Finite Group Databasebeta

← #12116675

Subgroups — #12116675

Order 1280.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615806C211yesmaximal, characteristic
2#10615803C211yesmaximal, characteristic
3#10610352C211yesmaximal, characteristic, complemented
4C5×#1789C211yesmaximal, characteristic
5#10601169C211yesmaximal, characteristic, complemented
6#10601169C211yesmaximal, characteristic, complemented
7#10601165C211yesmaximal, characteristic, complemented
8#10601164C211yesmaximal, characteristic, complemented
9#10601163C211yesmaximal, characteristic, complemented
10#10601162C211yesmaximal, characteristic, complemented
11#10601160C211yesmaximal, characteristic, complemented
12#10601160C211yesmaximal, characteristic, complemented
13#10600776C211yesmaximal, characteristic, complemented
14#10600241C211yesmaximal, characteristic, complemented
15#10600235C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C2×#4094C2211yescharacteristic
18C2×#4094C2211yescharacteristic
19C2×#4072C2211yescharacteristic
20C22×#681C2211yescharacteristic
21C2×C5×#104C2211yescharacteristic
22C2×C5×#104C2211yescharacteristic
23C2×C5×#104C2211yescharacteristic
24C2×C5×#104C2211yescharacteristic
25C5×#407C2211yescharacteristic
26C4×C5×C22⋊C4C2211yescharacteristic
27#65523—21no—
28#65523—21no—
29#65523C2211yescharacteristic
30#65523C2211yescharacteristic
31#65522C2211yescharacteristic
32#65522C2211yescharacteristic
33#65522C2211yescharacteristic
34#65522C2211yescharacteristic
35#65521C411yescharacteristic, complemented
36#65521C411yescharacteristic, complemented
37#65521C411yescharacteristic, complemented
38#65521C411yescharacteristic, complemented
39#65514C411yescharacteristic, complemented
40#65514C411yescharacteristic, complemented
41#65504C411yescharacteristic, complemented
42#65504C411yescharacteristic, complemented
43#65496—21no—
44#65496C2211yescharacteristic
45C2×C22⋊#168—21no—
46C2×C22⋊#168C2211yescharacteristic
47C2×#3954C2211yescharacteristic, complemented
48C2×#3954C2211yescharacteristic, complemented
49#65411C2211yescharacteristic, complemented
50#65411C2211yescharacteristic, complemented
51#65408C2211yescharacteristic, complemented
52#65408C2211yescharacteristic, complemented
53C2×#3935C2211yescharacteristic, complemented
54C2×C4×#168C2211yescharacteristic, complemented
55#65009—21no—
56#65009—21no—
57#65008—21no—
58#65007—21no—
59#64778C2211yescharacteristic, complemented
60#64778C2211yescharacteristic, complemented
61#64744C2211yescharacteristic, complemented
62#64744C2211yescharacteristic, complemented
63#64743C2211yescharacteristic, complemented
64#64743C2211yescharacteristic, complemented
65#64743C2211yescharacteristic, complemented
66#64743C2211yescharacteristic, complemented
67#22588—51nomaximal, Sylow
68C2×C5×#41—21no—
69C2×C5×#41—21no—
70C2×C5×#41—22no—
71C2×C5×#41—22no—
72C2×C5×#41—41no—
73C2×C5×#41—41no—
74C2×C5×#41C2×C411yescharacteristic
75C2×C5×#41C2×C411yescharacteristic
76C2×C5×#41C2311yescharacteristic
77C2×C5×#41C2311yescharacteristic
78C22×C5×Q8C2×C411yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2×C411yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5C2311yescharacteristic
83C2×C5×M16C2311yescharacteristic
84C2×C5×M16C2311yescharacteristic
85C2×C5×C22⋊C4—21no—
86C2×C42×C5C2311yescharacteristic
87C2×C42×C5C2311yescharacteristic
