Finite Group Databasebeta

← #12005926

Subgroups — #12005926

Order 1280.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#525C211yesmaximal, characteristic
2C2×#65525C211yesmaximal, characteristic, complemented
3#10615803C211yesmaximal, characteristic, complemented
4#10615758C211yesmaximal, characteristic, complemented
5C2×#65496C211yesmaximal, characteristic, complemented
6#10602371C211yesmaximal, characteristic, complemented
7C2×#64751C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C24×C4×C5C2211yescharacteristic
10C5×#525—22no—
11C5×#525—22no—
12C5×#525—22no—
13C5×#525C414yescomplemented
14C2×C5×#123—21no—
15C2×C5×C22⋊Q8—21no—
16C2×C5×#121—21no—
17C2×C5×#120—21no—
18C2×C4×C5×D4—22no—
19C2×C5×#117C2211yescharacteristic
20C2×#4072C2211yescharacteristic
21C2×#4072C2211yescharacteristic
22C22×#681C2211yescharacteristic
23C22×#681C2211yescharacteristic
24#65536—21no—
25#65525—22no—
26#65525—22no—
27C2×#3969—22no—
28#65522—22no—
29#65521—22no—
30#65514—21no—
31#65504—21no—
32#65501—22no—
33#65500—21no—
34C4×C22⋊Dic5—22no—
35#65496—22no—
36#65496—22no—
37C2×C22⋊#168—22no—
38#64751—22no—
39#64743—22no—
40#10994—51nomaximal, Sylow
41C25×C5D411yescharacteristic
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41—21no—
50C2×C5×#41—21no—
51C2×C5×#41—21no—
52C2×C5×#41C2×C412yes—
53C2×C5×#41D412yes—
54C22×C5×Q8D411yescharacteristic
55C22×C5×D4—22no—
56C22×C5×D4—21no—
57C22×C5×D4D411yescharacteristic
58C23×C4×C5—21no—
59C23×C4×C5—21no—
60C23×C4×C5—21no—
61C23×C4×C5—21no—
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C23×C4×C5C2×C412yes—
72C23×C4×C5D411yescharacteristic
73C23×C4×C5D412yes—
74C23×C4×C5C2311yescharacteristic
75C5×#123—24no—
76C5×#123—24no—
77C5×C22⋊Q8—24no—
78C5×C22⋊Q8—24no—
79C5×#121—24no—
80C5×#121—24no—
81C5×#120—24no—
82C5×#120—24no—
83C4×C5×D4—28no—
84C4×C5×D4—28no—
85C5×#117—21no—
86C5×#117—21no—
87C5×#117C2×C412yes—
88C5×#117D412yes—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—21no—
94C2×C42×C5D412yes—
95C2×C22⋊Dic5—24no—
96C2×C22⋊Dic5—21no—
97C2×C22⋊Dic5—21no—
98#4072—21no—
99#4072—21no—
100#4072—21no—
101#4072—21no—
102#4072—21no—
103#4072—21no—
104#4072—21no—
105#4072—21no—
106C2×C4⋊Dic5—21no—
107C2×C4⋊Dic5D412yescomplemented
108C2×C4×Dic5—21no—
109C2×C4×Dic5D412yescomplemented
110C2×#681—21no—
111C2×#681—21no—
112C2×#681—21no—
113C2×#681—21no—
114C2×#681—21no—
115C2×#681—21no—
116C2×#681—21no—
117C2×#681—21no—
118C2×#681—21no—
119C2×#681—21no—
120C2×#681—21no—
121C2×#681D412yescomplemented
122C22×#168—21no—
123C22×#168D412yescomplemented
124#3969—28no—
125#3967—24no—
126#3964—24no—
127#3963—24no—
128C22⋊#168—28no—
129C2×#525D511yescharacteristic
130C2×#421—51no—
131#2896—51no—
132C2×#407—51no—
133#2280—51no—
134#1733—51no—
135C2×H(3,ℤ/4)—51no—
136C24×C5—21no—
137C24×C5—21no—
138C24×C5—21no—
139C24×C5—21no—
140C24×C5—21no—
141C24×C5—21no—
142C24×C5—21no—
143C24×C5—44no—
144C24×C5C22⋊C412yes—
145C24×C5C2×D411yescharacteristic
146C5×#41—22no—
147C5×#41—22no—
148C5×#41—22no—
149C5×#41—22no—
150C5×#41—22no—
151C5×#41—22no—
152C5×#41—22no—
153C5×#41—22no—
154C5×#41—41no—
155C5×#41—41no—
156C5×#41—41no—
157C5×#41—41no—
158C5×#41—41no—
159C5×#41—41no—
160C5×#41—41no—
161C5×#41—41no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8C22⋊C412yescomplemented
168C2×C5×D4—28no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—48no—
177C2×C5×D4—41no—
178C2×C5×D4—41no—
179C2×C5×D4—41no—
180C2×C5×D4—41no—
181C2×C5×D4C22⋊C412yescomplemented
182C22×C4×C5—22no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—41no—
205C22×C4×C5—41no—
206C22×C4×C5—41no—
207C22×C4×C5—41no—
208C22×C4×C5—41no—
209C22×C4×C5—41no—
210C22×C4×C5—41no—
