Finite Group Databasebeta

← C2×#10600818 #12126738

Subgroups — C2×#10600818 #12126738

Order 1280.

1434 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65817C211yesmaximal, characteristic, complemented
2C22×C5×#99C211yesmaximal, characteristic
3C22×#3966C211yesmaximal, characteristic
4C22×#3966C211yesmaximal, characteristic
5C2×#64747C211yesmaximal, characteristic, complemented
6C2×#64747C211yesmaximal, characteristic, complemented
7C2×#64746C211yesmaximal, characteristic, complemented
8#10600818C218yesmaximal, direct product factor
9C23×C5×D4C2211yescharacteristic
10C22×C5×C22⋊C4C2211yescharacteristic
11C22×C5×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic5C2211yescharacteristic
13C22×C22⋊Dic5C2211yescharacteristic
14C22×C22⋊Dic5C2211yescharacteristic
15C22×C22⋊Dic5C2211yescharacteristic
16C2×#4070—22no—
17#65817—22no—
18#65817—22no—
19#65817—22no—
20#65817C2214yescomplemented
21C2×#4024—22no—
22C2×#4024—22no—
23C2×C5×#99—22no—
24C2×C5×#99—22no—
25C2×C5×#99C2214yes—
26C2×#3966—22no—
27C2×#3966—22no—
28C2×#3966—22no—
29C2×#3966—22no—
30C2×#3966C2214yes—
31C2×#3966C2214yes—
32#64747C2214yescomplemented
33#64747C2214yescomplemented
34#64746C2214yescomplemented
35C2×#2032—51nomaximal, Sylow
36C25×C5Q811yescharacteristic, complemented
37C25×C5C2311yescharacteristic
38C22×C5×D4—21no—
39C22×C5×D4—21no—
40C22×C5×D4—21no—
41C22×C5×D4—21no—
42C22×C5×D4—21no—
43C22×C5×D4—21no—
44C22×C5×D4—21no—
45C22×C5×D4—21no—
46C22×C5×D4—21no—
47C22×C5×D4—21no—
48C22×C5×D4—21no—
49C22×C5×D4—21no—
50C22×C5×D4Q812yescomplemented
51C22×C5×D4C2312yes—
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C23×C4×C5Q811yescharacteristic, complemented
55C23×Dic5—21no—
56C23×Dic5—21no—
57C23×Dic5—21no—
58C23×Dic5—21no—
59C22×Dic10—22no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4—21no—
66C2×C5×C22⋊C4—21no—
67C2×C5×C22⋊C4—21no—
68C2×C5×C22⋊C4D412yes—
69C2×C5×C22⋊C4D412yes—
70C2×C5×C22⋊C4C2312yes—
71C2×C5×C22⋊C4C2312yes—
72C2×C22⋊Dic5—21no—
73C2×C22⋊Dic5—21no—
74C2×C22⋊Dic5—21no—
75C2×C22⋊Dic5—21no—
76C2×C22⋊Dic5—21no—
77C2×C22⋊Dic5—21no—
78C2×C22⋊Dic5—21no—
79C2×C22⋊Dic5—21no—
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—21no—
82C2×C22⋊Dic5—21no—
83C2×C22⋊Dic5—21no—
84C2×C22⋊Dic5—21no—
85C2×C22⋊Dic5—21no—
86C2×C22⋊Dic5—21no—
87C2×C22⋊Dic5—21no—
88C2×C22⋊Dic5D412yes—
89C2×C22⋊Dic5D412yes—
90C2×C22⋊Dic5D412yes—
91C2×C22⋊Dic5D412yes—
92C2×C22⋊Dic5C2312yes—
93C2×C22⋊Dic5C2312yes—
94C2×C22⋊Dic5C2312yes—
95C2×C22⋊Dic5C2312yes—
96C2×C4⋊Dic5—22no—
97#4070—28no—
98#4070—28no—
99C2×#683—24no—
100#4024—28no—
101#4024—28no—
102#4024—28no—
103#4024—28no—
104C5×#99—28no—
105#3966—28no—
106#3966—28no—
107C2×#543—51no—
108C22×#99—51no—
109C22×#99—51no—
110C22×#99D511yescharacteristic
111#2032—58no—
112C2×#342—51no—
113C2×#342—51no—
114C2×#342—51no—
115C24×C5—21no—
116C24×C5—21no—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—21no—
120C24×C5—21no—