88C2×C22⋊Dic5—21no—
89#4094—22no—
90#4094—22no—
91#4094—41no—
92#4094—41no—
93#4072—21no—
94#4072—21no—
95#4072C2×C411yescharacteristic
96#4072C2×C411yescharacteristic
97#4072C2311yescharacteristic
98#4072C2311yescharacteristic
99C2×C4⋊Dic5C2×C411yescharacteristic
100C2×C4⋊Dic5C2×C411yescharacteristic
101C2×C4×Dic5—21no—
102C2×#681—21no—
103C2×#681—21no—
104C2×#681—41no—
105C2×#681—41no—
106C2×#681C2×C411yescharacteristic
107C2×#681C2×C411yescharacteristic
108C2×#681C2×C411yescharacteristic
109C2×#681C2×C411yescharacteristic
110C2×#681C2311yescharacteristic
111C2×#681C2311yescharacteristic
112C22×#168—21no—
113C22×#168—21no—
114C22×#168C2311yescharacteristic
115C22×#168C2311yescharacteristic
116C22×#168C2311yescharacteristic
117C22×#168C2311yescharacteristic
118C5×#104—22no—
119C5×#104—22no—
120C5×#104—41no—
121C5×#104—41no—
122C5×C22⋊C8—21no—
123C5×C22⋊C8—21no—
124C5×#95—21no—
125#3967C2×C411yescharacteristic
126#3967C2×C411yescharacteristic
127#3967C2×C411yescharacteristic
128#3967C2×C411yescharacteristic
129#3967C2×C411yescharacteristic
130#3967C2×C411yescharacteristic
131#3967C2×C411yescharacteristic
132#3967C2×C411yescharacteristic
133#3964C2×C411yescharacteristic
134#3964C2×C411yescharacteristic
135#3964C2×C411yescharacteristic
136#3964C2×C411yescharacteristic
137#3964C2×C411yescharacteristic
138#3964C2×C411yescharacteristic
139#3964C2×C411yescharacteristic
140#3964C2×C411yescharacteristic
141C22⋊#168—21no—
142C22⋊#168—21no—
143C22⋊#168—21no—
144C22⋊#168—21no—
145C22⋊#168—21no—
146C22⋊#168—21no—
147C22⋊#168D411yescharacteristic
148C22⋊#168D411yescharacteristic
149C22⋊#168D411yescharacteristic
150C22⋊#168D411yescharacteristic
151#3954—41no—
152#3954—41no—
153#3947—21no—
154#3947—21no—
155#3946—21no—
156#3946—21no—
157#3946—21no—
158#3946—21no—
159C8×Dic5—21no—
160C8×Dic5—21no—
161#3935—41no—
162C4×#168—41no—
163#2924—51no—
164#2896—51no—
165#2880—51no—
166#1938—51no—
167#1937—51no—
168#1929—51no—
169#1929—51no—
170#1866—51no—
171#1866—51no—
172#1826—51no—
173#1811—51no—
174#1789D511yescharacteristic
175#1765—51no—
176#1764—51no—
177#1753—51no—
178C24×C5—21no—
179C24×C5#4111yescharacteristic
180C5×#41—21no—
181C5×#41—21no—
182C5×#41—22no—
183C5×#41—22no—
184C5×#41—21no—
185C5×#41—21no—
186C5×#41—21no—
187C5×#41—21no—
188C5×#41—42no—
189C5×#41—42no—
190C5×#41—41no—
191C5×#41—41no—
192C5×#41—42no—
193C5×#41—42no—
194C5×#41#4112yes—
195C5×#41#4112yes—
196C2×C5×Q8—21no—
197C2×C5×Q8—22no—
198C2×C5×Q8—41no—
199C2×C5×Q8C22×C411yescharacteristic
200C2×C5×Q8C22×C411yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4—22no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—41no—
208C2×C5×D4—42no—
209C2×C5×D4—42no—
210C2×C5×D4C22×C411yescharacteristic
211C2×C5×D4C22×C411yescharacteristic
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—42no—
224C22×C4×C5—42no—
225C22×C4×C5C22×C411yescharacteristic
226C22×C4×C5C22×C411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5#4111yescharacteristic
230C22×C4×C5C2411yescharacteristic
231C22×Dic5—21no—
232C22×Dic5—21no—
233C5×M16—21no—
234C5×M16—21no—
235C5×M16—21no—
236C5×M16—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C5×C22⋊C4—42no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—21no—
244C22⋊Dic5—21no—
245C22⋊Dic5—21no—
246C22⋊Dic5—21no—
247C22⋊Dic5—21no—
248C4⋊Dic5—21no—
249C4⋊Dic5—21no—
