Finite Group Databasebeta

← C5×#8444 #11931164

Subgroups — C5×#8444 #11931164

Order 1280.

1116 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#550C211yesmaximal, characteristic
2C5×#1957C211yesmaximal, characteristic, complemented
3C5×#1803C211yesmaximal, characteristic, complemented
4C5×#1802C211yesmaximal, characteristic, complemented
5C2×C5×#331C211yesmaximal, characteristic, complemented
6C2×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
7C2×C5×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×C5×#41—21no—
9C5×#550—22no—
10C5×#550—22no—
11C5×#550—22no—
12C5×#550C414yescomplemented
13C2×C5×#127—21no—
14C2×C5×#127C2211yescharacteristic
15C2×C5×#121—22no—
16C2×C5×#121—21no—
17C2×C4×C5×Q8C2211yescharacteristic
18C2×C4×C5×D4—21no—
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×C4⋊C8C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×#103—21no—
23C2×C5×#102—21no—
24C2×C5×#102—22no—
25C2×C4×C5×C8C2211yescharacteristic
26C5×#384C2211yescharacteristic
27C5×#340—21no—
28C5×#340—21no—
29C5×#331—22no—
30C5×Q8⋊C8—22no—
31C5×D4⋊C8—22no—
32#8444C511yesmaximal, characteristic, direct product factor, Sylow
33C2×C5×#41—24no—
34C2×C5×#41—24no—
35C2×C5×#41—42no—
36C2×C5×#41—42no—
37C2×C5×#41—42no—
38C2×C5×#41—42no—
39C22×C5×Q8D411yescharacteristic
40C22×C5×D4—22no—
41C22×C5×D4—22no—
42C22×C5×D4—21no—
43C22×C5×D4—21no—
44C22×C5×D4D411yescharacteristic
45C22×C5×D4D412yes—
46C23×C4×C5—22no—
47C23×C4×C5—21no—
48C22×C5×C8—21no—
49C22×C5×C8—21no—
50C22×C5×C8—21no—
51C5×#127—24no—
52C5×#127—24no—
53C5×#127—21no—
54C5×#127—21no—
55C5×#127C2×C412yes—
56C5×#127D412yes—
57C5×#121—24no—
58C5×#121—28no—
59C5×#121—28no—
60C5×#121—24no—
61C4×C5×Q8—21no—
62C4×C5×Q8—21no—
63C4×C5×Q8C2×C412yes—
64C4×C5×Q8D412yes—
65C4×C5×D4—24no—
66C4×C5×D4—24no—
67C4×C5×D4—21no—
68C4×C5×D4—21no—
69C4×C5×D4C2×C412yes—
70C4×C5×D4D412yes—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4D411yescharacteristic
76C2×C5×C4⋊C4D411yescharacteristic
77C2×C5×C22⋊C4—22no—
78C2×C5×C22⋊C4—21no—
79C2×C42×C5—21no—
80C2×C42×C5C2311yescharacteristic
81C5×C4⋊C8—21no—
82C5×C4⋊C8—21no—
83C5×C4⋊C8—21no—
84C5×C4⋊C8—21no—
85C5×#103—42no—
86C5×#102—44no—
87C5×#102—42no—
88C4×C5×C8—21no—
89C4×C5×C8—21no—
90C2×#550C2×C511yescharacteristic
91#1957C2×C511yescharacteristic, complemented
92#1803C2×C511yescharacteristic, complemented
93#1802C2×C511yescharacteristic, complemented
94C2×#331C2×C511yescharacteristic, complemented
95C2×Q8⋊C8C2×C511yescharacteristic, complemented
96C2×D4⋊C8C2×C511yescharacteristic, complemented
97C24×C5—21no—
98C24×C5—22no—
99C5×#41—48no—
100C5×#41—48no—
101C5×#41—48no—
102C5×#41—48no—
103C2×C5×Q8—21no—
104C2×C5×Q8—21no—
105C2×C5×Q8—21no—
106C2×C5×Q8C22⋊C412yes—
107C2×C5×Q8D812yes—
108C2×C5×Q8SD1612yes—
109C2×C5×D4—28no—
110C2×C5×D4—28no—
111C2×C5×D4—22no—
112C2×C5×D4—22no—
113C2×C5×D4—21no—
114C2×C5×D4—22no—
115C2×C5×D4—22no—
116C2×C5×D4—22no—
117C2×C5×D4—21no—
118C2×C5×D4—21no—
119C2×C5×D4—21no—
120C2×C5×D4—21no—
121C2×C5×D4—44no—
122C2×C5×D4—44no—