211C22×C4×C5—41no—
212C22×C4×C5—41no—
213C22×C4×C5—41no—
214C22×C4×C5—41no—
215C22×C4×C5—41no—
216C22×C4×C5—41no—
217C22×C4×C5—41no—
218C22×C4×C5—41no—
219C22×C4×C5—41no—
220C22×C4×C5—41no—
221C22×C4×C5—41no—
222C22×C4×C5—41no—
223C22×C4×C5—41no—
224C22×C4×C5C22⋊C412yes—
225C22×C4×C5C22×C411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D411yescharacteristic
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5#4111yescharacteristic
236C22×C4×C5#4111yescharacteristic
237C22×C4×C5#4111yescharacteristic
238C22×C4×C5#4111yescharacteristic
239C22×Dic5—22no—
240C22×Dic5—22no—
241C5×C4⋊C4—28no—
242C5×C4⋊C4—22no—
243C5×C4⋊C4—22no—
244C5×C22⋊C4—28no—
245C5×C22⋊C4—28no—
246C5×C22⋊C4—22no—
247C5×C22⋊C4—22no—
248C42×C5—22no—
249C42×C5C22⋊C414yescomplemented
250C22⋊Dic5—48no—
251C22⋊Dic5—41no—
252C22⋊Dic5—41no—
253C22⋊Dic5—41no—
254C22⋊Dic5—41no—
255C4⋊Dic5—22no—
256C4⋊Dic5—22no—
257C4⋊Dic5—41no—
258C4⋊Dic5—41no—
259C4×Dic5—22no—
260C4×Dic5—22no—
261C4×Dic5—41no—
262C4×Dic5—41no—
263#681—22no—
264#681—22no—
265#681—41no—
266#681—41no—
267#681—41no—
268#681—41no—
269#681—41no—
270#681—41no—
271C2×#168—22no—
272C2×#168—22no—
273C2×#168—22no—
274C2×#168—22no—
275C2×#168—41no—
276C2×#168—41no—
277C22×#41C2×D511yescharacteristic
278C24×C4C2×D511yescharacteristic
279C22×M16—51no—
280C22×M16—51no—
281#525—22no—
282#525—22no—
283#525—22no—
284#525Dic514yescomplemented
285C2×#123—21no—
286C2×C22⋊Q8—21no—
287C2×#121—21no—
288C2×#120—21no—
289C2×C4×D4—22no—
290C2×#117—51no—
291C2×#117—51no—
292C2×#117C2×D511yescharacteristic
293#421—102no—
294#421—102no—
295C2×#104—102no—
296#419—101no—
297#418—101no—
298#417—102no—
299#416—102no—
300#407—102no—
301#407—102no—
302C2×C22⋊C8—102no—
303#381—101no—
304#380—102no—
305#379—101no—
306C4×C22⋊C4—102no—
307#339—102no—
308H(3,ℤ/4)—102no—
309C23×C5—24no—
310C23×C5—24no—
311C23×C5—24no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—44no—
317C23×C5—42no—
318C23×C5—42no—
319C23×C5—42no—
320C23×C5—42no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5—44no—
324C23×C5—44no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5C2×C22⋊C411yescharacteristic
332C23×C5#12011yescharacteristic
333C23×C5#12011yescharacteristic
334C23×C5#12011yescharacteristic
335C23×C5#12111yescharacteristic
336C23×C5#12111yescharacteristic
337C23×C5#12311yescharacteristic
338C5×Q8—22no—
339C5×Q8—22no—
340C5×Q8—41no—
341C5×Q8—41no—
342C5×D4—22no—
343C5×D4—22no—
344C5×D4—416no—
345C5×D4—42no—
346C5×D4—42no—
347C5×D4—42no—
348C5×D4—42no—
349C5×D4—41no—
350C5×D4—41no—
351C2×C4×C5—24no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—44no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—42no—
364C2×C4×C5—42no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—42no—
368C2×C4×C5—42no—
369C2×C4×C5—42no—
370C2×C4×C5—42no—
371C2×C4×C5—42no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5C2×C22⋊C411yescharacteristic
376C2×C4×C5C2×C22⋊C411yescharacteristic
377C2×C4×C5C4×D411yescharacteristic
378C2×C4×C5C4×D411yescharacteristic
379C2×C4×C5C4×D411yescharacteristic
380C2×C4×C5C4×D411yescharacteristic
381C2×C4×C5#12011yescharacteristic
382C2×C4×C5#12011yescharacteristic
383C2×C4×C5#12011yescharacteristic
384C2×C4×C5#12011yescharacteristic
385C2×C4×C5#12011yescharacteristic
386C2×C4×C5#12111yescharacteristic
387C2×C4×C5#12111yescharacteristic
388C2×C4×C5#12111yescharacteristic
389C2×C4×C5#12111yescharacteristic
390C2×C4×C5#12111yescharacteristic
391C2×C4×C5#12111yescharacteristic
392C2×C4×C5#12111yescharacteristic
393C2×C4×C5#12111yescharacteristic
394C2×C4×C5#12111yescharacteristic
395C2×C4×C5#12111yescharacteristic
396C2×C4×C5#12311yescharacteristic