121C24×C5—82no—
122C24×C5—82no—
123C24×C5C2×D411yescharacteristic
124C24×C5C2×D411yescharacteristic
125C24×C5C2×D411yescharacteristic
126C24×C5C2×D411yescharacteristic
127C24×C5C2×D411yescharacteristic
128C24×C5C2×D411yescharacteristic
129C24×C5C2×Q811yescharacteristic
130C24×C5C2×Q811yescharacteristic
131C24×C5C2×Q812yescomplemented
132C24×C5#4111yescharacteristic
133C24×C5#4111yescharacteristic
134C24×C5#4111yescharacteristic
135C24×C5#4111yescharacteristic
136C24×C5#4111yescharacteristic
137C24×C5#4111yescharacteristic
138C24×C5C2411yescharacteristic
139C2×C5×D4—22no—
140C2×C5×D4—22no—
141C2×C5×D4—22no—
142C2×C5×D4—22no—
143C2×C5×D4—22no—
144C2×C5×D4—22no—
145C2×C5×D4—22no—
146C2×C5×D4—22no—
147C2×C5×D4—22no—
148C2×C5×D4—22no—
149C2×C5×D4—22no—
150C2×C5×D4—22no—
151C2×C5×D4—41no—
152C2×C5×D4—41no—
153C2×C5×D4—41no—
154C2×C5×D4—41no—
155C2×C5×D4—41no—
156C2×C5×D4—41no—
157C2×C5×D4—41no—
158C2×C5×D4—41no—
159C2×C5×D4—41no—
160C2×C5×D4—41no—
161C2×C5×D4—41no—
162C2×C5×D4—41no—
163C2×C5×D4—41no—
164C2×C5×D4—41no—
165C2×C5×D4—41no—
166C2×C5×D4—41no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—41no—
178C22×C4×C5—41no—
179C22×C4×C5—82no—
180C22×C4×C5—82no—
181C22×C4×C5C2×Q812yescomplemented
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—41no—
191C22×Dic5—41no—
192C22×Dic5—41no—
193C22×Dic5—41no—
194C22×Dic5—82no—
195C22×Dic5—82no—
196C22×Dic5—82no—
197C22×Dic5—82no—
198C2×Dic10—28no—
199C2×Dic10—84no—
200C5×C22⋊C4—22no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4—22no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—41no—
206C5×C22⋊C4—41no—
207C5×C22⋊C4C2×D414yes—
208C22⋊Dic5—22no—
209C22⋊Dic5—22no—
210C22⋊Dic5—22no—
211C22⋊Dic5—22no—
212C22⋊Dic5—22no—
213C22⋊Dic5—22no—
214C22⋊Dic5—22no—
215C22⋊Dic5—22no—
216C22⋊Dic5—22no—
217C22⋊Dic5—22no—
218C22⋊Dic5—41no—
219C22⋊Dic5—41no—
220C22⋊Dic5—41no—
221C22⋊Dic5—41no—
222C22⋊Dic5C2×D414yes—
223C22⋊Dic5C2×D414yes—
224C4⋊Dic5—28no—
225#683—216no—
226C23×D4C2×D511yescharacteristic
227#543—54no—
228#543—102no—
229#543—102no—
230#543—102no—
231C2×C22⋊Q8—102no—
232C2×C22⋊Q8—102no—
233C2×C22⋊Q8—102no—
234C22×C22⋊C4—51no—
235C22×C22⋊C4—51no—
236C22×C22⋊C4—51no—
237C22×C22⋊C4—51no—
238C22×C22⋊C4C2×D511yescharacteristic
239C22×C22⋊C4C2×D511yescharacteristic
240C2×#99—22no—
241C2×#99—22no—
242C2×#99—54no—
243C2×#99—54no—
244C2×#99—102no—
245C2×#99—102no—
246C2×#99—102no—
247C2×#99—102no—
248C2×#99C2×D514yes—
249#342—54no—
250#342—54no—
251#342—54no—
252C23×C5—22no—
253C23×C5—22no—
254C23×C5—22no—
255C23×C5—42no—
256C23×C5—42no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5—42no—
261C23×C5—42no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5—82no—
267C23×C5—82no—
268C23×C5—82no—
269C23×C5—81no—
270C23×C5—81no—
271C23×C5—81no—
272C23×C5—81no—
273C23×C5—81no—
274C23×C5—81no—
275C23×C5—81no—
276C23×C5—81no—
277C23×C5—82no—
278C23×C5—82no—
279C23×C5—82no—
280C23×C5—82no—
