Finite Group Databasebeta

← C2×#10611986 #12975883

Subgroups — C2×#10611986 #12975883

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×#66165C211yesmaximal, characteristic
2C2×#65969C211yesmaximal, characteristic, complemented
3C2×C5×#452C211yesmaximal, characteristic, complemented
4C2×#65521C211yesmaximal, characteristic, complemented
5C2×#65475C211yesmaximal, characteristic, complemented
6C2×#65473C211yesmaximal, characteristic, complemented
7C2×#65460C211yesmaximal, characteristic, complemented
8C2×#65455C211yesmaximal, characteristic, complemented
9C2×#65341C211yesmaximal, characteristic, complemented
10#10611986C2116yesmaximal, direct product factor
11C2×D5×#103C211yesmaximal, characteristic, complemented
12C2×#65080C211yesmaximal, characteristic, complemented
13C2×#65066C211yesmaximal, characteristic, complemented
14C2×#65054C211yesmaximal, characteristic, complemented
15C2×#65017C211yesmaximal, characteristic, complemented
16C2×#65010C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×Q8×D5C2211yescharacteristic
19C22×C5×Q16C2211yescharacteristic
20C22×C5×SD16C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22#66165—24no—
23#66165C2218yes—
24C2×#4092C2211yescharacteristic
25C2×Q8×Dic5C2211yescharacteristic
26C2×Q8×Dic5C2211yescharacteristic
27C22×#689C2211yescharacteristic
28C2×#4084—21no—
29C2×#4084C2211yescharacteristic
30C2×#4082—21no—
31C2×#4082C2211yescharacteristic
32C2×C4×C22⋊D5—21no—
33C2×C4×C22⋊D5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C2×#4070—21no—
36C2×#4070C2211yescharacteristic
37C22×#681C2211yescharacteristic
38C22×C8×D5C2211yescharacteristic
39#65969—24no—
40#65969C2218yescomplemented
41C2×#4043—21no—
42C2×D5×C4⋊C4C2211yescharacteristic
43C2×#4035—21no—
44C2×#4034C2211yescharacteristic
45C2×#4027—21no—
46C2×#4024—21no—
47C5×#452C2218yescomplemented
48C2×C5×#103C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51#65521C2218yescomplemented
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3964C2211yescharacteristic
56C2×#3964C2211yescharacteristic
57#65475C2218yescomplemented
58#65473C2218yescomplemented
59#65460C2218yescomplemented
60#65455C2218yescomplemented
61C2×#3952C2211yescharacteristic
62C2×#3949C2211yescharacteristic
63C2×#3949C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3947C2211yescharacteristic
67C2×#3946C2211yescharacteristic
68#65341C2218yescomplemented
69C2×#3942C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71D5×#103C2218yescomplemented
72#65080C2218yescomplemented
73#65066C2218yescomplemented
74#65054C2218yescomplemented
75#65017C2218yescomplemented
76#65010C2218yescomplemented
77C2×#3316—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—24no—
80C2×C5×#41—42no—
81C2×C5×#41C2314yes—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—21no—
89C22×C22⋊D5D411yescharacteristic
90C23×Dic5—21no—
91C2×Q8×D5—22no—
92C2×Q8×D5—24no—
93C2×Q8×D5—42no—
94C2×Q8×D5C2314yes—
95C22×C4×D5—21no—
96C22×C4×D5—21no—
97C22×C4×D5C2311yescharacteristic
98C22×Dic10—21no—
99C22×Dic10—21no—
100C22×Dic10C2311yescharacteristic
101C2×C5×Q16—24no—
102C2×C5×Q16C2314yes—
103C2×C5×SD16—42no—
104C2×C5×SD16C2314yes—
