Finite Group Databasebeta

← C2×#10615271 #12976153

Subgroups — C2×#10615271 #12976153

Order 1280.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#548C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic, complemented
3C2×#65527C211yesmaximal, characteristic, complemented
4C2×#65521C211yesmaximal, characteristic, complemented
5C2×#65516C211yesmaximal, characteristic, complemented
6C2×#65514C211yesmaximal, characteristic, complemented
7#10615271C2116yesmaximal, direct product factor
8C2×#65346C211yesmaximal, characteristic, complemented
9C2×#65345C211yesmaximal, characteristic, complemented
10C2×#65338C211yesmaximal, characteristic, complemented
11C2×#65332C211yesmaximal, characteristic, complemented
12C2×#65328C211yesmaximal, characteristic, complemented
13C2×#65324C211yesmaximal, characteristic, complemented
14C2×#65311C211yesmaximal, characteristic, complemented
15C2×C4×#688C211yesmaximal, characteristic, complemented
16C2×#65301C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic
19C5×#548—24no—
20C5×#548C2218yescomplemented
21C2×C5×#124—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C22×#688C2211yescharacteristic
32C2×#4085—21no—
33C22×#686C2211yescharacteristic
34C2×#4076C2211yescharacteristic
35C2×#4076C2211yescharacteristic
36C2×#4072C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C22×#681C2211yescharacteristic
40#65899—24no—
41#65899C2218yescomplemented
42C2×#4044—21no—
43C2×#4029—21no—
44C2×#4027—21no—
45C2×C4×D20C2211yescharacteristic
46C2×#4016C2211yescharacteristic
47#65527C2218yescomplemented
48#65521C2218yescomplemented
49#65516C2218yescomplemented
50#65514C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3967C2211yescharacteristic
56C2×#3967C2211yescharacteristic
57C2×#3964C2211yescharacteristic
58C2×#3964C2211yescharacteristic
59C2×#3964C2211yescharacteristic
60C2×C22⋊#168C2211yescharacteristic
61C2×C22⋊#168C2211yescharacteristic
62#65346C2218yescomplemented
63#65345C2218yescomplemented
64#65338C2218yescomplemented
65#65332C2218yescomplemented
66#65328C2218yescomplemented
67#65324C2218yescomplemented
68C4×#688C2218yescomplemented
69#65311C2218yescomplemented
70#65301C2218yescomplemented
71C2×#3941C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3326—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—24no—
80C2×C5×#41—42no—
81C2×C5×#41C2314yes—
82C22×C5×Q8—21no—
83C22×C5×Q8—22no—
84C22×C5×Q8—24no—
85C22×C5×Q8—42no—
86C22×C5×Q8C2311yescharacteristic
87C22×C5×Q8C2314yes—
88C22×C5×Q8C2311yescharacteristic
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4D411yescharacteristic
92C22×C5×D4C2311yescharacteristic
93C23×C4×C5—21no—
94C23×C4×C5—21no—
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C22×C22⋊D5—21no—
98C22×C22⋊D5—21no—
99C23×Dic5—21no—
100C22×D20C2311yescharacteristic
101C22×C4×D5—21no—
102C5×#124—28no—
103C5×#124—22no—
104C5×#124C2314yes—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8—28no—
107C5×C22⋊Q8C2314yes—
108C5×#121—28no—
109C5×#121—22no—
110C5×#121C2314yes—
111C4×C5×Q8—22no—
112C4×C5×Q8C2314yes—
113C4×C5×D4—28no—
114C4×C5×D4D414yes—
115C4×C5×D4C2314yes—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4C2311yescharacteristic
