22×D4—51no—
452C22×D4—101no—
453C22×D4—102no—
454C22×D4—101no—
455C22×D4—104no—
456C22×D4—101no—
457C22×D4—202no—
458C22×D4C22×D511yescharacteristic
459C23×C4—21no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—101no—
463C23×C4—101no—
464C2×Q16—54no—
465C2×Q16—202no—
466C2×SD16—54no—
467C2×SD16—54no—
468C2×SD16—104no—
469C2×SD16—202no—
470C2×M16—54no—
471C2×M16—54no—
472C2×M16—202no—
473C2×M16—202no—
474C22×C8—51no—
475C22×C8—51no—
476C22×C8C22×D511yescharacteristic
477C22×C8C22×D511yescharacteristic
478#126—108no—
479#125—22no—
480#125—108no—
481#125C22×D514yescomplemented
482#124—54no—
483#124—102no—
484#123—108no—
485#123—108no—
486C22⋊Q8—54no—
487C22⋊Q8—54no—
488C22⋊Q8—54no—
489C22⋊Q8—102no—
490C22⋊Q8—102no—
491C22⋊Q8—102no—
492#121—54no—
493#121—108no—
494#121—102no—
495#120—108no—
496C4×Q8—54no—
497C4×Q8—102no—
498C4×D4—22no—
499C4×D4—54no—
500C4×D4—54no—
501C4×D4C22×D514yes—
502#117—54no—
503#117—108no—
504#117—102no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—102no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4C22×D511yescharacteristic
517C2×C4⋊C4C22×D511yescharacteristic
518C2×C4⋊C4C22×D511yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—51no—
521C2×C22⋊C4—51no—
522C2×C22⋊C4—108no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C22⋊C4—101no—
528C2×C22⋊C4—101no—
529C2×C22⋊C4—101no—
530C2×C42—101no—
531C2×C42—101no—
532C2×C42C22×D511yescharacteristic
533#107C22×D514yescomplemented
534#106—54no—
535#106C22×D514yescomplemented
536C4⋊C8C22×D514yescomplemented
537#103—54no—
538#103—54no—
539#103—54no—
540#103—54no—
541#102—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102C22×D514yes—
546#102C22×D514yes—
547C22⋊C8—54no—
548C22⋊C8—54no—
549C4×C8—54no—
550C22×C5—24no—
551C22×C5—48no—
552C22×C5—42no—
553C22×C5—42no—
554C22×C5#54612yes—
555C22×C5#57512yes—
556C22×C5#57712yes—
557C22×C5C23×D411yescharacteristic
558C2×D5—22no—
559C2×D5—22no—
560C2×D5—22no—
561C2×D5—22no—
562C2×D5—22no—
563C2×D5—22no—
564C2×D5—44no—
565C2×D5—44no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—816no—
570C2×D5—84no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5#54612yes—
577C4×C5C22×#4111yescharacteristic
578C4×C5C2×H(5,𝔽2)11yescharacteristic
579Dic5—22no—
580Dic5—22no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584C24—21no—
585C24—51no—
586C24—51no—
587C24—104no—
588C24—101no—
589C24—204no—
590C24—204no—
591C24—402no—
592#41—108no—
593#41—204no—
594#41—208no—
595C2×Q8—52no—
596C2×Q8—52no—
597C2×Q8—101no—
598C2×Q8—101no—
599C2×Q8—102no—
600C2×Q8—102no—
601C2×Q8—102no—
602C2×Q8—102no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—54no—
606C2×D4—52no—
607C2×D4—104no—
608C2×D4—104no—
609C2×D4—108no—
610C2×D4—104no—
611C2×D4—101no—
612C2×D4—102no—
613C2×D4—102no—
614C2×D4—202no—
615C2×D4—204no—
616C2×D4—208no—
617C2×D4—204no—
618C2×D4—204no—
619C2×D4—402no—
620C2×D4#71314yes—
621C2×D4C23×D512yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—51no—
627C22×C4—51no—
628C22×C4—52no—
629C22×C4—52no—
630C22×C4—52no—
631C22×C4—52no—
632C22×C4—82no—
633C22×C4—104no—
634C22×C4—104no—
635C22×C4—102no—
636C22×C4—102no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—101no—
640C22×C4—101no—
641C22×C4—101no—
642C22×C4—204no—
643C22×C4—204no—
644C22×C4D4×D511yescharacteristic
645C22×C4D4×D511yescharacteristic
646C22×C4C23×D511yescharacteristic
647Q16—204no—
648SD16—108no—
649SD16—204no—
650M16—204no—
651M16—204no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—52no—
655C2×C8—52no—
656C2×C8—102no—
657C2×C8—102no—
658C2×C8C23×D512yes—
659C2×C8C23×D512yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—54no—
666C4⋊C4—52no—
667C4⋊C4—104no—
668C4⋊C4—104no—
669C4⋊C4—104no—
670C4⋊C4—104no—
671C4⋊C4—101no—
672C4⋊C4—104no—
673C4⋊C4C23×D512yes—
674C4⋊C4C23×D512yes—
675C4⋊C4C23×D512yes—
676C22⋊C4—24no—
677C22⋊C4—54no—
678C22⋊C4—54no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4—104no—
682C22⋊C4—104no—
683C22⋊C4—104no—
684C22⋊C4—104no—
685C22⋊C4—104no—
686C42—104no—
687C42—104no—
688C42D4×D512yes—
689C42C23×D512yes—
690C2×C5—44no—
691C2×C5#332314yescomplemented
692C2×C5C2×#54611yescharacteristic
693C2×C5C2×#57511yescharacteristic