281C23×C5#12011yescharacteristic
282C23×C5#12011yescharacteristic
283C23×C5#12011yescharacteristic
284C23×C5#12011yescharacteristic
285C23×C5C22⋊Q811yescharacteristic
286C23×C5C22⋊Q811yescharacteristic
287C23×C5C22⋊Q811yescharacteristic
288C23×C5C22⋊Q811yescharacteristic
289C23×C5C22⋊Q811yescharacteristic
290C23×C5C22⋊Q811yescharacteristic
291C23×C5C22⋊Q811yescharacteristic
292C23×C5C22⋊Q811yescharacteristic
293C23×C5C22⋊Q811yescharacteristic
294C23×C5C22⋊Q811yescharacteristic
295C23×C5C22⋊Q811yescharacteristic
296C23×C5C22⋊Q811yescharacteristic
297C23×C5#12411yescharacteristic
298C23×C5#12411yescharacteristic
299C23×C5#12411yescharacteristic
300C23×C5#12411yescharacteristic
301C23×C5#12411yescharacteristic
302C23×C5#12411yescharacteristic
303C23×C5#12411yescharacteristic
304C23×C5#12411yescharacteristic
305C23×C5#12411yescharacteristic
306C23×C5#12411yescharacteristic
307C23×C5#12411yescharacteristic
308C23×C5#12411yescharacteristic
309C23×C5C22×D411yescharacteristic
310C23×C5C22×D411yescharacteristic
311C23×C5C22×D411yescharacteristic
312C23×C5C22×Q811yescharacteristic
313C23×C5C2×#4111yescharacteristic
314C23×C5C2×#4111yescharacteristic
315C23×C5C2×#4111yescharacteristic
316C5×D4—42no—
317C5×D4—42no—
318C5×D4—42no—
319C5×D4—42no—
320C5×D4—42no—
321C5×D4—42no—
322C5×D4—42no—
323C5×D4—42no—
324C2×C4×C5—24no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—44no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—42no—
334C2×C4×C5—82no—
335C2×C4×C5—82no—
336C2×C4×C5—82no—
337C2×C4×C5—82no—
338C2×C4×C5—82no—
339C2×Dic5—24no—
340C2×Dic5—24no—
341C2×Dic5—44no—
342C2×Dic5—44no—
343C2×Dic5—42no—
344C2×Dic5—42no—
345C2×Dic5—82no—
346C2×Dic5—82no—
347C2×Dic5—82no—
348C2×Dic5—82no—
349C2×Dic5—82no—
350C2×Dic5—82no—
351C2×Dic5—82no—
352C2×Dic5—82no—
353C2×Dic5—82no—
354C2×Dic5—82no—
355Dic10—88no—
356C25Dic1011yescharacteristic, complemented
357C25C22×D511yescharacteristic
358C22×Q8—102no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4Dic1012yescomplemented
372C22×D4C22×D512yes—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—101no—
376C23×C4—101no—
377C23×C4—101no—
378C23×C4—101no—
379C23×C4Dic1011yescharacteristic, complemented
380C22⋊Q8—108no—
381C22⋊Q8—108no—
382C22⋊Q8—108no—
383C22⋊Q8—108no—
384C22⋊Q8—108no—
385C22⋊Q8—108no—
386C2×C4⋊C4—104no—
387C2×C4⋊C4—102no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—52no—
398C2×C22⋊C4—52no—
399C2×C22⋊C4—52no—
400C2×C22⋊C4—52no—
401C2×C22⋊C4—52no—
402C2×C22⋊C4—52no—
403C2×C22⋊C4—52no—
404C2×C22⋊C4—101no—
405C2×C22⋊C4—101no—
406C2×C22⋊C4—101no—
407C2×C22⋊C4—101no—
408C2×C22⋊C4—101no—
409C2×C22⋊C4—101no—
410C2×C22⋊C4—101no—
411C2×C22⋊C4—101no—
412C2×C22⋊C4—101no—
413C2×C22⋊C4—101no—
414C2×C22⋊C4—101no—
415C2×C22⋊C4—101no—
416C2×C22⋊C4—101no—
417C2×C22⋊C4—101no—
418C2×C22⋊C4—101no—
419C2×C22⋊C4—101no—
420C2×C22⋊C4C22⋊D512yes—
421C2×C22⋊C4C22⋊D512yes—
422C2×C22⋊C4C22×D512yes—
