Finite Group Databasebeta

← C5×#11036 #11933756

Subgroups — C5×#11036 #11933756

Order 1280.

1310 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic
2C2×C5×#421C211yesmaximal, characteristic, complemented
3C2×C5×#417C211yesmaximal, characteristic, complemented
4C2×C5×#410C211yesmaximal, characteristic, complemented
5C5×#2311C211yesmaximal, characteristic, complemented
6C2×C5×#344C211yesmaximal, characteristic, complemented
7C5×#1736C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×#41C2211yescharacteristic
10C5×#575—22no—
11C5×#575—22no—
12C5×#575—22no—
13C5×#575C414yescomplemented
14C2×C5×#137—21no—
15C2×C5×#137—21no—
16C2×C5×AGL(1,ℤ/8)—21no—
17C2×C5×AGL(1,ℤ/8)—21no—
18C2×C5×#135—22no—
19C22×C5×M16C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#421—22no—
25C5×#421—22no—
26C2×C5×#104—22no—
27C5×#417—22no—
28C5×#417—22no—
29C2×C5×#103—21no—
30C2×C5×#102—21no—
31C5×#410—22no—
32C5×#410—22no—
33C2×C5×#99—22no—
34C5×#391—21no—
35C5×#390—21no—
36C5×#386—22no—
37C5×#380—22no—
38C5×#344—22no—
39C5×#340—22no—
40#11036C511yesmaximal, characteristic, direct product factor, Sylow
41C2×C5×#41—21no—
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×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41—21no—
55C2×C5×#41—21no—
56C2×C5×#41—21no—
57C2×C5×#41—21no—
58C2×C5×#41—21no—
59C2×C5×#41—21no—
60C2×C5×#41—21no—
61C2×C5×#41C2×C412yes—
62C2×C5×#41C2×C412yes—
63C2×C5×#41D412yes—
64C2×C5×#41D412yes—
65C22×C5×Q8D411yescharacteristic
66C22×C5×Q8D411yescharacteristic
67C22×C5×D4—21no—
68C22×C5×D4—21no—
69C22×C5×D4D411yescharacteristic
70C22×C5×D4D411yescharacteristic
71C23×C4×C5—21no—
72C23×C4×C5—21no—
73C23×C4×C5—21no—
74C23×C4×C5C2311yescharacteristic
75C5×#137—24no—
76C5×#137—24no—
77C5×#137—24no—
78C5×#137—24no—
79C5×AGL(1,ℤ/8)—24no—
80C5×AGL(1,ℤ/8)—24no—
81C5×AGL(1,ℤ/8)—24no—
82C5×AGL(1,ℤ/8)—24no—
83C5×#135—28no—
84C5×#135—28no—
85C2×C5×Q16—22no—
86C2×C5×SD16—22no—
87C2×C5×SD16—22no—
88C2×C5×D8—22no—
89C2×C5×M16—21no—
90C2×C5×M16—21no—
91C2×C5×M16—21no—
92C2×C5×M16—21no—
93C2×C5×M16—21no—
94C2×C5×M16—21no—
95C2×C5×M16—21no—
96C2×C5×M16—21no—
97C2×C5×M16—21no—
98C2×C5×M16C2×C412yes—
99C2×C5×M16D412yes—
100C2×C5×M16D412yes—
101C22×C5×C8—21no—
102C22×C5×C8D412yes—
103C5×#117—21no—
104C5×#117—21no—
105C5×#117—21no—
106C5×#117—21no—
107C5×#117—21no—
108C5×#117—21no—
109C5×#117—21no—
110C5×#117D412yes—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4D412yes—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—24no—
121C2×C5×C22⋊C4D412yes—
122C2×C42×C5—21no—
123C2×C42×C5—21no—
124C5×#104—28no—
125C5×#103—24no—
126C5×#102—24no—
127C5×#99—28no—
128C5×#95—24no—
129C2×#575C2×C511yescharacteristic
130C2×#421C2×C511yescharacteristic, complemented
131C2×#417C2×C511yescharacteristic, complemented
132C2×#410C2×C511yescharacteristic, complemented
133#2311C2×C511yescharacteristic, complemented
134C2×#344C2×C511yescharacteristic, complemented
135#1736C2×C511yescharacteristic, complemented
136C24×C5—21no—
137C24×C5—21no—
138C24×C5C2×D411yescharacteristic
139C5×#41—22no—
140C5×#41—22no—
141C5×#41—22no—
142C5×#41—22no—
143C5×#41—22no—
144C5×#41—22no—
145C5×#41—22no—
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—22no—
155C5×#41—41no—
156C5×#41—41no—
157C5×#41—41no—
158C5×#41—41no—
159C5×#41—41no—
160C5×#41—41no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—41no—
164C5×#41—41no—
165C5×#41—41no—
166C5×#41—41no—
167C5×#41—41no—
168C5×#41—41no—
169C5×#41—41no—