250C4⋊Dic5C22×C411yescharacteristic
251C4⋊Dic5C22×C411yescharacteristic
252C4⋊Dic5C22×C411yescharacteristic
253C4⋊Dic5C22×C411yescharacteristic
254C4×Dic5—21no—
255C4×Dic5—21no—
256C4×Dic5—21no—
257C4×Dic5—21no—
258#681—21no—
259#681—21no—
260#681—21no—
261#681—21no—
262#681—41no—
263#681—41no—
264#681—41no—
265#681—41no—
266#681—42no—
267#681—42no—
268C2×#168—21no—
269C2×#168—21no—
270C2×#168—21no—
271C2×#168—21no—
272C2×#168—21no—
273C2×#168—21no—
274C2×#168—21no—
275C2×#168—21no—
276C2×#168—21no—
277C2×#168—21no—
278C2×#168—42no—
279C2×#168—42no—
280C2×#168C22×C411yescharacteristic
281C2×#168C22×C411yescharacteristic
282C2×#168C22×C411yescharacteristic
283C2×#168C22×C411yescharacteristic
284C2×#168C2×D411yescharacteristic
285C2×#168C2×D411yescharacteristic
286C2×#168C2×D411yescharacteristic
287C2×#168C2×D411yescharacteristic
288C22×#41C2×D511yescharacteristic
289C2×#131—51no—
290C2×#131—51no—
291C22×M16—51no—
292C2×#117—51no—
293#433—101no—
294#433—101no—
295#432—101no—
296#431—101no—
297C2×#108—51no—
298C2×#108—51no—
299#424—51no—
300#424—51no—
301C2×#104C2×D511yescharacteristic
302C2×#104C2×D511yescharacteristic
303C2×#104C2×D511yescharacteristic
304C2×#104C2×D511yescharacteristic
305#419—51no—
306#419—51no—
307#418—51no—
308#418—51no—
309#417—51no—
310#417—51no—
311#417—51no—
312#417—51no—
313#416—51no—
314#416—51no—
315#416—51no—
316#416—51no—
317#408—51no—
318#408—51no—
319#408—101no—
320#408—101no—
321#407—51no—
322#407—101no—
323#407C2×D511yescharacteristic
324C2×C22⋊C8—51no—
325C2×C22⋊C8—101no—
326#405—51no—
327#405—51no—
328C2×#97—51no—
329C2×C4×C8—51no—
330C4×C22⋊C4C2×D511yescharacteristic
331#341—51no—
332#341—51no—
333#339—51no—
334#339—51no—
335#339—51no—
336#339—51no—
337#336—51no—
338#336—51no—
339C23×C5—21no—
340C23×C5—21no—
341C23×C5—21no—
342C23×C5—21no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—42no—
346C23×C5—42no—
347C23×C5—81no—
348C23×C5C4×D411yescharacteristic
349C23×C5C4×D411yescharacteristic
350C23×C5C2×#4111yescharacteristic
351C5×Q8—21no—
352C5×Q8—21no—
353C5×Q8—21no—
354C5×Q8—42no—
355C5×Q8#11712yes—
356C5×D4—22no—
357C5×D4—22no—
358C5×D4—21no—
359C5×D4—21no—
360C5×D4—21no—
361C5×D4—42no—
362C5×D4—42no—
363C5×D4—42no—
364C5×D4—41no—
365C5×D4—41no—
366C5×D4#11712yes—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—21no—
372C2×C4×C5—21no—
373C2×C4×C5—21no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—21no—
377C2×C4×C5—21no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—22no—
381C2×C4×C5—21no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5C4×D411yescharacteristic
393C2×C4×C5C4×D411yescharacteristic
394C2×C4×C5C23×C411yescharacteristic
395C2×C4×C5C22×D411yescharacteristic
396C2×C4×C5C2×#4111yescharacteristic
397C2×C4×C5C2×#4111yescharacteristic
398C2×C4×C5H(5,𝔽2)11yescharacteristic
399C2×C4×C5H(5,𝔽2)11yescharacteristic
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—42no—
405C2×Dic5—81no—
406C5×C8—41no—
407C5×C8—41no—
408#168—21no—
409#168—21no—
410#168—21no—
411#168—21no—
412#168—21no—
413#168—21no—
414#168—21no—
415#168—21no—
416#168—41no—
417#168—41no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41C4×D511yescharacteristic
425C2×#41C4×D511yescharacteristic
426C2×#41C22×D511yescharacteristic
427C2×#41C22×D511yescharacteristic
428C22×Q8C4×D511yescharacteristic
429C22×D4—21no—
430C22×D4C4×D511yescharacteristic
