Finite Group Databasebeta

← #12116667

Subgroups — #12116667

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
1C5×#2880C211yesmaximal, characteristic
2#10615803C211yesmaximal, characteristic
3#10610315C211yesmaximal, characteristic, complemented
4#10602931C211yesmaximal, characteristic
5#10602810C211yesmaximal, characteristic, complemented
6#10602810C211yesmaximal, characteristic, complemented
7#10602802C211yesmaximal, characteristic, complemented
8#10602801C211yesmaximal, characteristic, complemented
9#10600791C211yesmaximal, characteristic, complemented
10#10600790C211yesmaximal, characteristic, complemented
11#10600789C211yesmaximal, characteristic, complemented
12#10600789C211yesmaximal, characteristic, complemented
13#10600776C211yesmaximal, characteristic, complemented
14#10600768C211yesmaximal, characteristic, complemented
15#10600742C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C2×C5×#131C2211yescharacteristic
18C2×C5×#131C2211yescharacteristic
19C2×#4072C2211yescharacteristic
20C22×#681C2211yescharacteristic
21C5×#408—21no—
22C5×#408—21no—
23C5×#408C2211yescharacteristic
24C5×#408C2211yescharacteristic
25C5×#407—21no—
26C5×#407C2211yescharacteristic
27C2×C5×C22⋊C8—21no—
28C2×C5×C22⋊C8C2211yescharacteristic
29C2×#3969C2211yescharacteristic
30C2×#3969C2211yescharacteristic
31C2×#3969C2211yescharacteristic
32C2×#3969C2211yescharacteristic
33#65522C2211yescharacteristic
34#65522C2211yescharacteristic
35#65522C2211yescharacteristic
36#65522C2211yescharacteristic
37#65521C411yescharacteristic, complemented
38#65521C411yescharacteristic, complemented
39#65521C411yescharacteristic, complemented
40#65521C411yescharacteristic, complemented
41#65514C411yescharacteristic, complemented
42#65514C411yescharacteristic, complemented
43#65504C411yescharacteristic, complemented
44#65504C411yescharacteristic, complemented
45C4×C22⋊Dic5C2211yescharacteristic
46#65496C2211yescharacteristic
47C2×#3954C2211yescharacteristic, complemented
48C2×#3954C2211yescharacteristic, complemented
49#65391C2211yescharacteristic, complemented
50#65391C2211yescharacteristic, complemented
51#65390C2211yescharacteristic, complemented
52#65390C2211yescharacteristic, complemented
53C2×#3947C2211yescharacteristic, complemented
54C2×C8×Dic5C2211yescharacteristic, complemented
55#65009—21no—
56#65009—21no—
57#65008—21no—
58#65007—21no—
59#64778C2211yescharacteristic, complemented
60#64778C2211yescharacteristic, complemented
61#64775C2211yescharacteristic, complemented
62#64775C2211yescharacteristic, complemented
63#64775C2211yescharacteristic, complemented
64#64775C2211yescharacteristic, complemented
65#64770C2211yescharacteristic, complemented
66#64770C2211yescharacteristic, 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
83C5×#131—22no—
84C5×#131—22no—
85C5×#131—41no—
86C5×#131—41no—
87C2×C5×M16—21no—
88C2×C5×M16—21no—
89C2×C5×M16C2311yescharacteristic
90C2×C5×M16C2311yescharacteristic
91C22×C5×C8—21no—
92C22×C5×C8—21no—
93C22×C5×C8C2311yescharacteristic
94C22×C5×C8C2311yescharacteristic
95C2×C22⋊Dic5—21no—
96C2×C22⋊Dic5—21no—
97#4072—21no—
98#4072—21no—
99#4072C2×C411yescharacteristic
100#4072C2×C411yescharacteristic
101#4072C2311yescharacteristic
102#4072C2311yescharacteristic