170C5×#41—41no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—21no—
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8—21no—
180C2×C5×Q8—21no—
181C2×C5×Q8C22⋊C412yes—
182C2×C5×Q8C22⋊C412yescomplemented
183C2×C5×D4—22no—
184C2×C5×D4—22no—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—41no—
198C2×C5×D4—41no—
199C2×C5×D4—41no—
200C2×C5×D4—41no—
201C2×C5×D4—41no—
202C2×C5×D4—41no—
203C2×C5×D4—41no—
204C2×C5×D4—41no—
205C2×C5×D4C22⋊C412yes—
206C2×C5×D4C22⋊C412yescomplemented
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
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×C5—41no—
225C22×C4×C5—41no—
226C22×C4×C5—82no—
227C22×C4×C5C22×C411yescharacteristic
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×C5C2×D411yescharacteristic
236C22×C4×C5C2×D411yescharacteristic
237C22×C4×C5#4111yescharacteristic
238C22×C4×C5#4111yescharacteristic
239C22×C4×C5#4111yescharacteristic
240C22×C4×C5#4111yescharacteristic
241C5×Q16—28no—
242C5×SD16—28no—
243C5×SD16—28no—
244C5×D8—28no—
245C5×M16—22no—
246C5×M16—22no—
247C5×M16—22no—
248C5×M16—22no—
249C5×M16—22no—
250C5×M16—22no—
251C5×M16—41no—
252C5×M16—41no—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8—22no—
256C2×C5×C8—41no—
257C2×C5×C8—41no—
258C2×C5×C8C22⋊C414yescomplemented
259C5×C4⋊C4—22no—
260C5×C4⋊C4—22no—
261C5×C4⋊C4—22no—
262C5×C4⋊C4—41no—
263C5×C4⋊C4—41no—
264C5×C4⋊C4—41no—
265C5×C4⋊C4—41no—
266C5×C4⋊C4—41no—
267C5×C22⋊C4—22no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—22no—
270C5×C22⋊C4—41no—
271C5×C22⋊C4—84no—
272C42×C5—22no—
273C42×C5—41no—
274C42×C5—41no—
275C42×C5—41no—
276C22×#41C22×C511yescharacteristic
277C22×#41C22×C511yescharacteristic
278#575—22no—
279#575—22no—
280#575—22no—
281#575C4×C514yescomplemented
282C2×#137—21no—
283C2×#137—21no—
284C2×AGL(1,ℤ/8)—21no—
285C2×AGL(1,ℤ/8)—21no—
286C2×#135—22no—
287C22×M16C22×C511yescharacteristic
288C22×M16C22×C511yescharacteristic
289C2×#117C22×C511yescharacteristic
290C2×#117C22×C511yescharacteristic
291C22×C4⋊C4C22×C511yescharacteristic
292#421—22no—
293#421—22no—
294C2×#104—22no—
295#417—22no—
296#417—22no—
297C2×#103—21no—
298C2×#102—21no—
299#410—22no—
300#410—22no—
301C2×#99—22no—
302#391—21no—
303#390—21no—
304#386—22no—
305#380—22no—
306#344—22no—
307#340—22no—
308C23×C5—22no—
309C23×C5—22no—
310C23×C5—41no—
311C23×C5—41no—
312C23×C5—42no—
313C23×C5—42no—
314C23×C5—41no—
315C23×C5—41no—
316C23×C5—41no—
317C23×C5—41no—
318C23×C5—81no—
319C23×C5—81no—
320C23×C5C4×D411yescharacteristic
321C23×C5#12011yescharacteristic
322C23×C5#12011yescharacteristic
323C23×C5#12111yescharacteristic
324C23×C5#12111yescharacteristic
325C23×C5#12111yescharacteristic
326C23×C5#12711yescharacteristic
327C5×Q8—22no—
328C5×Q8—22no—
329C5×Q8—22no—
330C5×Q8—22no—
331C5×Q8—41no—
332C5×Q8—41no—
333C5×Q8—41no—
334C5×Q8—41no—
335C5×D4—22no—
336C5×D4—22no—
337C5×D4—22no—
338C5×D4—22no—
339C5×D4—42no—
340C5×D4—42no—
341C5×D4—42no—
342C5×D4—42no—
343C5×D4—42no—
344C5×D4—42no—
345C5×D4—42no—
346C5×D4—42no—
347C5×D4—41no—
348C5×D4—41no—
349C5×D4—41no—
350C5×D4—41no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—42no—
358C2×C4×C5—42no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5—42no—
363C2×C4×C5—42no—
364C2×C4×C5—42no—
365C2×C4×C5—42no—
366C2×C4×C5—44no—
367C2×C4×C5—42no—
368C2×C4×C5—42no—
369C2×C4×C5—42no—
370C2×C4×C5—42no—
371C2×C4×C5—81no—
372C2×C4×C5—81no—
373C2×C4×C5—82no—
374C2×C4×C5—82no—
375C2×C4×C5C2×C22⋊C411yescharacteristic