123C2×C5×D4—42no—
124C2×C5×D4—42no—
125C2×C5×D4—41no—
126C2×C5×D4—41no—
127C2×C5×D4—41no—
128C2×C5×D4—41no—
129C2×C5×D4—41no—
130C2×C5×D4—41no—
131C2×C5×D4—41no—
132C2×C5×D4—41no—
133C2×C5×D4—82no—
134C2×C5×D4—82no—
135C2×C5×D4C22⋊C412yes—
136C2×C5×D4C22⋊C414yes—
137C22×C4×C5—21no—
138C22×C4×C5—28no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—44no—
144C22×C4×C5—44no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5—41no—
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C2×C5×C8—22no—
154C2×C5×C8—41no—
155C2×C5×C8—41no—
156C2×C5×C8—41no—
157C2×C5×C8—41no—
158C2×C5×C8—41no—
159C2×C5×C8—41no—
160C2×C5×C8—41no—
161C2×C5×C8—41no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—42no—
167C5×C4⋊C4—41no—
168C5×C4⋊C4—41no—
169C5×C4⋊C4—41no—
170C5×C4⋊C4—41no—
171C5×C4⋊C4C22⋊C412yes—
172C5×C4⋊C4C22⋊C412yes—
173C5×C22⋊C4—28no—
174C5×C22⋊C4—22no—
175C5×C22⋊C4—22no—
176C42×C5—22no—
177C42×C5—22no—
178C42×C5C22×C411yescharacteristic
179C42×C5C2×D411yescharacteristic
180C42×C5C2×D411yescharacteristic
181C42×C5C2×D411yescharacteristic
182C22×#41—21no—
183#550—22no—
184#550—22no—
185#550—22no—
186#550C4×C514yescomplemented
187C2×#127—21no—
188C2×#127C22×C511yescharacteristic
189C2×#121—22no—
190C2×#121—21no—
191C2×C4×Q8C22×C511yescharacteristic
192C2×C4×D4—21no—
193C2×C4×D4C22×C511yescharacteristic
194C2×C4⋊C8C22×C511yescharacteristic
195C2×C4⋊C8C22×C511yescharacteristic
196C2×#103—21no—
197C2×#102—21no—
198C2×#102—22no—
199C2×C4×C8C22×C511yescharacteristic
200#384C22×C511yescharacteristic
201#340—21no—
202#340—21no—
203#331—22no—
204Q8⋊C8—22no—
205D4⋊C8—22no—
206C23×C5—24no—
207C23×C5—22no—
208C23×C5—42no—
209C23×C5—41no—
210C23×C5—41no—
211C23×C5—42no—
212C23×C5—42no—
213C23×C5—41no—
214C23×C5—41no—
215C23×C5—42no—
216C23×C5—42no—
217C23×C5—41no—
218C23×C5—42no—
219C23×C5—41no—
220C23×C5#12011yescharacteristic
221C5×Q8—22no—
222C5×Q8—22no—
223C5×Q8—22no—
224C5×Q8#10214yescomplemented
225C5×D4—22no—
226C5×D4—22no—
227C5×D4—44no—
228C5×D4—416no—
229C5×D4—42no—
230C5×D4—42no—
231C5×D4—42no—
232C5×D4—42no—
233C5×D4—42no—
234C5×D4—41no—
235C5×D4—42no—
236C5×D4—42no—
237C5×D4—41no—
238C5×D4—42no—
239C5×D4—82no—
240C5×D4—88no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—416no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—81no—
258C2×C4×C5—81no—
259C2×C4×C5—81no—
260C2×C4×C5C2×C22⋊C411yescharacteristic
261C2×C4×C5C2×C22⋊C411yescharacteristic
262C2×C4×C5C2×C22⋊C411yescharacteristic
263C2×C4×C5#12011yescharacteristic
264C2×C4×C5#12011yescharacteristic
265C2×C4×C5#12011yescharacteristic
266C2×C4×C5C2×D811yescharacteristic
267C2×C4×C5C2×SD1611yescharacteristic
268C2×C4×C5#13511yescharacteristic
269C2×C4×C5#13511yescharacteristic
270C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
271C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
272C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
273C2×C4×C5#13711yescharacteristic
274C5×C8—42no—
275C5×C8—81no—
276C5×C8—81no—
277C2×#41—24no—
278C2×#41—24no—
279C2×#41—42no—