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8C2314yes—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C22⋊C4—21no—
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5—21no—
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5D411yescharacteristic
117#4092—22no—
118#4092C2314yes—
119Q8×Dic5—22no—
120Q8×Dic5—22no—
121Q8×Dic5C2314yes—
122Q8×Dic5C2314yes—
123C2×#689—42no—
124C2×#689C2314yes—
125#4084—28no—
126#4084—22no—
127#4084C2314yes—
128#4082—28no—
129#4082—22no—
130#4082C2314yes—
131C4×C22⋊D5—28no—
132C4×C22⋊D5D414yes—
133C4×C22⋊D5C2314yes—
134C2×#685—21no—
135C2×#685D411yescharacteristic
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5—22no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2314yes—
144#4070—22no—
145#4070—28no—
146#4070C2314yes—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683—21no—
150C2×#683—21no—
151C2×#683D411yescharacteristic
152C2×C4×Dic5—21no—
153C2×C4×Dic5—21no—
154C2×C4×Dic5C2311yescharacteristic
155C2×#681—42no—
156C2×#681C2314yes—
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C2×C8×D5—42no—
160C2×C8×D5C2314yes—
161#4043—28no—
162D5×C4⋊C4—22no—
163D5×C4⋊C4C2314yes—
164#4035—28no—
165#4034—22no—
166#4034C2314yes—
167#4027—28no—
168#4024—28no—
169C5×#103C2314yes—
170C5×#102C2314yes—
171C5×C22⋊C8C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177#3952C2314yes—
178#3949C2314yes—
179#3949C2314yes—
180#3948C2314yes—
181#3948C2314yes—
182#3947C2314yes—
183#3946C2314yes—
184#3942C2314yes—
185#3940C2314yes—
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×#452D511yescharacteristic, complemented
197C2×#451—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#417—51no—
201C22×#103—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C23×D5C2×D411yescharacteristic
205C5×#41—28no—
206C5×#41—44no—
207C5×#41—48no—
208C2×C5×Q8—21no—
209C2×C5×Q8—21no—
210C2×C5×Q8—22no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8#4114yes—
214C2×C5×Q8C2412yes—
215C2×C5×Q8C2412yes—
216C2×C5×D4—24no—
217C2×C5×D4—21no—
218C2×C5×D4—22no—
219C2×C5×D4—22no—
220C2×C5×D4—44no—
221C2×C5×D4C2412yes—
222C22×C4×C5—21no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—24no—
228C22×C4×C5—44no—
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2411yescharacteristic
233C2×C22⋊D5—24no—
234C2×C22⋊D5—24no—
235C2×C22⋊D5—44no—
236C2×C22⋊D5C2×D414yes—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—24no—
242C22×Dic5—82no—
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245C22×Dic5C2×D411yescharacteristic
246Q8×D5—28no—
247Q8×D5—44no—
248Q8×D5—48no—
249C2×C4×D5—22no—
250C2×C4×D5—22no—
251C2×C4×D5—24no—
252C2×C4×D5—24no—
253C2×C4×D5—44no—
254C2×C4×D5—82no—
255C2×C4×D5C2×D412yes—
256C2×C4×D5C2412yes—
257C2×Dic10—22no—
258C2×Dic10—22no—
259C2×Dic10—21no—
260C2×Dic10—24no—
261C2×Dic10—24no—
262C2×Dic10—44no—
263C2×Dic10—82no—
264C2×Dic10C2412yes—
265C5×Q16—28no—
266C5×SD16—44no—
267C2×C5×C8—22no—
268C2×C5×C8—22no—
269C2×C5×C8C2412yes—
270C2×C5×C8C2412yes—
271C5×C4⋊C4—24no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4C2412yes—
274C5×C22⋊C4—24no—
275C22⋊Dic5—24no—
276C22⋊Dic5—24no—
277C22⋊Dic5—24no—
278C22⋊Dic5—24no—
279C22⋊Dic5C2×D414yes—
280#689—44no—
281#685—24no—
282#685C2×D414yes—