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C5×C22⋊C4D411yescharacteristic
126C2×C42×C5—21no—
127C2×C42×C5C2311yescharacteristic
128C2×C22⋊Dic5—21no—
129C2×#688—24no—
130C2×#688—42no—
131C2×#688C2314yes—
132C2×#688C2314yes—
133#4085—28no—
134C2×#686—42no—
135C2×#686C2314yes—
136#4076—22no—
137#4076—22no—
138#4076C2314yes—
139#4076C2314yes—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685—21no—
143#4072—22no—
144#4072C2314yes—
145C2×C4⋊Dic5—21no—
146C2×C4⋊Dic5—22no—
147C2×C4⋊Dic5C2311yescharacteristic
148C2×C4⋊Dic5C2311yescharacteristic
149C2×C4⋊Dic5C2311yescharacteristic
150C2×C4⋊Dic5C2314yes—
151C2×#683—21no—
152C2×#683—21no—
153C2×C4×Dic5—21no—
154C2×#681—42no—
155C2×#681—42no—
156C2×#681C2314yes—
157C2×#681C2314yes—
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2311yescharacteristic
161C22×#168C2311yescharacteristic
162#4044—28no—
163#4029—28no—
164#4027—28no—
165C4×D20—22no—
166C4×D20C2314yes—
167#4016—22no—
168#4016C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3967C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177#3964C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3940C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185C4×#168C2314yes—
186C2×#553—51no—
187C2×#548D511yescharacteristic, complemented
188#3326—516no—
189C2×#488—51no—
190C2×#482—51no—
191C2×#483—51no—
192C2×#479—51no—
193C2×#469—51no—
194C2×#468—51no—
195C2×#463—51no—
196C2×#449—51no—
197C2×#448—51no—
198C2×C4×SD16—51no—
199C2×#436—51no—
200C2×#417—51no—
201C2×#419—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C24×C5C2×D411yescharacteristic
205C23×D5—21no—
206C5×#41—28no—
207C5×#41—44no—
208C5×#41—48no—
209C2×C5×Q8—21no—
210C2×C5×Q8—24no—
211C2×C5×Q8—21no—
212C2×C5×Q8—22no—
213C2×C5×Q8—28no—
214C2×C5×Q8—22no—
215C2×C5×Q8—22no—
216C2×C5×Q8—44no—
217C2×C5×Q8—44no—
218C2×C5×Q8—48no—
219C2×C5×Q8#4114yes—
220C2×C5×Q8C2412yes—
221C2×C5×Q8C2412yes—
222C2×C5×D4—24no—
223C2×C5×D4—24no—
224C2×C5×D4—21no—
225C2×C5×D4—22no—
226C2×C5×D4—22no—
227C2×C5×D4—42no—
228C2×C5×D4—44no—
229C2×C5×D4—44no—
230C2×C5×D4C2×D414yes—
231C2×C5×D4C2412yes—
232C22×C4×C5—21no—
233C22×C4×C5—22no—
234C22×C4×C5—22no—
235C22×C4×C5—22no—
236C22×C4×C5—22no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—24no—
240C22×C4×C5—24no—
241C22×C4×C5—44no—
242C22×C4×C5—44no—
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2×D412yes—
249C22×C4×C5C2412yes—
250C22×C4×C5C2412yes—
251C22×C4×C5C2411yescharacteristic
252C2×C22⋊D5—24no—
253C2×C22⋊D5—24no—
254C2×C22⋊D5—44no—
255C2×C22⋊D5—82no—
256C22×Dic5—21no—
257C22×Dic5—21no—
258C22×Dic5—21no—
259C22×Dic5—24no—
260C22×Dic5—82no—
261C2×D20—22no—
262C2×D20—22no—
263C2×D20—21no—
264C2×D20C2412yes—
265C2×C4×D5—24no—
266C2×C4×D5—82no—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—24no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4C2×D414yes—
271C5×C4⋊C4C2412yes—
272C5×C22⋊C4—24no—
273C5×C22⋊C4—24no—
274C5×C22⋊C4—24no—
275C5×C22⋊C4—24no—
276C5×C22⋊C4C2×D414yes—
277C5×C22⋊C4C2×D414yes—
278C42×C5—24no—
279C42×C5C2×D412yes—
280C42×C5C2412yes—
281C22⋊Dic5—24no—
282#688—28no—
283#688—44no—
284#686—44no—
285#685—24no—
286#685—24no—