376C2×C4×C5C2×C22⋊C411yescharacteristic
377C2×C4×C5C2×C22⋊C411yescharacteristic
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#12011yescharacteristic
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#12311yescharacteristic
400C2×C4×C5#12411yescharacteristic
401C2×C4×C5#12411yescharacteristic
402C2×C4×C5#12711yescharacteristic
403C5×C8—24no—
404C5×C8—42no—
405C2×#41—21no—
406C2×#41—21no—
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
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×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41C2×C4×C512yes—
426C2×#41C2×C4×C512yes—
427C2×#41C5×D412yes—
428C2×#41C5×D412yes—
429C22×Q8C5×D411yescharacteristic
430C22×Q8C5×D411yescharacteristic
431C22×D4—21no—
432C22×D4—21no—
433C22×D4C5×D411yescharacteristic
434C22×D4C5×D411yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C23×C511yescharacteristic
439#137—24no—
440#137—24no—
441#137—24no—
442#137—24no—
443AGL(1,ℤ/8)—24no—
444AGL(1,ℤ/8)—24no—
445AGL(1,ℤ/8)—24no—
446AGL(1,ℤ/8)—24no—
447#135—28no—
448#135—28no—
449C2×Q16—22no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×D8—22no—
453C2×M16—21no—
454C2×M16—21no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16C2×C4×C512yes—
463C2×M16C5×D412yes—
464C2×M16C5×D412yes—
465C22×C8—21no—
466C22×C8C5×D412yes—
467#117—21no—
468#117—21no—
469#117—21no—
470#117—21no—
471#117—21no—
472#117—21no—
473#117—21no—
474#117C5×D412yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4C5×D412yes—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4C5×D412yes—
486C2×C42—21no—
487C2×C42—21no—
488#104—28no—
489#103—24no—
490#102—24no—
491#99—28no—
492#95—24no—
493C22×C5—21no—
494C22×C5—21no—
495C22×C5—21no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5—21no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—44no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—82no—
507C22×C5—82no—
508C22×C5—82no—
509C22×C5—81no—
510C22×C5—81no—
511C22×C5—81no—
512C22×C5—81no—
513C22×C5#38611yescharacteristic
514C22×C5#38611yescharacteristic
515C22×C5#39011yescharacteristic
516C22×C5#39211yescharacteristic
517C22×C5#39211yescharacteristic
518C22×C5#39211yescharacteristic
519C22×C5#39411yescharacteristic
520C4×C5—42no—
521C4×C5—42no—
522C4×C5—82no—
523C4×C5—82no—
524C4×C5—82no—
525C4×C5#37911yescharacteristic
526C4×C5#38611yescharacteristic
527C4×C5#38611yescharacteristic
528C4×C5#39011yescharacteristic
529C4×C5#39211yescharacteristic
530C4×C5#39411yescharacteristic
531C4×C5#39411yescharacteristic
532C4×C5#39411yescharacteristic
533C24—21no—
534C24—21no—
535C24C2×C5×D411yescharacteristic
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C5×C22⋊C412yes—
579C2×Q8C5×C22⋊C412yescomplemented
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C5×C22⋊C412yes—
603C2×D4C5×C22⋊C412yescomplemented
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
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—82no—
624C22×C4C22×C4×C511yescharacteristic
625C22×C4C2×C5×D411yescharacteristic
626C22×C4C2×C5×D411yescharacteristic
627C22×C4C2×C5×D411yescharacteristic
628C22×C4C2×C5×D411yescharacteristic
629C22×C4C2×C5×D411yescharacteristic
630C22×C4C2×C5×D411yescharacteristic
631C22×C4C2×C5×D411yescharacteristic
632C22×C4C2×C5×D411yescharacteristic
633C22×C4C2×C5×D411yescharacteristic
634C22×C4C5×#4111yescharacteristic
635C22×C4C5×#4111yescharacteristic
636C22×C4C5×#4111yescharacteristic
637C22×C4C5×#4111yescharacteristic
638Q16—28no—
639SD16—28no—
640SD16—28no—