423C2×C22⋊C4C22×D512yes—
424#99—28no—
425#99—108no—
426#99—108no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—41no—
454C22×C5—41no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—41no—
460C22×C5—41no—
461C22×C5—41no—
462C22×C5—42no—
463C22×C5—82no—
464C22×C5—82no—
465C22×C5—82no—
466C22×C5—82no—
467C22×C5—82no—
468C22×C5—82no—
469C22×C5—82no—
470C22×C5#39311yescharacteristic
471C22×C5#39311yescharacteristic
472C22×C5#39311yescharacteristic
473C22×C5#39311yescharacteristic
474C22×C5#39311yescharacteristic
475C22×C5#39311yescharacteristic
476C22×C5#39311yescharacteristic
477C22×C5#39311yescharacteristic
478C22×C5C2×#12011yescharacteristic
479C22×C5C2×C22⋊Q811yescharacteristic
480C22×C5C2×C22⋊Q811yescharacteristic
481C22×C5C2×C22⋊Q811yescharacteristic
482C22×C5C2×#12411yescharacteristic
483C22×C5C2×#12411yescharacteristic
484C22×C5C2×#12411yescharacteristic
485C4×C5—44no—
486C4×C5—42no—
487C4×C5—82no—
488Dic5—44no—
489Dic5—44no—
490Dic5—82no—
491Dic5—82no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—82no—
499C24—82no—
500C24C2×Dic1011yescharacteristic
501C24C2×Dic1011yescharacteristic
502C24C2×Dic1012yescomplemented
503C24#70911yescharacteristic
504C24#70911yescharacteristic
505C24D4×D511yescharacteristic
506C24D4×D511yescharacteristic
507C24D4×D511yescharacteristic
508C24D4×D511yescharacteristic
509C24#71111yescharacteristic
510C24#71111yescharacteristic
511C24#71111yescharacteristic
512C24#71111yescharacteristic
513C24C2×C22⋊D511yescharacteristic
514C24C2×C22⋊D511yescharacteristic
515C24C23×D511yescharacteristic
516C2×Q8—108no—
517C2×Q8—404no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—201no—
569C22×C4—201no—
570C22×C4—201no—
571C22×C4—201no—
572C22×C4—402no—
573C22×C4—402no—
574C22×C4—402no—
575C22×C4—402no—
576C22×C4C2×Dic1012yescomplemented
577C4⋊C4—1016no—
578C4⋊C4—108no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—54no—
587C22⋊C4—54no—
588C22⋊C4—102no—
589C22⋊C4—102no—
590C22⋊C4—102no—
591C22⋊C4—102no—
592C22⋊C4—102no—
593C22⋊C4—102no—
594C22⋊C4—102no—
595C22⋊C4—102no—
596C22⋊C4—102no—
597C22⋊C4—102no—
598C22⋊C4—201no—
599C22⋊C4—201no—
600C22⋊C4—201no—
601C22⋊C4—201no—
602C22⋊C4C2×C22⋊D514yes—
603C2×C5—21no—
604C2×C5—21no—
605C2×C5—21no—
606C2×C5—21no—
607C2×C5—21no—
608C2×C5—21no—
609C2×C5—21no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—21no—
613C2×C5—21no—
614C2×C5—21no—
615C2×C5—21no—
616C2×C5—21no—
617C2×C5—82no—
618C2×C5#203212yescomplemented
619C2×C5C2×#39311yescharacteristic
620C23—22no—
621C23—22no—
622C23—22no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—82no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23#402411yescharacteristic
650C23#402411yescharacteristic
651C23#402411yescharacteristic
652C23#402411yescharacteristic
653C23#402411yescharacteristic
654C23#402411yescharacteristic
655C23#402411yescharacteristic
656C23#402411yescharacteristic
657C23#403111yescharacteristic