280C2×#41—42no—
281C2×#41—42no—
282C2×#41—42no—
283C22×Q8C5×D411yescharacteristic
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C5×D411yescharacteristic
289C22×D4C5×D412yes—
290C23×C4—22no—
291C23×C4—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295#127—24no—
296#127—24no—
297#127—21no—
298#127—21no—
299#127C2×C4×C512yes—
300#127C5×D412yes—
301#121—24no—
302#121—28no—
303#121—28no—
304#121—24no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8C2×C4×C512yes—
308C4×Q8C5×D412yes—
309C4×D4—24no—
310C4×D4—24no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4C2×C4×C512yes—
314C4×D4C5×D412yes—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C5×D411yescharacteristic
320C2×C4⋊C4C5×D411yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C42—21no—
324C2×C42C23×C511yescharacteristic
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329#103—42no—
330#102—44no—
331#102—42no—
332C4×C8—21no—
333C4×C8—21no—
334C22×C5—44no—
335C22×C5—42no—
336C22×C5—44no—
337C22×C5—42no—
338C22×C5—42no—
339C22×C5—44no—
340C22×C5—81no—
341C22×C5—82no—
342C22×C5—81no—
343C22×C5—82no—
344C22×C5—81no—
345C22×C5—82no—
346C22×C5—81no—
347C22×C5—82no—
348C22×C5#37911yescharacteristic
349C22×C5#44711yescharacteristic
350C22×C5#44911yescharacteristic
351C22×C5#45011yescharacteristic
352C22×C5#45211yescharacteristic
353C22×C5#45311yescharacteristic
354C22×C5#45511yescharacteristic
355C4×C5—21no—
356C4×C5—21no—
357C4×C5—24no—
358C4×C5—42no—
359C4×C5—42no—
360C4×C5—161no—
361C4×C5C2×#10211yescharacteristic
362C4×C5#41611yescharacteristic
363C4×C5#41711yescharacteristic
364C4×C5#41811yescharacteristic
365C4×C5#44711yescharacteristic
366C4×C5#44911yescharacteristic
367C4×C5#45011yescharacteristic
368C4×C5#45211yescharacteristic
369C24—21no—
370C24—22no—
371#41—48no—
372#41—48no—
373#41—48no—
374#41—48no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8C5×C22⋊C412yes—
379C2×Q8C5×D812yes—
380C2×Q8C5×SD1612yes—
381C2×D4—28no—
382C2×D4—28no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4C5×C22⋊C412yes—
408C2×D4C5×C22⋊C414yes—
409C22×C4—21no—
410C22×C4—28no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4C2×C5×D411yescharacteristic
423C22×C4C2×C5×D411yescharacteristic
424C22×C4C2×C5×D411yescharacteristic
425C2×C8—22no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—41no—
429C2×C8—41no—
430C2×C8—41no—
431C2×C8—41no—
432C2×C8—41no—
433C2×C8—41no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—42no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4C5×C22⋊C412yes—
444C4⋊C4C5×C22⋊C412yes—
445C22⋊C4—28no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C42—22no—
449C42—22no—
450C42C22×C4×C511yescharacteristic
451C42C2×C5×D411yescharacteristic
452C42C2×C5×D411yescharacteristic
453C42C2×C5×D411yescharacteristic
454C2×C5—84no—
455C2×C5—82no—
456C2×C5#162111yescharacteristic
457C2×C5#163111yescharacteristic
458C2×C5#164111yescharacteristic
459C2×C5#164211yescharacteristic
460C2×C5#178611yescharacteristic
461C2×C5#178811yescharacteristic