431C23×C4—21no—
432C23×C4C22×D511yescharacteristic
433#131—102no—
434#131—102no—
435#131—201no—
436#131—201no—
437C2×M16—51no—
438C2×M16—51no—
439C2×M16—51no—
440C2×M16—51no—
441C2×M16—51no—
442C2×M16—51no—
443C2×M16—101no—
444C2×M16—101no—
445C2×M16—201no—
446C2×M16—201no—
447C2×M16C22×D511yescharacteristic
448C2×M16C22×D511yescharacteristic
449C22×C8—51no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—51no—
453C22×C8—101no—
454C22×C8—101no—
455#117—51no—
456#117—51no—
457#117—51no—
458#117—51no—
459#117—101no—
460#117—101no—
461C2×C4⋊C4—51no—
462C2×C4⋊C4—51no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—101no—
465C2×C42—101no—
466C2×C42C22×D511yescharacteristic
467C2×C42C22×D511yescharacteristic
468#108—201no—
469#108—201no—
470C4⋊C8—101no—
471C4⋊C8—101no—
472C4⋊C8—101no—
473C4⋊C8—101no—
474#104—22no—
475#104—22no—
476#104—41no—
477#104—41no—
478#103—51no—
479#103—51no—
480#103—51no—
481#103—51no—
482#103—51no—
483#103—51no—
484#103—51no—
485#103—51no—
486#102—51no—
487#102—51no—
488#102—51no—
489#102—51no—
490#102—51no—
491#102—51no—
492#102—51no—
493#102—51no—
494C22⋊C8—21no—
495C22⋊C8—21no—
496C22⋊C8—51no—
497C22⋊C8—51no—
498C22⋊C8—51no—
499C22⋊C8—51no—
500C22⋊C8—101no—
501C22⋊C8—101no—
502C22⋊C8—101no—
503C22⋊C8—101no—
504C22⋊C8—101no—
505C22⋊C8—101no—
506#97—101no—
507#97—101no—
508#97—201no—
509C4×C8—101no—
510C4×C8—101no—
511C4×C8—201no—
512#95—21no—
513C22×C5—21no—
514C22×C5—21no—
515C22×C5—21no—
516C22×C5—21no—
517C22×C5—22no—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—21no—
521C22×C5—21no—
522C22×C5—41no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5—81no—
528C22×C5—81no—
529C22×C5—84no—
530C22×C5C2×C4×D411yescharacteristic
531C22×C5#55111yescharacteristic
532C22×C5#55111yescharacteristic
533C4×C5—21no—
534C4×C5—21no—
535C4×C5—22no—
536C4×C5—42no—
537C4×C5—41no—
538C4×C5—81no—
539C4×C5C2×#11711yescharacteristic
540C4×C5#51811yescharacteristic
541C4×C5#54611yescharacteristic
542C4×C5#54611yescharacteristic
543Dic5—41no—
544Dic5—41no—
545Dic5—41no—
546Dic5—41no—
547C24—21no—
548C24#71111yescharacteristic
549#41—21no—
550#41—21no—
551#41—22no—
552#41—22no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—42no—
558#41—42no—
559#41—41no—
560#41—41no—
561#41—42no—
562#41—42no—
563#41#71112yes—
564#41#71112yes—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—41no—
568C2×Q8C2×C4×D511yescharacteristic
569C2×Q8C2×C4×D511yescharacteristic
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—41no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4C2×C4×D511yescharacteristic
580C2×D4C2×C4×D511yescharacteristic
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4C2×C4×D511yescharacteristic
597C22×C4C2×C4×D511yescharacteristic
598C22×C4D4×D511yescharacteristic
599C22×C4D4×D511yescharacteristic
600C22×C4#71111yescharacteristic
601C22×C4C23×D511yescharacteristic
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—101no—
607M16—101no—
608M16—101no—
609M16—101no—
610M16—201no—
611M16—201no—
612M16—201no—
613M16—201no—
614M16—202no—
615M16—202no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—51no—
619C2×C8—51no—
620C2×C8—51no—
621C2×C8—51no—
622C2×C8—51no—
623C2×C8—51no—
624C2×C8—51no—
625C2×C8—51no—
626C2×C8—101no—
627C2×C8—101no—
628C2×C8—101no—
629C2×C8—101no—
630C2×C8—101no—
631C2×C8—101no—
632C2×C8—101no—