397C2×C4×C5#12311yescharacteristic
398C2×C4×C5#12311yescharacteristic
399C2×C4×C5#12411yescharacteristic
400C2×C4×C5#12411yescharacteristic
401C2×C4×C5#12711yescharacteristic
402C2×C4×C5#12711yescharacteristic
403C2×Dic5—44no—
404C2×Dic5—44no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407#168—42no—
408#168—42no—
409C25C22⋊D511yescharacteristic
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41C2×Dic512yes—
421C2×#41C22⋊D512yes—
422C22×Q8C22⋊D511yescharacteristic
423C22×D4—22no—
424C22×D4—21no—
425C22×D4C22⋊D511yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4C2×Dic512yes—
440C23×C4C22⋊D511yescharacteristic
441C23×C4C22⋊D512yes—
442C23×C4C22×D511yescharacteristic
443C2×M16—52no—
444C2×M16—101no—
445C2×M16—101no—
446C2×M16—101no—
447C2×M16—101no—
448C2×M16—101no—
449C2×M16—101no—
450C2×M16—101no—
451C2×M16—101no—
452C2×M16—101no—
453C2×M16—101no—
454C2×M16—101no—
455C22×C8—52no—
456C22×C8—101no—
457#123—24no—
458#123—24no—
459C22⋊Q8—24no—
460C22⋊Q8—24no—
461#121—24no—
462#121—24no—
463#120—24no—
464#120—24no—
465C4×D4—28no—
466C4×D4—28no—
467#117—21no—
468#117—21no—
469#117—101no—
470#117—101no—
471#117—101no—
472#117—101no—
473#117—101no—
474#117—101no—
475#117—101no—
476#117—101no—
477#117C2×Dic512yes—
478#117C22⋊D512yes—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—52no—
482C2×C4⋊C4—101no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—104no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C42—52no—
490C2×C42—101no—
491C2×C42C22⋊D512yes—
492#104—108no—
493#103—104no—
494#102—104no—
495C22⋊C8—108no—
496#95—104no—
497C22×C5—22no—
498C22×C5—22no—
499C22×C5—22no—
500C22×C5—24no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5—44no—
508C22×C5—42no—
509C22×C5—42no—
510C22×C5—42no—
511C22×C5—44no—
512C22×C5—44no—
513C22×C5—44no—
514C22×C5—42no—
515C22×C5—44no—
516C22×C5—42no—
517C22×C5—82no—
518C22×C5—82no—
519C22×C5#37911yescharacteristic
520C22×C5#38611yescharacteristic
521C22×C5#38611yescharacteristic
522C22×C5#39211yescharacteristic
523C22×C5#39211yescharacteristic
524C22×C5#39411yescharacteristic
525C22×C5#39411yescharacteristic
526C4×C5—44no—
527C4×C5—42no—
528C4×C5—42no—
529C4×C5#38611yescharacteristic
530C4×C5#38611yescharacteristic
531C4×C5#39011yescharacteristic
532C4×C5#39011yescharacteristic
533C4×C5#39211yescharacteristic
534C4×C5#39211yescharacteristic
535C4×C5#39411yescharacteristic
536C4×C5#39411yescharacteristic
537Dic5—82no—
538Dic5—82no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—44no—
547C24C22⋊Dic512yes—
548C24C2×C22⋊D511yescharacteristic
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8C22⋊Dic512yescomplemented
571C2×D4—28no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—48no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4C22⋊Dic512yescomplemented
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4C22⋊Dic512yes—
630C22×C4D4×D511yescharacteristic
631C22×C4D4×D511yescharacteristic
632C22×C4D4×D511yescharacteristic
633C22×C4D4×D511yescharacteristic
634C22×C4#71111yescharacteristic
635C22×C4#71111yescharacteristic
636C22×C4#71111yescharacteristic
637C22×C4#71111yescharacteristic
638C22×C4C22×Dic511yescharacteristic
639C22×C4C2×C22⋊D511yescharacteristic
640C22×C4C2×C22⋊D511yescharacteristic
641C22×C4C2×C22⋊D511yescharacteristic
642C22×C4C2×C22⋊D511yescharacteristic
643C22×C4C2×C22⋊D511yescharacteristic
644M16—102no—
645M16—102no—
646M16—201no—
647M16—201no—
648M16—201no—
649M16—201no—
650M16—201no—
651M16—201no—
652C2×C8—102no—
653C2×C8—102no—
654C2×C8—102no—
655C2×C8—102no—
656C2×C8—201no—
657C2×C8—201no—
658C4⋊C4—28no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—102no—
662C4⋊C4—102no—