462C2×C5#179211yescharacteristic
463C23—22no—
464C23—24no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—42no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—41no—
475C23—42no—
476C23—41no—
477C23C5×#12011yescharacteristic
478Q8—22no—
479Q8—22no—
480Q8—22no—
481Q8C5×#10214yescomplemented
482D4—22no—
483D4—22no—
484D4—44no—
485D4—416no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—41no—
492D4—42no—
493D4—42no—
494D4—41no—
495D4—42no—
496D4—82no—
497D4—88no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—416no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—81no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4C2×C5×C22⋊C411yescharacteristic
518C2×C4C2×C5×C22⋊C411yescharacteristic
519C2×C4C2×C5×C22⋊C411yescharacteristic
520C2×C4C5×#12011yescharacteristic
521C2×C4C5×#12011yescharacteristic
522C2×C4C5×#12011yescharacteristic
523C2×C4C2×C5×D811yescharacteristic
524C2×C4C2×C5×SD1611yescharacteristic
525C2×C4C5×#13511yescharacteristic
526C2×C4C5×#13511yescharacteristic
527C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
528C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
529C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
530C2×C4C5×#13711yescharacteristic
531C8—42no—
532C8—81no—
533C8—81no—
534C5#844411yescharacteristic, direct product factor, Sylow
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22—42no—
541C22—81no—
542C22—82no—
543C22—81no—
544C22—82no—
545C22—81no—
546C22—82no—
547C22—81no—
548C22—82no—
549C22C5×#37911yescharacteristic
550C22C5×#44711yescharacteristic
551C22C5×#44911yescharacteristic
552C22C5×#45011yescharacteristic
553C22C5×#45211yescharacteristic
554C22C5×#45311yescharacteristic
555C22C5×#45511yescharacteristic
556C4—24no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—42no—
561C4—161no—
562C4C2×C5×#10211yescharacteristic
563C4C5×#41611yescharacteristic
564C4C5×#41711yescharacteristic
565C4C5×#41811yescharacteristic
566C4C5×#44711yescharacteristic
567C4C5×#44911yescharacteristic
568C4C5×#45011yescharacteristic
569C4C5×#45211yescharacteristic
570C2—82no—
571C2—84no—
572C2C5×#162111yescharacteristic
573C2C5×#163111yescharacteristic
574C2C5×#164111yescharacteristic
575C2C5×#164211yescharacteristic
576C2C5×#178611yescharacteristic
577C2C5×#178811yescharacteristic
578C2C5×#179211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#550C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1957C2semidirect
3. C5×#1803C2semidirect
4. C5×#1802C2semidirect
5. C2×C5×#331C2semidirect
6. C2×C5×Q8⋊C8C2semidirect
7. C2×C5×D4⋊C8C2semidirect
12. C5×#550C4semidirect
32. #8444C5direct (N × H)
91. #1957C2×C5semidirect
92. #1803C2×C5semidirect
93. #1802C2×C5semidirect
94. C2×#331C2×C5semidirect
95. C2×Q8⋊C8C2×C5semidirect
96. C2×D4⋊C8C2×C5semidirect
186. #550C4×C5semidirect
224. C5×Q8#102semidirect
481. Q8C5×#102semidirect
534. C5#8444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5502
C5×#19572
C5×#18032
C5×#18022
C2×C5×#3312
C2×C5×Q8⋊C82
C2×C5×D4⋊C82
#84445