Finite Group Databasebeta

← C2×C5×#2034 #11946197

Subgroups — C2×C5×#2034 #11946197

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#121C211yesmaximal, characteristic
2C22×C5×#106C211yesmaximal, characteristic, complemented
3C22×C5×#102C211yesmaximal, characteristic, complemented
4C22×C5×#102C211yesmaximal, characteristic, complemented
5C22×C5×C22⋊C8C211yesmaximal, characteristic, complemented
6C2×C5×#380C211yesmaximal, characteristic, complemented
7C5×#2034C218yesmaximal, direct product factor
8C2×C5×#340C211yesmaximal, characteristic, complemented
9C23×C5×D4—21no—
10C23×C5×D4C2211yescharacteristic
11C24×C4×C5C2211yescharacteristic
12C23×C5×C8C2211yescharacteristic
13C23×C5×C8C2211yescharacteristic
14C2×C5×#121—24no—
15C2×C5×#121—22no—
16C2×C5×#121—24no—
17C2×C5×#121C2214yes—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4—21no—
22C22×C5×C22⋊C4—21no—
23C2×C5×#106—24no—
24C2×C5×#106C2214yescomplemented
25C2×C5×#102—24no—
26C2×C5×#102—24no—
27C2×C5×#102C2214yescomplemented
28C2×C5×#102C2214yescomplemented
29C2×C5×C22⋊C8—24no—
30C2×C5×C22⋊C8C2214yescomplemented
31C5×#380—22no—
32C5×#380C2214yescomplemented
33C2×C5×#95—21no—
34C5×#340C2214yescomplemented
35C2×#2034C511yesmaximal, characteristic, direct product factor, Sylow
36C25×C5—21no—
37C25×C5D411yescharacteristic
38C22×C5×D4—28no—
39C22×C5×D4—24no—
40C22×C5×D4—22no—
41C22×C5×D4—21no—
42C22×C5×D4—22no—
43C22×C5×D4—22no—
44C22×C5×D4—22no—
45C22×C5×D4—22no—
46C22×C5×D4—44no—
47C22×C5×D4—44no—
48C22×C5×D4D414yes—
49C22×C5×D4C2312yes—
50C23×C4×C5—21no—
51C23×C4×C5—22no—
52C23×C4×C5—22no—
53C23×C4×C5—22no—
54C23×C4×C5—22no—
55C23×C4×C5—22no—
56C23×C4×C5—22no—
57C23×C4×C5—21no—
58C23×C4×C5—21no—
59C23×C4×C5D412yes—
60C23×C4×C5D411yescharacteristic
61C23×C4×C5C2312yes—
62C23×C4×C5C2311yescharacteristic
63C22×C5×C8—22no—
64C22×C5×C8—22no—
65C22×C5×C8—22no—
66C22×C5×C8—22no—
67C22×C5×C8—22no—
68C22×C5×C8D414yescomplemented
69C22×C5×C8C2312yes—
70C22×C5×C8C2312yes—
71C5×#121—216no—
72C5×#121—28no—
73C5×#121—28no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4D414yes—
83C2×C5×C4⋊C4C2312yes—
84C2×C5×C4⋊C4C2312yes—
85C2×C5×C4⋊C4C2312yes—
86C2×C5×C22⋊C4—28no—
87C2×C5×C22⋊C4—24no—
88C2×C5×C22⋊C4—24no—
89C2×C5×C22⋊C4—44no—
90C5×#106—28no—
91C5×#102—28no—
92C5×#102—28no—
93C5×C22⋊C8—28no—
94C5×#95—24no—
95C22×#121C2×C511yescharacteristic
96C22×#106C2×C511yescharacteristic, complemented
97C22×#102C2×C511yescharacteristic, complemented
98C22×#102C2×C511yescharacteristic, complemented
99C22×C22⋊C8C2×C511yescharacteristic, complemented
100C2×#380C2×C511yescharacteristic, complemented
101#2034C2×C518yesdirect product factor
102C2×#340C2×C511yescharacteristic, complemented
103C24×C5—22no—
104C24×C5—22no—
105C24×C5—22no—
106C24×C5—22no—
107C24×C5—22no—
108C24×C5—22no—
109C24×C5—24no—
110C24×C5—22no—
111C24×C5—42no—
112C24×C5—42no—
113C24×C5—42no—
114C24×C5—42no—
115C24×C5—42no—
116C24×C5—42no—
117C24×C5SD1614yes—
118C24×C5C2×D412yes—
119C24×C5C2×D411yescharacteristic
120C2×C5×D4—216no—
121C2×C5×D4—24no—
122C2×C5×D4—28no—
123C2×C5×D4—28no—
124C2×C5×D4—22no—
125C2×C5×D4—22no—
126C2×C5×D4—22no—
127C2×C5×D4—22no—