287#685—24no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—21no—
291C4⋊Dic5—24no—
292C4⋊Dic5C2412yes—
293C4⋊Dic5C2412yes—
294C4⋊Dic5C2412yes—
295#683—24no—
296#683—24no—
297C4×Dic5—24no—
298#681—44no—
299#681—44no—
300C2×#168—22no—
301C2×#168—22no—
302C2×#168—22no—
303C2×#168—22no—
304C2×#168C2412yes—
305C2×#168C2412yes—
306C2×#168C2412yes—
307C2×#168C2412yes—
308C22×#41C2×D511yescharacteristic
309C23×Q8C2×D511yescharacteristic
310C22×SD16—51no—
311C22×SD16—51no—
312C22×D8—51no—
313C22×M16—51no—
314C22×M16—51no—
315#553—58no—
316#553—104no—
317#548—24no—
318#548C2×D518yescomplemented
319C2×#126—101no—
320C2×#125—51no—
321C2×#124—21no—
322C2×#124C2×D511yescharacteristic
323C2×#123—101no—
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×#121—21no—
327C2×#121—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×#121C2×D511yescharacteristic
331C2×C4×Q8C2×D511yescharacteristic
332C2×C4×D4—21no—
333C2×C4×D4—51no—
334C2×C4×D4—101no—
335C2×C4×D4C2×D511yescharacteristic
336C2×#117—51no—
337C22×C4⋊C4—51no—
338#488—58no—
339#483—58no—
340#482—58no—
341#479—58no—
342#469—58no—
343#468—58no—
344#463—58no—
345#449—58no—
346#448—58no—
347C4×SD16—58no—
348#436—58no—
349C2×#107—51no—
350C2×#106—51no—
351C2×#106—51no—
352C2×C4⋊C8—51no—
353#419—58no—
354#417—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×C22⋊C8—51no—
366C2×C22⋊C8—51no—
367C2×C4×C8—51no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—42no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5C22×D412yes—
379C23×C5C22×D412yes—
380C23×C5C22×D411yescharacteristic
381C22×D5—22no—
382C22×D5—42no—
383C22×D5—42no—
384C22×D5—42no—
385C5×Q8—24no—
386C5×Q8—22no—
387C5×Q8—22no—
388C5×Q8—22no—
389C5×Q8—48no—
390C5×Q8—42no—
391C5×Q8C2×#4114yes—
392C5×D4—22no—
393C5×D4—22no—
394C5×D4—44no—
395C5×D4—48no—
396C5×D4—48no—
397C5×D4—42no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—24no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—24no—
405C2×C4×C5—24no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—48no—
413C2×C4×C5—48no—
414C2×C4×C5—42no—
415C2×C4×C5—42no—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D412yes—
418C2×C4×C5C22×D412yes—
419C2×C4×C5C22×D412yes—
420C2×C4×C5C22×D411yescharacteristic
421C2×C4×C5C2×#4112yes—
422C2×C4×C5H(5,𝔽2)12yes—
423C2×C4×C5C2511yescharacteristic
424C22⋊D5—48no—
425C22⋊D5—84no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431C2×Dic5—42no—
432C2×Dic5—84no—
433D20—22no—
434D20—22no—
435D20—42no—
436C4×D5—84no—
437#168—22no—
438#168—22no—
439#168—22no—
440#168—22no—
441C2×#41—22no—
442C2×#41—24no—
443C2×#41—42no—
444C2×#41C22×D514yes—
445C22×Q8—21no—
446C22×Q8—22no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8C22×D511yescharacteristic
450C22×Q8C22×D514yes—
451C22×Q8C22×D511yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—51no—
455C22×D4—101no—
456C22×D4—101no—
457C22×D4C22⋊D511yescharacteristic
458C22×D4C22×D511yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—101no—
462C23×C4—101no—
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465C2×SD16—54no—
466C2×SD16—54no—
467C2×SD16—104no—
468C2×SD16—202no—
469C2×D8—54no—
470C2×D8—202no—
471C2×M16—54no—
472C2×M16—54no—
473C2×M16—202no—