283C4⋊Dic5—21no—
284C4⋊Dic5—24no—
285C4⋊Dic5—21no—
286C4⋊Dic5—21no—
287C4⋊Dic5—24no—
288C4⋊Dic5—24no—
289C4⋊Dic5C2412yes—
290C4⋊Dic5C2412yes—
291C4⋊Dic5C2412yes—
292#683—24no—
293#683—24no—
294#683—24no—
295#683—24no—
296#683C2×D414yes—
297C4×Dic5—24no—
298C4×Dic5—24no—
299C4×Dic5C2×D412yes—
300C4×Dic5C2412yes—
301#681—44no—
302C2×#168—22no—
303C2×#168—22no—
304C2×#168C2412yes—
305C2×#168C2412yes—
306C8×D5—44no—
307C22×#41C2×D511yescharacteristic
308C23×Q8—51no—
309C22×Q16—51no—
310C22×Q16C2×D511yescharacteristic
311C22×SD16C2×D511yescharacteristic
312C22×M16—51no—
313C23×C8—51no—
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—101no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C22⋊Q8C2×D511yescharacteristic
328C2×#121—51no—
329C2×#121—101no—
330C2×C4×Q8—51no—
331C2×C4×Q8—51no—
332C2×C4×D4—51no—
333C2×C4×D4—101no—
334C2×C4×D4—101no—
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#452C2×D518yescomplemented
345#451—58no—
346#441—58no—
347#435—58no—
348C2×#106—51no—
349C2×#106—51no—
350C2×#106—51no—
351C2×C4⋊C8—51no—
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×#103C2×D511yescharacteristic
361C2×#102—51no—
362C2×#102—51no—
363C2×#102C2×D511yescharacteristic
364C2×C22⋊C8—51no—
365C2×C22⋊C8C2×D511yescharacteristic
366C2×#97—51no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—42no—
372C23×C5—42no—
373C23×C5—42no—
374C23×C5C22×D412yes—
375C23×C5C22×D411yescharacteristic
376C22×D5—22no—
377C22×D5—22no—
378C22×D5#13714yes—
379C22×D5C22×D412yes—
380C5×Q8—24no—
381C5×Q8—22no—
382C5×Q8—22no—
383C5×Q8—22no—
384C5×Q8—42no—
385C5×Q8C2×#4114yes—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—48no—
389C5×D4—42no—
390C2×C4×C5—24no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—24no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—48no—
399C2×C4×C5—42no—
400C2×C4×C5—42no—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D411yescharacteristic
403C2×C4×C5C2×#4112yes—
404C2×C4×C5H(5,𝔽2)12yes—
405C2×C4×C5C2511yescharacteristic
406C22⋊D5—28no—
407C22⋊D5—48no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5—42no—
418C2×Dic5—42no—
419C2×Dic5—84no—
420C2×Dic5C22×D412yes—
421C2×Dic5C22×D412yes—
422C2×Dic5C22×D412yes—
423C4×D5—24no—
424C4×D5—22no—
425C4×D5—22no—
426C4×D5—48no—
427C4×D5—84no—
428Dic10—22no—
429Dic10—22no—
430Dic10—48no—
431Dic10—42no—
432Dic10—84no—
433C5×C8—22no—
434C5×C8—22no—
435#168—22no—
436#168—22no—
437C2×#41—22no—
438C2×#41—24no—
439C2×#41—42no—
440C2×#41C22×D514yes—
441C22×Q8—54no—
442C22×Q8—51no—
443C22×Q8—101no—
444C22×Q8—101no—
445C22×Q8—102no—
446C22×Q8—104no—
447C22×Q8—202no—
448C22×Q8C22×D511yescharacteristic
449C22×Q8C22×D511yescharacteristic
450C22×D4—21no—
451C22×D4—51no—
452C22×D4—101no—
453C22×D4C22×D511yescharacteristic
454C23×C4—21no—
455C23×C4—51no—
456C23×C4—101no—
457C23×C4—101no—
458C23×C4—101no—
459C23×C4C22×D511yescharacteristic
460C2×Q16—24no—
461C2×Q16—54no—
462C2×Q16—202no—
463C2×Q16C22×D514yes—
464C2×SD16—42no—
465C2×SD16C22×D514yes—
466C2×M16—54no—
467C2×M16—202no—
468C22×C8—51no—
469C22×C8—51no—
470C22×C8—54no—
471C22×C8—202no—
472C22×C8C22×D511yescharacteristic
473C22×C8C22×D511yescharacteristic
474C4⋊Q8—54no—