128C2×C5×D4—22no—
129C2×C5×D4—48no—
130C2×C5×D4—432no—
131C2×C5×D4—48no—
132C2×C5×D4—44no—
133C2×C5×D4—42no—
134C2×C5×D4—42no—
135C2×C5×D4—44no—
136C2×C5×D4C2×D414yes—
137C22×C4×C5—22no—
138C22×C4×C5—24no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—24no—
143C22×C4×C5—24no—
144C22×C4×C5—24no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—42no—
154C22×C4×C5—42no—
155C22×C4×C5—44no—
156C22×C4×C5—44no—
157C22×C4×C5—44no—
158C22×C4×C5—44no—
159C22×C4×C5—42no—
160C22×C4×C5—42no—
161C22×C4×C5—42no—
162C22×C4×C5—42no—
163C22×C4×C5—42no—
164C22×C4×C5—42no—
165C22×C4×C5C2×D412yes—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D412yes—
168C22×C4×C5C2×D412yes—
169C22×C4×C5C2×D412yes—
170C22×C4×C5#4112yes—
171C22×C4×C5#4112yes—
172C22×C4×C5#4112yes—
173C22×C4×C5C2411yescharacteristic
174C2×C5×C8—28no—
175C2×C5×C8—22no—
176C2×C5×C8—22no—
177C2×C5×C8—22no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8—44no—
181C2×C5×C8C2×D414yescomplemented
182C5×C4⋊C4—24no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—42no—
189C5×C4⋊C4—42no—
190C5×C4⋊C4C2×D414yes—
191C5×C22⋊C4—216no—
192C5×C22⋊C4—48no—
193C23×D4—21no—
194C23×D4C22×C511yescharacteristic
195C24×C4C22×C511yescharacteristic
196C23×C8C22×C511yescharacteristic
197C23×C8C22×C511yescharacteristic
198C2×#121—24no—
199C2×#121—22no—
200C2×#121—24no—
201C2×#121C22×C514yes—
202C22×C4⋊C4C22×C511yescharacteristic
203C22×C4⋊C4C22×C511yescharacteristic
204C22×C4⋊C4C22×C511yescharacteristic
205C22×C22⋊C4—21no—
206C22×C22⋊C4—21no—
207C2×#106—24no—
208C2×#106C22×C514yescomplemented
209C2×#102—24no—
210C2×#102—24no—
211C2×#102C22×C514yescomplemented
212C2×#102C22×C514yescomplemented
213C2×C22⋊C8—24no—
214C2×C22⋊C8C22×C514yescomplemented
215#380—22no—
216#380C22×C514yescomplemented
217C2×#95—21no—
218#340C22×C514yescomplemented
219C23×C5—22no—
220C23×C5—22no—
221C23×C5—22no—
222C23×C5—22no—
223C23×C5—22no—
224C23×C5—22no—
225C23×C5—28no—
226C23×C5—28no—
227C23×C5—28no—
228C23×C5—24no—
229C23×C5—44no—
230C23×C5—44no—
231C23×C5—44no—
232C23×C5—44no—
233C23×C5—42no—
234C23×C5—42no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5—42no—
239C23×C5—48no—
240C23×C5—48no—
241C23×C5—48no—
242C23×C5—84no—
243C23×C5—84no—
244C23×C5—84no—
245C23×C5—84no—
246C23×C5#12012yes—
247C23×C5#12112yes—
248C23×C5#12312yes—
249C23×C5C2×SD1614yes—
250C23×C5C2×SD1612yes—
251C23×C5#13512yes—
252C23×C5AGL(1,ℤ/8)12yes—
253C23×C5AGL(1,ℤ/8)12yes—
254C23×C5C22×D411yescharacteristic
255C5×D4—24no—
256C5×D4—24no—
257C5×D4—432no—
258C5×D4—42no—
259C5×D4—42no—
260C5×D4—48no—
261C2×C4×C5—22no—
262C2×C4×C5—24no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—44no—
268C2×C4×C5—48no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—48no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—84no—
281C2×C4×C5—84no—
282C2×C4×C5#12012yes—
283C2×C4×C5#12114yes—
284C2×C4×C5#12114yes—
285C2×C4×C5#12112yes—
286C2×C4×C5#12314yes—
287C2×C4×C5#12312yes—
288C2×C4×C5#12414yes—
289C2×C4×C5C22×D411yescharacteristic
290C2×C4×C5C22×D411yescharacteristic
291C2×C4×C5C22×D411yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×C4×C5C2×#4111yescharacteristic