103C2×C4⋊Dic5C2×C411yescharacteristic
104C2×C4⋊Dic5C2×C411yescharacteristic
105C2×C4×Dic5—21no—
106C2×C4×Dic5C2311yescharacteristic
107C2×C4×Dic5C2311yescharacteristic
108C2×#681—41no—
109C2×#681—41no—
110C2×#681C2×C411yescharacteristic
111C2×#681C2×C411yescharacteristic
112C2×#681C2×C411yescharacteristic
113C2×#681C2×C411yescharacteristic
114C2×#681C2311yescharacteristic
115C2×#681C2311yescharacteristic
116C22×#168C2311yescharacteristic
117C22×#168C2311yescharacteristic
118C5×C22⋊C8—21no—
119C5×C22⋊C8—21no—
120C5×C22⋊C8—21no—
121C5×C22⋊C8—21no—
122C5×C22⋊C8—21no—
123C5×C22⋊C8—21no—
124C5×C22⋊C8D411yescharacteristic
125C5×C22⋊C8D411yescharacteristic
126C5×C22⋊C8D411yescharacteristic
127C5×C22⋊C8D411yescharacteristic
128#3969—22no—
129#3969—22no—
130#3969—41no—
131#3969—41no—
132#3967C2×C411yescharacteristic
133#3967C2×C411yescharacteristic
134#3967C2×C411yescharacteristic
135#3967C2×C411yescharacteristic
136#3967C2×C411yescharacteristic
137#3967C2×C411yescharacteristic
138#3967C2×C411yescharacteristic
139#3967C2×C411yescharacteristic
140#3964C2×C411yescharacteristic
141#3964C2×C411yescharacteristic
142#3964C2×C411yescharacteristic
143#3964C2×C411yescharacteristic
144#3964C2×C411yescharacteristic
145#3964C2×C411yescharacteristic
146#3964C2×C411yescharacteristic
147#3964C2×C411yescharacteristic
148#3963—21no—
149C22⋊#168—21no—
150C22⋊#168—21no—
151#3954—41no—
152#3954—41no—
153#3947—21no—
154#3947—21no—
155#3947—41no—
156#3946—21no—
157#3946—21no—
158#3946—21no—
159#3946—21no—
160C8×Dic5—21no—
161C8×Dic5—21no—
162C8×Dic5—41no—
163#2924—51no—
164#2896—51no—
165#2880D511yescharacteristic
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#1789—51no—
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—42no—
222C22×C4×C5—42no—
223C22×C4×C5C22×C411yescharacteristic
224C22×C4×C5C22×C411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5#4111yescharacteristic
228C22×C4×C5C2411yescharacteristic
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C5×M16—21no—
234C5×M16—21no—
235C5×M16—21no—
236C5×M16—21no—
237C5×M16—42no—
238C5×M16—42no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—21no—
243C2×C5×C8—21no—
244C2×C5×C8—21no—
245C2×C5×C8—42no—
246C2×C5×C8—42no—
247C2×C5×C8C2×D411yescharacteristic
248C2×C5×C8C2×D411yescharacteristic
249C2×C5×C8C2×D411yescharacteristic
250C2×C5×C8C2×D411yescharacteristic
251C22⋊Dic5—21no—
252C22⋊Dic5—21no—
253C22⋊Dic5—21no—
254C22⋊Dic5—21no—
255C22⋊Dic5—42no—
256C4⋊Dic5—21no—
257C4⋊Dic5—21no—
258C4⋊Dic5C22×C411yescharacteristic
259C4⋊Dic5C22×C411yescharacteristic
260C4⋊Dic5C22×C411yescharacteristic
261C4⋊Dic5C22×C411yescharacteristic
262C4×Dic5—21no—
263C4×Dic5—21no—
264C4×Dic5—21no—
265C4×Dic5—21no—
266C4×Dic5—21no—
267C4×Dic5—21no—
268C4×Dic5—21no—
269C4×Dic5—21no—
270#681—21no—
271#681—21no—
272#681—21no—
273#681—21no—
274#681—41no—
275#681—41no—
276#681—41no—
277#681—41no—
278C2×#168—21no—
279C2×#168—21no—
280C2×#168—21no—
281C2×#168—21no—
282C2×#168—21no—
283C2×#168—21no—
284C2×#168C22×C411yescharacteristic
285C2×#168C22×C411yescharacteristic
286C2×#168C22×C411yescharacteristic
287C2×#168C22×C411yescharacteristic
288C22×#41C2×D511yescharacteristic
289C2×#131C2×D511yescharacteristic
290C2×#131C2×D511yescharacteristic