475C4⋊Q8—102no—
476#125—108no—
477#124—54no—
478#124—102no—
479#124—108no—
480C22⋊Q8—22no—
481C22⋊Q8—54no—
482C22⋊Q8—54no—
483C22⋊Q8—108no—
484C22⋊Q8—108no—
485C22⋊Q8—108no—
486C22⋊Q8—102no—
487C22⋊Q8—102no—
488C22⋊Q8C22×D514yes—
489#121—54no—
490#121—102no—
491#121—108no—
492C4×Q8—54no—
493C4×Q8—54no—
494C4×Q8—102no—
495C4×Q8—102no—
496C4×D4—54no—
497C4×D4—54no—
498C4×D4—108no—
499C4×D4—108no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—51no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—54no—
505C2×C4⋊C4—51no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—102no—
508C2×C4⋊C4—101no—
509C2×C4⋊C4—101no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—102no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4C22×D511yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—51no—
519C2×C22⋊C4—51no—
520C2×C22⋊C4—101no—
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C42—51no—
526C2×C42—101no—
527C2×C42—101no—
528#106—54no—
529#106—54no—
530#106—54no—
531C4⋊C8—54no—
532#103—54no—
533#103—54no—
534#103—54no—
535#103—54no—
536#103—54no—
537#103—54no—
538#103C22×D514yes—
539#102—54no—
540#102—54no—
541#102C22×D514yes—
542C22⋊C8—54no—
543C22⋊C8C22×D514yes—
544#97—54no—
545C22×C5—22no—
546C22×C5—22no—
547C22×C5—22no—
548C22×C5—44no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—84no—
553C22×C5#54612yes—
554C22×C5C2×#13712yes—
555C22×C5#57712yes—
556C22×C5C23×D411yescharacteristic
557C2×D5—22no—
558C2×D5—28no—
559C2×D5—22no—
560C2×D5C2×#13714yes—
561C4×C5—24no—
562C4×C5—22no—
563C4×C5—42no—
564C4×C5—42no—
565C4×C5#54612yes—
566C4×C5C22×#4111yescharacteristic
567C4×C5C2×H(5,𝔽2)11yescharacteristic
568Dic5—22no—
569Dic5—22no—
570Dic5—22no—
571Dic5—42no—
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575C24—21no—
576C24—51no—
577C24D4×D511yescharacteristic
578#41—28no—
579#41—44no—
580#41—48no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—52no—
587C2×Q8—104no—
588C2×Q8—104no—
589C2×Q8—101no—
590C2×Q8—108no—
591C2×Q8—102no—
592C2×Q8—102no—
593C2×Q8—204no—
594C2×Q8—204no—
595C2×Q8—208no—
596C2×Q8—402no—
597C2×Q8#71114yes—
598C2×Q8C23×D512yes—
599C2×Q8C23×D512yes—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—44no—
605C2×D4—54no—
606C2×D4—104no—
607C2×D4—104no—
608C2×D4—204no—
609C2×D4C23×D512yes—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—51no—
618C22×C4—51no—
619C22×C4—51no—
620C22×C4—52no—
621C22×C4—52no—
622C22×C4—104no—
623C22×C4—104no—
624C22×C4—102no—
625C22×C4—102no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4—101no—
630C22×C4—104no—
631C22×C4—204no—
632C22×C4—402no—
633C22×C4—402no—
634C22×C4D4×D512yes—
635C22×C4D4×D511yescharacteristic
636C22×C4C23×D512yes—
637C22×C4C23×D511yescharacteristic
638Q16—28no—
639Q16—204no—
640SD16—44no—
641M16—204no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—52no—
645C2×C8—52no—
646C2×C8—102no—
647C2×C8—102no—
648C2×C8—204no—
649C2×C8C23×D512yes—
650C2×C8C23×D512yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—54no—
654C4⋊C4—52no—
655C4⋊C4—52no—
656C4⋊C4—52no—
657C4⋊C4—104no—
658C4⋊C4—104no—
659C4⋊C4—104no—
660C4⋊C4—104no—
661C4⋊C4—104no—
662C4⋊C4—101no—
663C4⋊C4—104no—
664C4⋊C4—101no—
665C4⋊C4—101no—