694C2×C5C2×#57711yescharacteristic
695D5—42no—
696D5—42no—
697D5—82no—
698C23—24no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—52no—
703C23—52no—
704C23—102no—
705C23—102no—
706C23—102no—
707C23—102no—
708C23—102no—
709C23—102no—
710C23—102no—
711C23—208no—
712C23—208no—
713C23—202no—
714C23—202no—
715C23—202no—
716C23—404no—
717C23—4016no—
718C23C2×D4×D511yescharacteristic
719Q8—102no—
720Q8—102no—
721Q8—102no—
722Q8—102no—
723Q8—202no—
724Q8—202no—
725D4—24no—
726D4—22no—
727D4—102no—
728D4—102no—
729D4—204no—
730D4—208no—
731D4—208no—
732D4—202no—
733D4—404no—
734D4C2×#71314yes—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—52no—
744C2×C4—52no—
745C2×C4—84no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—104no—
749C2×C4—104no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—208no—
758C2×C4—208no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4C2×D4×D512yes—
763C2×C4C2×D4×D512yes—
764C2×C4C2×D4×D511yescharacteristic
765C2×C4C2×#71312yes—
766C2×C4#414912yes—
767C2×C4C24×D511yescharacteristic
768C8—22no—
769C8—22no—
770C8—102no—
771C8—102no—
772C5C2×#332311yescharacteristic, complemented, Sylow
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—102no—
778C22—102no—
779C22—102no—
780C22—102no—
781C22—102no—
782C22—102no—
783C22—204no—
784C22—204no—
785C22—202no—
786C22—202no—
787C22—202no—
788C22—4016no—
789C22—404no—
790C22#6596412yes—
791C22#6610212yes—
792C22#6610912yes—
793C22C22×D4×D511yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—102no—
800C4—102no—
801C4—202no—
802C4—202no—
803C4—202no—
804C4#6596412yes—
805C4C22×#71311yescharacteristic
806C4C2×#414911yescharacteristic
807C2—44no—
808C2—202no—
809C2—202no—
810C2—402no—
811C2#1061292414yesdirect product factor
812C2C2×#6596411yescharacteristic
813C2C2×#6610211yescharacteristic
814C2C2×#6610911yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#478C2
socleC23×C5C22×D4
prime radicalC2×#65888C2
hypercenterC2×#478D5
hypocenterC5C2×#3323
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#66028C2semidirect
3. C2×C5×#478C2semidirect
4. C2×#65357C2semidirect
5. C2×C4×#687C2semidirect
6. #10612924C2direct (N × H)
7. C2×#65177C2semidirect
8. C2×#65175C2semidirect
9. C2×#65152C2semidirect
10. C2×#65157C2semidirect
11. C2×#65134C2semidirect
12. C2×#65127C2semidirect
13. C2×#65072C2semidirect
14. C2×#65065C2semidirect
15. C2×#65060C2semidirect
16. C2×#65059C2semidirect
19. C2×C5×#125C22semidirect
24. C22×Dic20C22semidirect
27. C22×#676C22semidirect
29. #66028C22semidirect
35. C2×#4043C22semidirect
40. C2×D5×C4⋊C4C22semidirect
46. C2×C4×Dic10C22semidirect
47. C5×#478C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#106C22semidirect
50. C2×C5×C4⋊C8C22semidirect
56. C2×#3952C22semidirect
57. C2×#3948C22semidirect
58. #65357C22semidirect
59. C4×#687C22semidirect
60. C2×#3942C22semidirect
61. C2×#3942C22semidirect
62. C2×#3942C22semidirect
65. C2×#3940C22semidirect
66. C2×C4×#168C22semidirect
67. #65177C22semidirect
68. #65175C22semidirect
69. #65157C22semidirect
70. #65152C22semidirect
71. #65134C22semidirect
72. #65127C22semidirect
73. #65072C22semidirect
74. #65065C22semidirect
75. #65060C22semidirect
76. #65059C22semidirect
103. C5×#125C23semidirect
138. C2×Dic20C23semidirect
144. C2×#676C23semidirect
151. #4043C23semidirect
159. D5×C4⋊C4C23semidirect
168. C4×Dic10C23semidirect
169. C5×#107C23semidirect
170. C5×#106C23semidirect
171. C5×C4⋊C8C23semidirect
177. #3952C23semidirect
178. #3948C23semidirect
179. #3942C23semidirect
180. #3942C23semidirect
181. #3942C23semidirect
184. #3940C23semidirect
185. C4×#168C23semidirect
192. C2×#478D5semidirect
321. C2×#125C2×D5semidirect
341. #478C2×D5semidirect
349. C2×#107C2×D5semidirect
351. C2×#106C2×D5semidirect
352. C2×C4⋊C8C2×D5semidirect
481. #125C22×D5semidirect
533. #107C22×D5semidirect
535. #106C22×D5semidirect
536. C4⋊C8C22×D5semidirect
691. C2×C5#3323semidirect
772. C5C2×#3323semidirect
811. C2#10612924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660282
C2×#658882
C2×C5×#4782
C2×#653572
C2×C4×#6872
#106129242
C2×#651772
C2×#651752
C2×#651522
C2×#651572
C2×#651342
C2×#651272
C2×#650722
C2×#650652
C2×#650602
C2×#650592
C2×#33235