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×#104—51no—
302C2×#104—51no—
303C2×#104—51no—
304C2×#104—51no—
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—21no—
318#408—21no—
319#408C2×D511yescharacteristic
320#408C2×D511yescharacteristic
321#407—21no—
322#407—51no—
323#407C2×D511yescharacteristic
324C2×C22⋊C8—21no—
325C2×C22⋊C8C2×D511yescharacteristic
326#405—51no—
327#405—51no—
328C2×#97—51no—
329C2×C4×C8—51no—
330C4×C22⋊C4—51no—
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—21no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5C4×D411yescharacteristic
387C2×C4×C5C4×D411yescharacteristic
388C2×C4×C5C23×C411yescharacteristic
389C2×C4×C5C22×D411yescharacteristic
390C2×C4×C5C2×#4111yescharacteristic
391C2×C4×C5C2×#4111yescharacteristic
392C2×C4×C5H(5,𝔽2)11yescharacteristic
393C2×C4×C5H(5,𝔽2)11yescharacteristic
394C2×Dic5—22no—
395C2×Dic5—21no—
396C2×Dic5—21no—
397C2×Dic5—21no—
398C2×Dic5—21no—
399C2×Dic5—41no—
400C2×Dic5—42no—
401C2×Dic5—41no—
402C2×Dic5—41no—
403C2×Dic5—41no—
404C2×Dic5—41no—
405C2×Dic5—81no—
406C5×C8—21no—
407C5×C8—21no—
408C5×C8—21no—
409C5×C8—21no—
410C5×C8—41no—
411C5×C8—41no—
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—22no—
434#131—22no—
435#131—41no—
436#131—41no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—51no—
440C2×M16—51no—
441C2×M16—51no—
442C2×M16—51no—
443C2×M16—51no—
444C2×M16—51no—
445C2×M16—201no—
446C2×M16—201no—
447C2×M16C22×D511yescharacteristic
448C2×M16C22×D511yescharacteristic
449C22×C8—21no—
450C22×C8—21no—
451C22×C8—51no—
452C22×C8—51no—
453C22×C8C22×D511yescharacteristic
454C22×C8C22×D511yescharacteristic
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—101no—
464C2×C22⋊C4—101no—
465C2×C42—51no—
466C2×C42—51no—
467C2×C42—101no—
468#108—201no—
469#108—201no—
470C4⋊C8—101no—
471C4⋊C8—101no—
472C4⋊C8—101no—
473C4⋊C8—101no—
474#104—102no—
475#104—102no—
476#104—201no—
477#104—201no—
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—21no—
497C22⋊C8—21no—
498C22⋊C8—21no—
499C22⋊C8—21no—
500C22⋊C8—101no—
501C22⋊C8—101no—
502C22⋊C8C22⋊D511yescharacteristic
503C22⋊C8C22⋊D511yescharacteristic
504C22⋊C8C22⋊D511yescharacteristic
505C22⋊C8C22⋊D511yescharacteristic
506#97—101no—
507#97—101no—
508#97—201no—
509C4×C8—101no—
510C4×C8—101no—
511C4×C8—201no—
512#95—101no—
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—41no—
537C4×C5C2×#11711yescharacteristic
538C4×C5#51811yescharacteristic
539C4×C5#54611yescharacteristic
540C4×C5#54611yescharacteristic
541Dic5—42no—
542Dic5—41no—
543Dic5—41no—
544Dic5—41no—
545Dic5—41no—
546Dic5—81no—
547C24—21no—
548C24#70911yescharacteristic
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—42no—
591C22×C4—42no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4C2×C4×D511yescharacteristic
597C22×C4C2×C4×D511yescharacteristic
598C22×C4#70911yescharacteristic
599C22×C4C2×C22⋊D511yescharacteristic
600C22×C4C2×C22⋊D511yescharacteristic
601C22×C4C23×D511yescharacteristic
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—42no—
607M16—42no—
608M16—101no—
609M16—101no—
610M16—101no—
611M16—101no—
612M16—201no—
613M16—201no—
614M16—201no—
615M16—201no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—42no—
623C2×C8—42no—
624C2×C8—51no—
625C2×C8—51no—
626C2×C8—51no—