641D8—28no—
642M16—22no—
643M16—22no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—41no—
649M16—41no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8C5×C22⋊C414yescomplemented
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—84no—
669C42—22no—
670C42—41no—
671C42—41no—
672C42—41no—
673C2×C5—21no—
674C2×C5—21no—
675C2×C5—21no—
676C2×C5—21no—
677C2×C5—21no—
678C2×C5—21no—
679C2×C5—82no—
680C2×C5—82no—
681C2×C5#143811yescharacteristic
682C2×C5#200811yescharacteristic
683C2×C5#200911yescharacteristic
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23C4×C5×D411yescharacteristic
697C23C5×#12011yescharacteristic
698C23C5×#12011yescharacteristic
699C23C5×#12111yescharacteristic
700C23C5×#12111yescharacteristic
701C23C5×#12111yescharacteristic
702C23C5×#12711yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4C2×C5×C22⋊C411yescharacteristic
752C2×C4C2×C5×C22⋊C411yescharacteristic
753C2×C4C2×C5×C22⋊C411yescharacteristic
754C2×C4C4×C5×D411yescharacteristic
755C2×C4C4×C5×D411yescharacteristic
756C2×C4C4×C5×D411yescharacteristic
757C2×C4C5×#12011yescharacteristic
758C2×C4C5×#12011yescharacteristic
759C2×C4C5×#12011yescharacteristic
760C2×C4C5×#12011yescharacteristic
761C2×C4C5×#12011yescharacteristic
762C2×C4C5×#12011yescharacteristic
763C2×C4C5×#12111yescharacteristic
764C2×C4C5×#12111yescharacteristic
765C2×C4C5×#12111yescharacteristic
766C2×C4C5×#12111yescharacteristic
767C2×C4C5×#12111yescharacteristic
768C2×C4C5×#12111yescharacteristic
769C2×C4C5×#12111yescharacteristic
770C2×C4C5×#12111yescharacteristic
771C2×C4C5×#12111yescharacteristic
772C2×C4C5×#12311yescharacteristic
773C2×C4C5×#12311yescharacteristic
774C2×C4C5×#12311yescharacteristic
775C2×C4C5×#12311yescharacteristic
776C2×C4C5×#12411yescharacteristic
777C2×C4C5×#12411yescharacteristic
778C2×C4C5×#12711yescharacteristic
779C8—24no—
780C8—42no—
781C5#1103611yescharacteristic, direct product factor, Sylow
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C5×#38611yescharacteristic
803C22C5×#38611yescharacteristic
804C22C5×#39011yescharacteristic
805C22C5×#39211yescharacteristic
806C22C5×#39211yescharacteristic
807C22C5×#39211yescharacteristic
808C22C5×#39411yescharacteristic
809C4—42no—
810C4—42no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4C5×#37911yescharacteristic
815C4C5×#38611yescharacteristic
816C4C5×#38611yescharacteristic
817C4C5×#39011yescharacteristic
818C4C5×#39211yescharacteristic
819C4C5×#39411yescharacteristic
820C4C5×#39411yescharacteristic
821C4C5×#39411yescharacteristic
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—82no—
829C2—82no—
830C2C5×#143811yescharacteristic
831C2C5×#200811yescharacteristic
832C2C5×#200911yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#421C2semidirect
3. C2×C5×#417C2semidirect
4. C2×C5×#410C2semidirect
5. C5×#2311C2semidirect
6. C2×C5×#344C2semidirect
7. C5×#1736C2semidirect
13. C5×#575C4semidirect
40. #11036C5direct (N × H)
130. C2×#421C2×C5semidirect
131. C2×#417C2×C5semidirect
132. C2×#410C2×C5semidirect
133. #2311C2×C5semidirect
134. C2×#344C2×C5semidirect
135. #1736C2×C5semidirect
182. C2×C5×Q8C22⋊C4semidirect
206. C2×C5×D4C22⋊C4semidirect
258. C2×C5×C8C22⋊C4semidirect
281. #575C4×C5semidirect
579. C2×Q8C5×C22⋊C4semidirect
603. C2×D4C5×C22⋊C4semidirect
655. C2×C8C5×C22⋊C4semidirect
781. C5#11036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5752
C2×C5×#4212
C2×C5×#4172
C2×C5×#4102
C5×#23112
C2×C5×#3442
C5×#17362
#110365