474C2×M16—202no—
475C22×C8—51no—
476C22×C8—51no—
477C22×C8—51no—
478C22×C8—51no—
479#126—108no—
480#125—54no—
481#125—102no—
482#124—28no—
483#124—22no—
484#124C22×D514yes—
485#123—108no—
486C22⋊Q8—22no—
487C22⋊Q8—28no—
488C22⋊Q8C22×D514yes—
489#121—28no—
490#121—22no—
491#121—54no—
492#121—54no—
493#121—108no—
494#121—102no—
495#121—102no—
496#121C22×D514yes—
497C4×Q8—22no—
498C4×Q8C22×D514yes—
499C4×D4—28no—
500C4×D4—54no—
501C4×D4—108no—
502C4×D4—102no—
503C4×D4C22⋊D514yes—
504C4×D4C22×D514yes—
505#117—54no—
506#117—102no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—51no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—102no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4—101no—
517C2×C4⋊C4C22⋊D511yescharacteristic
518C2×C4⋊C4C22×D511yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C22⋊C4C22⋊D511yescharacteristic
528C2×C22⋊C4C22⋊D511yescharacteristic
529C2×C42—21no—
530C2×C42—101no—
531C2×C42C22×D511yescharacteristic
532#107—54no—
533#106—54no—
534#106—54no—
535C4⋊C8—54no—
536#103—54no—
537#103—54no—
538#103—54no—
539#103—54no—
540#103—54no—
541#103—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102—54no—
546C22⋊C8—54no—
547C22⋊C8—54no—
548C4×C8—54no—
549C22×C5—22no—
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—44no—
556C22×C5—44no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—84no—
561C22×C5#54612yes—
562C22×C5#57512yes—
563C22×C5#57712yes—
564C22×C5C23×D411yescharacteristic
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—84no—
569C4×C5—22no—
570C4×C5—22no—
571C4×C5—24no—
572C4×C5—22no—
573C4×C5—22no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5#54612yes—
577C4×C5C22×#4111yescharacteristic
578C4×C5C2×H(5,𝔽2)11yescharacteristic
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—21no—
583C24—101no—
584C24C2×C22⋊D511yescharacteristic
585C24C2×C22⋊D511yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—22no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8#71114yes—
600C2×Q8C23×D512yes—
601C2×Q8C23×D512yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—52no—
611C2×D4—104no—
612C2×D4—104no—
613C2×D4—102no—
614C2×D4—102no—
615C2×D4—101no—
616C2×D4—204no—
617C2×D4—402no—
618C2×D4C2×C22⋊D514yes—
619C2×D4C23×D512yes—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—24no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—101no—
632C22×C4—101no—
633C22×C4—101no—
634C22×C4—104no—
635C22×C4—104no—
636C22×C4—402no—
637C22×C4—402no—
638C22×C4C2×C22⋊D512yes—
639C22×C4C2×C22⋊D512yes—
640C22×C4C2×C22⋊D511yescharacteristic
641C22×C4C2×C22⋊D511yescharacteristic
642C22×C4C2×C22⋊D511yescharacteristic
643C22×C4C2×C22⋊D511yescharacteristic
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D511yescharacteristic
647SD16—108no—
648SD16—204no—
649D8—204no—
650M16—204no—
651M16—204no—
652C2×C8—52no—
653C2×C8—52no—
654C2×C8—52no—
655C2×C8—52no—
656C2×C8—102no—
657C2×C8—102no—
658C2×C8—102no—
659C2×C8—102no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—52no—
664C4⋊C4—52no—
665C4⋊C4—52no—
666C4⋊C4—101no—
667C4⋊C4—101no—
668C4⋊C4—104no—
669C4⋊C4—101no—
670C4⋊C4—104no—
671C4⋊C4—104no—
672C4⋊C4C2×C22⋊D514yes—