294C2×C4×C5C2×#4111yescharacteristic
295C5×C8—24no—
296C5×C8—42no—
297C25—21no—
298C25C5×D411yescharacteristic
299C22×D4—28no—
300C22×D4—24no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4C5×D414yes—
310C22×D4C23×C512yes—
311C23×C4—21no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4C5×D411yescharacteristic
321C23×C4C5×D412yes—
322C23×C4C23×C512yes—
323C23×C4C23×C511yescharacteristic
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8C5×D414yescomplemented
330C22×C8C23×C512yes—
331C22×C8C23×C512yes—
332#121—216no—
333#121—28no—
334#121—28no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C5×D414yes—
344C2×C4⋊C4C23×C512yes—
345C2×C4⋊C4C23×C512yes—
346C2×C4⋊C4C23×C512yes—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—44no—
351#106—28no—
352#102—28no—
353#102—28no—
354C22⋊C8—28no—
355#95—24no—
356C22×C5—24no—
357C22×C5—24no—
358C22×C5—24no—
359C22×C5—42no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—416no—
364C22×C5—44no—
365C22×C5—44no—
366C22×C5—44no—
367C22×C5—82no—
368C22×C5—82no—
369C22×C5—82no—
370C22×C5—82no—
371C22×C5—816no—
372C22×C5#39414yes—
373C22×C5#44914yes—
374C22×C5#45014yes—
375C22×C5#46514yes—
376C22×C5#46914yes—
377C22×C5#48114yes—
378C22×C5#48214yes—
379C22×C5C2×#12011yescharacteristic
380C22×C5C2×#12111yescharacteristic
381C22×C5C2×#12311yescharacteristic
382C22×C5C22×SD1611yescharacteristic
383C22×C5C2×#13511yescharacteristic
384C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
386C4×C5—42no—
387C4×C5—44no—
388C4×C5—82no—
389C4×C5—82no—
390C4×C5#39414yes—
391C4×C5C2×#12111yescharacteristic
392C4×C5C2×#12111yescharacteristic
393C4×C5C2×#12311yescharacteristic
394C4×C5C2×#12411yescharacteristic
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—22no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24C5×SD1614yes—
410C24C2×C5×D412yes—
411C24C2×C5×D411yescharacteristic
412C2×D4—216no—
413C2×D4—24no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—432no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—42no—
425C2×D4—44no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4C2×C5×D414yes—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4C2×C5×D412yes—
458C22×C4C2×C5×D411yescharacteristic
459C22×C4C2×C5×D412yes—
460C22×C4C2×C5×D412yes—
461C22×C4C2×C5×D412yes—
462C22×C4C5×#4112yes—
463C22×C4C5×#4112yes—
464C22×C4C5×#4112yes—
465C22×C4C24×C511yescharacteristic
466C2×C8—28no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—44no—
473C2×C8C2×C5×D414yescomplemented
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4C2×C5×D414yes—
483C22⋊C4—216no—
484C22⋊C4—48no—
485C2×C5—44no—
486C2×C5—84no—
487C2×C5#203418yesdirect product factor
488C2×C5C2×#39411yescharacteristic
489C2×C5C2×#45011yescharacteristic
490C2×C5C2×#44911yescharacteristic
491C2×C5C2×#46511yescharacteristic
492C2×C5C2×#46911yescharacteristic
493C2×C5C2×#48211yescharacteristic
494C2×C5C2×#48111yescharacteristic
495C23—28no—
496C23—28no—
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—44no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—48no—
510C23—48no—
511C23—48no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23C5×#12012yes—