633C2×C8—101no—
634C2×C8—101no—
635C2×C8—101no—
636C2×C8—202no—
637C2×C8—202no—
638C4⋊C4—51no—
639C4⋊C4—51no—
640C4⋊C4—51no—
641C4⋊C4—51no—
642C4⋊C4—101no—
643C4⋊C4—101no—
644C22⋊C4—42no—
645C22⋊C4—101no—
646C22⋊C4—101no—
647C22⋊C4—101no—
648C22⋊C4—101no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—101no—
654C42—101no—
655C42—101no—
656C42—101no—
657C2×C5—21no—
658C2×C5—21no—
659C2×C5—41no—
660C2×C5—41no—
661C2×C5—42no—
662C2×C5—81no—
663C2×C5#234211yescharacteristic
664C2×C5#295511yescharacteristic
665C2×C5#295611yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—81no—
675C23#402711yescharacteristic
676C23#402711yescharacteristic
677C23C2×#71111yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—42no—
682Q8#402312yes—
683D4—22no—
684D4—22no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—41no—
692D4—41no—
693D4#402312yes—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—101no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—202no—
724C2×C4—401no—
725C2×C4#402711yescharacteristic
726C2×C4#402711yescharacteristic
727C2×C4C22×C4×D511yescharacteristic
728C2×C4C2×D4×D511yescharacteristic
729C2×C4C2×#71111yescharacteristic
730C2×C4C2×#71111yescharacteristic
731C2×C4#414411yescharacteristic
732C2×C4#414411yescharacteristic
733C8—41no—
734C8—41no—
735C8—101no—
736C8—101no—
737C8—101no—
738C8—101no—
739C8—101no—
740C8—101no—
741C8—101no—
742C8—101no—
743C8—201no—
744C8—201no—
745C5#2258811yescharacteristic, complemented, Sylow
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×#402711yescharacteristic
764C22#6592111yescharacteristic
765C22#6592111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—81no—
772C4—201no—
773C4—201no—
774C4—201no—
775C4—201no—
776C4C2×#402311yescharacteristic
777C4#6582011yescharacteristic
778C4#6592511yescharacteristic
779C4#6592511yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1060555311yescharacteristic
787C2#1061071111yescharacteristic
788C2#1061072011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1789C2
socleC22×C5C2×C4×D4
prime radicalC22×C5×#41C22
cosocleC22×C4×C5C24
hypercenter#1789D5
hypocenterC5#22588
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
3. #10610352C2semidirect
5. #10601169C2semidirect
6. #10601169C2semidirect
7. #10601165C2semidirect
8. #10601164C2semidirect
9. #10601163C2semidirect
10. #10601162C2semidirect
11. #10601160C2semidirect
12. #10601160C2semidirect
13. #10600776C2semidirect
14. #10600241C2semidirect
15. #10600235C2semidirect
35. #65521C4semidirect
36. #65521C4semidirect
37. #65521C4semidirect
38. #65521C4semidirect
39. #65514C4semidirect
40. #65514C4semidirect
41. #65504C4semidirect
42. #65504C4semidirect
47. C2×#3954C22semidirect
48. C2×#3954C22semidirect
49. #65411C22semidirect
50. #65411C22semidirect
51. #65408C22semidirect
52. #65408C22semidirect
53. C2×#3935C22semidirect
54. C2×C4×#168C22semidirect
59. #64778C22semidirect
60. #64778C22semidirect
61. #64744C22semidirect
62. #64744C22semidirect
63. #64743C22semidirect
64. #64743C22semidirect
65. #64743C22semidirect
66. #64743C22semidirect
745. C5#22588semidirect

Maximal subgroups

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

subgroupindex
#106158062
#106158032
#106103522
C5×#17892
#106011692
#106011652
#106011642
#106011632
#106011622
#106011602
#106007762
#106002412
#106002352
#225885