627C2×C8—51no—
628C2×C8—101no—
629C2×C8—101no—
630C2×C8—101no—
631C2×C8—101no—
632C2×C8—101no—
633C2×C8—101no—
634C2×C8C2×C22⋊D511yescharacteristic
635C2×C8C2×C22⋊D511yescharacteristic
636C2×C8C2×C22⋊D511yescharacteristic
637C2×C8C2×C22⋊D511yescharacteristic
638C4⋊C4—51no—
639C4⋊C4—51no—
640C4⋊C4—51no—
641C4⋊C4—51no—
642C4⋊C4—101no—
643C4⋊C4—101no—
644C22⋊C4—101no—
645C22⋊C4—101no—
646C22⋊C4—101no—
647C22⋊C4—101no—
648C22⋊C4—202no—
649C42—101no—
650C42—101no—
651C42—101no—
652C42—101no—
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—
675C23C4×C22⋊D511yescharacteristic
676C23C4×C22⋊D511yescharacteristic
677C23C2×#70911yescharacteristic
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—21no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—102no—
714C2×C4—101no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—101no—
718C2×C4—201no—
719C2×C4—202no—
720C2×C4—201no—
721C2×C4—201no—
722C2×C4—201no—
723C2×C4—201no—
724C2×C4—401no—
725C2×C4C4×C22⋊D511yescharacteristic
726C2×C4C4×C22⋊D511yescharacteristic
727C2×C4C22×C4×D511yescharacteristic
728C2×C4C2×#71111yescharacteristic
729C2×C4C2×#71111yescharacteristic
730C2×C4#414411yescharacteristic
731C2×C4#414411yescharacteristic
732C2×C4C22×C22⋊D511yescharacteristic
733C8—21no—
734C8—21no—
735C8—21no—
736C8—21no—
737C8—41no—
738C8—41no—
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—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22#6582911yescharacteristic
764C22#6582911yescharacteristic
765C22C2×C4×C22⋊D511yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—202no—
771C4—201no—
772C4—201no—
773C4—201no—
774C4—201no—
775C4—401no—
776C4C2×#402311yescharacteristic
777C4#6582011yescharacteristic
778C4#6614011yescharacteristic
779C4#6614011yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1061382911yescharacteristic
787C2#1061552311yescharacteristic
788C2#1061554211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2880C2
socleC22×C5C2×C4×D4
prime radicalC22×C5×#41C22
cosocleC22×C4×C5C24
hypercenter#2880D5
hypocenterC5#22588
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
3. #10610315C2semidirect
5. #10602810C2semidirect
6. #10602810C2semidirect
7. #10602802C2semidirect
8. #10602801C2semidirect
9. #10600791C2semidirect
10. #10600790C2semidirect
11. #10600789C2semidirect
12. #10600789C2semidirect
13. #10600776C2semidirect
14. #10600768C2semidirect
15. #10600742C2semidirect
37. #65521C4semidirect
38. #65521C4semidirect
39. #65521C4semidirect
40. #65521C4semidirect
41. #65514C4semidirect
42. #65514C4semidirect
43. #65504C4semidirect
44. #65504C4semidirect
47. C2×#3954C22semidirect
48. C2×#3954C22semidirect
49. #65391C22semidirect
50. #65391C22semidirect
51. #65390C22semidirect
52. #65390C22semidirect
53. C2×#3947C22semidirect
54. C2×C8×Dic5C22semidirect
59. #64778C22semidirect
60. #64778C22semidirect
61. #64775C22semidirect
62. #64775C22semidirect
63. #64775C22semidirect
64. #64775C22semidirect
65. #64770C22semidirect
66. #64770C22semidirect
745. C5#22588semidirect

Maximal subgroups

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

subgroupindex
C5×#28802
#106158032
#106103152
#106029312
#106028102
#106028022
#106028012
#106007912
#106007902
#106007892
#106007762
#106007682
#106007422
#225885