523C23C5×#12112yes—
524C23C5×#12312yes—
525C23C2×C5×SD1614yes—
526C23C2×C5×SD1612yes—
527C23C5×#13512yes—
528C23C5×AGL(1,ℤ/8)12yes—
529C23C5×AGL(1,ℤ/8)12yes—
530C23C22×C5×D411yescharacteristic
531D4—24no—
532D4—24no—
533D4—432no—
534D4—48no—
535D4—42no—
536D4—42no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4C5×#12012yes—
559C2×C4C5×#12112yes—
560C2×C4C5×#12114yes—
561C2×C4C5×#12114yes—
562C2×C4C5×#12312yes—
563C2×C4C5×#12314yes—
564C2×C4C5×#12414yes—
565C2×C4C22×C5×D411yescharacteristic
566C2×C4C22×C5×D411yescharacteristic
567C2×C4C22×C5×D411yescharacteristic
568C2×C4C2×C5×#4111yescharacteristic
569C2×C4C2×C5×#4111yescharacteristic
570C2×C4C2×C5×#4111yescharacteristic
571C8—24no—
572C8—42no—
573C5C2×#203411yescharacteristic, direct product factor, Sylow
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—416no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—816no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22C5×#39414yes—
591C22C5×#44914yes—
592C22C5×#45014yes—
593C22C5×#46514yes—
594C22C5×#46914yes—
595C22C5×#48114yes—
596C22C5×#48214yes—
597C22C2×C5×#12011yescharacteristic
598C22C2×C5×#12111yescharacteristic
599C22C2×C5×#12311yescharacteristic
600C22C22×C5×SD1611yescharacteristic
601C22C2×C5×#13511yescharacteristic
602C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
603C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
604C4—44no—
605C4—42no—
606C4—82no—
607C4—82no—
608C4C5×#39414yes—
609C4C2×C5×#12111yescharacteristic
610C4C2×C5×#12111yescharacteristic
611C4C2×C5×#12311yescharacteristic
612C4C2×C5×#12411yescharacteristic
613C2—44no—
614C2—84no—
615C2C5×#203418yesdirect product factor
616C2C2×C5×#39411yescharacteristic
617C2C2×C5×#45011yescharacteristic
618C2C2×C5×#44911yescharacteristic
619C2C2×C5×#46511yescharacteristic
620C2C2×C5×#46911yescharacteristic
621C2C2×C5×#48211yescharacteristic
622C2C2×C5×#48111yescharacteristic
subgroupG/H
center, socleC24×C5C2×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C5 ◁ C24×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C5×#106C2semidirect
3. C22×C5×#102C2semidirect
4. C22×C5×#102C2semidirect
5. C22×C5×C22⋊C8C2semidirect
6. C2×C5×#380C2semidirect
7. C5×#2034C2direct (N × H)
8. C2×C5×#340C2semidirect
24. C2×C5×#106C22semidirect
27. C2×C5×#102C22semidirect
28. C2×C5×#102C22semidirect
30. C2×C5×C22⋊C8C22semidirect
32. C5×#380C22semidirect
34. C5×#340C22semidirect
35. C2×#2034C5direct (N × H)
68. C22×C5×C8D4semidirect
96. C22×#106C2×C5semidirect
97. C22×#102C2×C5semidirect
98. C22×#102C2×C5semidirect
99. C22×C22⋊C8C2×C5semidirect
100. C2×#380C2×C5semidirect
101. #2034C2×C5direct (N × H)
102. C2×#340C2×C5semidirect
181. C2×C5×C8C2×D4semidirect
208. C2×#106C22×C5semidirect
211. C2×#102C22×C5semidirect
212. C2×#102C22×C5semidirect
214. C2×C22⋊C8C22×C5semidirect
216. #380C22×C5semidirect
218. #340C22×C5semidirect
329. C22×C8C5×D4semidirect
473. C2×C8C2×C5×D4semidirect
487. C2×C5#2034direct (N × H)
573. C5C2×#2034direct (N × H)
615. C2C5×#2034direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1212
C22×C5×#1062
C22×C5×#1022
C22×C5×C22⋊C82
C2×C5×#3802
C5×#20342
C2×C5×#3402
C2×#20345