663C4⋊C4—201no—
664C4⋊C4—201no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—208no—
670C22⋊C4—201no—
671C22⋊C4—201no—
672C22⋊C4—201no—
673C22⋊C4—201no—
674C42—22no—
675C42—102no—
676C42—102no—
677C42—201no—
678C42—201no—
679C42C22⋊Dic514yescomplemented
680C2×C5—21no—
681C2×C5—21no—
682C2×C5—21no—
683C2×C5—21no—
684C2×C5—21no—
685C2×C5—21no—
686C2×C5—44no—
687C2×C5—82no—
688C2×C5#143811yescharacteristic
689C2×C5#201012yes—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23#408111yescharacteristic
713C23#408311yescharacteristic
714C23#408511yescharacteristic
715C23#408511yescharacteristic
716C23C2×C22⋊Dic511yescharacteristic
717C23#409911yescharacteristic
718C23#409911yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—416no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—41no—
731D4—41no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—44no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—204no—
757C2×C4—204no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4D4×Dic511yescharacteristic
761C2×C4D4×Dic511yescharacteristic
762C2×C4D4×Dic511yescharacteristic
763C2×C4D4×Dic511yescharacteristic
764C2×C4#408111yescharacteristic
765C2×C4#408111yescharacteristic
766C2×C4#408111yescharacteristic
767C2×C4#408211yescharacteristic
768C2×C4#408211yescharacteristic
769C2×C4#408311yescharacteristic
770C2×C4#408311yescharacteristic
771C2×C4#408311yescharacteristic
772C2×C4#408411yescharacteristic
773C2×C4#408411yescharacteristic
774C2×C4#408411yescharacteristic
775C2×C4#408411yescharacteristic
776C2×C4#408511yescharacteristic
777C2×C4#408511yescharacteristic
778C2×C4#408511yescharacteristic
779C2×C4#408511yescharacteristic
780C2×C4#408511yescharacteristic
781C2×C4#408511yescharacteristic
782C2×C4#408611yescharacteristic
783C2×C4#408611yescharacteristic
784C2×C4C2×C22⋊Dic511yescharacteristic
785C2×C4C2×C22⋊Dic511yescharacteristic
786C2×C4#409911yescharacteristic
787C2×C4#409911yescharacteristic
788C8—202no—
789C8—202no—
790C5#1099411yescharacteristic, complemented, Sylow
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—42no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22#6550911yescharacteristic
814C22#6550911yescharacteristic
815C22#6551111yescharacteristic
816C22#6551111yescharacteristic
817C22#6551211yescharacteristic
818C22#6551211yescharacteristic
819C22#6553611yescharacteristic
820C4—44no—
821C4—42no—
822C4—42no—
823C4—402no—
824C4—402no—
825C4#6550911yescharacteristic
826C4#6550911yescharacteristic
827C4#6551011yescharacteristic
828C4#6551011yescharacteristic
829C4#6551111yescharacteristic
830C4#6551111yescharacteristic
831C4#6551211yescharacteristic
832C4#6551211yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—44no—
840C2—82no—
841C2#1060250812yes—
842C2#1060292411yescharacteristic
subgroupG/H
centerC2×C4#4086
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
Fitting, prime radicalC2×C5×#525C2
socleC22×C5#392
cosocleC23×C4×C5C23
hypercenterC2×#525D5
hypocenterC5#10994
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. C2×#65525C2semidirect
3. #10615803C2semidirect
4. #10615758C2semidirect
5. C2×#65496C2semidirect
6. #10602371C2semidirect
7. C2×#64751C2semidirect
13. C5×#525C4semidirect
107. C2×C4⋊Dic5D4semidirect
109. C2×C4×Dic5D4semidirect
121. C2×#681D4semidirect
123. C22×#168D4semidirect
167. C2×C5×Q8C22⋊C4semidirect
181. C2×C5×D4C22⋊C4semidirect
249. C42×C5C22⋊C4semidirect
284. #525Dic5semidirect
570. C2×Q8C22⋊Dic5semidirect
584. C2×D4C22⋊Dic5semidirect
679. C42C22⋊Dic5semidirect
790. C5#10994semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5252
C2×#655252
#106158032
#106157582
C2×#654962
#106023712
C2×#647512
#109945