658C23#403111yescharacteristic
659C23#403111yescharacteristic
660C23#403111yescharacteristic
661C23#403111yescharacteristic
662C23#403111yescharacteristic
663C23#403111yescharacteristic
664C23#403111yescharacteristic
665C23#407011yescharacteristic
666C23#407011yescharacteristic
667C23#407011yescharacteristic
668C23#407011yescharacteristic
669C23#408211yescharacteristic
670C23#408211yescharacteristic
671C23#408211yescharacteristic
672C23#408211yescharacteristic
673C23#408311yescharacteristic
674C23#408311yescharacteristic
675C23#408311yescharacteristic
676C23#408311yescharacteristic
677C23C22×Dic1011yescharacteristic
678C23C2×#70911yescharacteristic
679C23C2×D4×D511yescharacteristic
680C23C2×D4×D511yescharacteristic
681C23C2×#71111yescharacteristic
682C23C2×#71111yescharacteristic
683C23C22×C22⋊D511yescharacteristic
684Q8—408no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—104no—
709C2×C4—104no—
710C2×C4—204no—
711C2×C4—204no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—402no—
715C2×C4—402no—
716C2×C4—402no—
717C2×C4—402no—
718C2×C4—402no—
719C2×C4—402no—
720C2×C4—402no—
721C2×C4—402no—
722C2×C4—402no—
723C2×C4—402no—
724C5C2×#203211yescharacteristic, complemented, Sylow
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#6523611yescharacteristic
769C22#6523611yescharacteristic
770C22#6523611yescharacteristic
771C22#6523611yescharacteristic
772C22#6523611yescharacteristic
773C22#6523611yescharacteristic
774C22#6523611yescharacteristic
775C22#6523611yescharacteristic
776C22C2×#402411yescharacteristic
777C22C2×#402411yescharacteristic
778C22C2×#403111yescharacteristic
779C22C2×#403111yescharacteristic
780C22C2×#407011yescharacteristic
781C22C2×#408211yescharacteristic
782C22C2×#408311yescharacteristic
783C4—44no—
784C4—42no—
785C4—82no—
786C4—204no—
787C4—204no—
788C4—402no—
789C4—402no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—82no—
805C2#1060081812yesdirect product factor
806C2C2×#6523611yescharacteristic
subgroupG/H
centerC22#65236
commutator, cosocleC24×C5C24
FrattiniC24C23×D5
FittingC22×C5×#99C2
socleC22×C5#393
prime radicalC23×C5×D4C22
hypercenterC22×#99D5
hypocenterC5C2×#2032
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
1. C2×#65817C2semidirect
5. C2×#64747C2semidirect
6. C2×#64747C2semidirect
7. C2×#64746C2semidirect
8. #10600818C2direct (N × H)
20. #65817C22semidirect
32. #64747C22semidirect
33. #64747C22semidirect
34. #64746C22semidirect
36. C25×C5Q8semidirect
50. C22×C5×D4Q8semidirect
54. C23×C4×C5Q8semidirect
131. C24×C5C2×Q8semidirect
181. C22×C4×C5C2×Q8semidirect
356. C25Dic10semidirect
371. C22×D4Dic10semidirect
379. C23×C4Dic10semidirect
502. C24C2×Dic10semidirect
576. C22×C4C2×Dic10semidirect
618. C2×C5#2032semidirect
724. C5C2×#2032semidirect
805. C2#10600818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658172
C22×C5×#992
C22×#39662
C2×#647472
C2×#647462
#106008182
C2×#20325