673C4⋊C4C23×D512yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—104no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4—104no—
682C22⋊C4C2×C22⋊D514yes—
683C22⋊C4C2×C22⋊D514yes—
684C42—24no—
685C42—104no—
686C42C2×C22⋊D512yes—
687C42C23×D512yes—
688C2×C5—42no—
689C2×C5—42no—
690C2×C5—82no—
691C2×C5#332614yescomplemented
692C2×C5C2×#54611yescharacteristic
693C2×C5C2×#57511yescharacteristic
694C2×C5C2×#57711yescharacteristic
695D5—82no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—102no—
707C23—202no—
708C23—202no—
709C23—202no—
710C23C22×C22⋊D512yes—
711C23C22×C22⋊D512yes—
712C23C22×C22⋊D511yescharacteristic
713Q8—24no—
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—48no—
718Q8—42no—
719Q8C2×#71114yes—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—48no—
725D4—42no—
726D4—102no—
727D4—102no—
728D4—208no—
729D4—202no—
730D4—404no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—48no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—202no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—404no—
756C2×C4—404no—
757C2×C4C2×#71112yes—
758C2×C4#414412yes—
759C2×C4C22×C22⋊D512yes—
760C2×C4C22×C22⋊D512yes—
761C2×C4C22×C22⋊D512yes—
762C2×C4C22×C22⋊D512yes—
763C2×C4C22×C22⋊D511yescharacteristic
764C2×C4C24×D511yescharacteristic
765C8—102no—
766C8—102no—
767C8—102no—
768C8—102no—
769C5C2×#332611yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—202no—
783C22—202no—
784C22—202no—
785C22—404no—
786C22#6614012yes—
787C22#6615612yes—
788C22#6617112yes—
789C22C23×C22⋊D511yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—24no—
795C4—42no—
796C4—42no—
797C4—202no—
798C4—202no—
799C4—202no—
800C4#6614012yes—
801C4C22×#71111yescharacteristic
802C4C2×#414411yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—402no—
807C2#1061527114yesdirect product factor
808C2C2×#6614011yescharacteristic
809C2C2×#6615611yescharacteristic
810C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#548C2
socleC23×C5C22×D4
hypercenterC2×#548D5
hypocenterC5C2×#3326
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C5×#548C2semidirect
2. C2×#65899C2semidirect
3. C2×#65527C2semidirect
4. C2×#65521C2semidirect
5. C2×#65516C2semidirect
6. C2×#65514C2semidirect
7. #10615271C2direct (N × H)
8. C2×#65346C2semidirect
9. C2×#65345C2semidirect
10. C2×#65338C2semidirect
11. C2×#65332C2semidirect
12. C2×#65328C2semidirect
13. C2×#65324C2semidirect
14. C2×#65311C2semidirect
15. C2×C4×#688C2semidirect
16. C2×#65301C2semidirect
20. C5×#548C22semidirect
41. #65899C22semidirect
47. #65527C22semidirect
48. #65521C22semidirect
49. #65516C22semidirect
50. #65514C22semidirect
62. #65346C22semidirect
63. #65345C22semidirect
64. #65338C22semidirect
65. #65332C22semidirect
66. #65328C22semidirect
67. #65324C22semidirect
68. C4×#688C22semidirect
69. #65311C22semidirect
70. #65301C22semidirect
187. C2×#548D5semidirect
318. #548C2×D5semidirect
691. C2×C5#3326semidirect
769. C5C2×#3326semidirect
807. C2#10615271direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5482
C2×#658992
C2×#655272
C2×#655212
C2×#655162
C2×#655142
#106152712
C2×#653462
C2×#653452
C2×#653382
C2×#653322
C2×#653282
C2×#653242
C2×#653112
C2×C4×#6882
C2×#653012
C2×#33265