666C4⋊C4—104no—
667C4⋊C4C23×D512yes—
668C22⋊C4—24no—
669C22⋊C4—54no—
670C22⋊C4—54no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C22⋊C4—104no—
674C22⋊C4—104no—
675C22⋊C4—104no—
676C42—52no—
677C42—52no—
678C42—104no—
679C42—104no—
680C2×C5—42no—
681C2×C5—82no—
682C2×C5#331614yescomplemented
683C2×C5C2×#54611yescharacteristic
684C2×C5C22×#13711yescharacteristic
685C2×C5C2×#57711yescharacteristic
686D5—24no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—54no—
695C23—52no—
696C23—102no—
697C23—102no—
698C23C2×D4×D512yes—
699C23C2×D4×D511yescharacteristic
700Q8—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—102no—
706Q8—102no—
707Q8—208no—
708Q8—202no—
709Q8—404no—
710Q8C2×#71114yes—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—42no—
715D4—108no—
716D4—208no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—52no—
729C2×C4—52no—
730C2×C4—52no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—104no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—208no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—404no—
747C2×C4—404no—
748C2×C4C2×D4×D512yes—
749C2×C4C2×D4×D511yescharacteristic
750C2×C4C2×#71112yes—
751C2×C4#414412yes—
752C2×C4C24×D511yescharacteristic
753C8—22no—
754C8—22no—
755C8—102no—
756C8—102no—
757C5C2×#331611yescharacteristic, complemented, Sylow
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—54no—
766C22—84no—
767C22—108no—
768C22—102no—
769C22—102no—
770C22#6592512yes—
771C22#6610412yes—
772C22D5×#13712yes—
773C22C22×D4×D511yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—102no—
779C4—102no—
780C4—102no—
781C4—202no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4#6592512yes—
786C4C22×#71111yescharacteristic
787C4C2×#414411yescharacteristic
788C2—42no—
789C2—82no—
790C2—104no—
791C2#1061198614yesdirect product factor
792C2C2×#6592511yescharacteristic
793C2C2×#6610411yescharacteristic
794C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#452C2
socleC23×C5C22×D4
prime radicalC2×#66165C2
hypercenterC2×#452D5
hypocenterC5C2×#3316
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#65969C2semidirect
3. C2×C5×#452C2semidirect
4. C2×#65521C2semidirect
5. C2×#65475C2semidirect
6. C2×#65473C2semidirect
7. C2×#65460C2semidirect
8. C2×#65455C2semidirect
9. C2×#65341C2semidirect
10. #10611986C2direct (N × H)
11. C2×D5×#103C2semidirect
12. C2×#65080C2semidirect
13. C2×#65066C2semidirect
14. C2×#65054C2semidirect
15. C2×#65017C2semidirect
16. C2×#65010C2semidirect
40. #65969C22semidirect
47. C5×#452C22semidirect
51. #65521C22semidirect
57. #65475C22semidirect
58. #65473C22semidirect
59. #65460C22semidirect
60. #65455C22semidirect
68. #65341C22semidirect
71. D5×#103C22semidirect
72. #65080C22semidirect
73. #65066C22semidirect
74. #65054C22semidirect
75. #65017C22semidirect
76. #65010C22semidirect
196. C2×#452D5semidirect
344. #452C2×D5semidirect
682. C2×C5#3316semidirect
757. C5C2×#3316semidirect
791. C2#10611986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661652
C2×#659692
C2×C5×#4522
C2×#655212
C2×#654752
C2×#654732
C2×#654602
C2×#654552
C2×#653412
#106119862
C2×D5×#1032
C2×#650802
C2×#650662
C2×#650542
C2×#650172
C2×#650102
C2×#33165