Finite Group Databasebeta

← C5×#24010 #11946730

Subgroups — C5×#24010 #11946730

Order 1280.

1428 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C5×#485C212yesmaximal, complemented
3C5×#2280C211yesmaximal, characteristic
4C5×#2036C212yesmaximal, complemented
5C5×#2035C212yesmaximal, complemented
6C5×#1873C212yesmaximal, complemented
7C5×#1853C211yesmaximal, characteristic, complemented
8C5×#1852C211yesmaximal, characteristic, complemented
9C5×#1787C211yesmaximal, characteristic, complemented
10C5×#1787C211yesmaximal, characteristic, complemented
11C5×#1779C211yesmaximal, characteristic
12C23×C5×Q8C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C2×C5×C22⋊Q8—21no—
15C2×C5×C22⋊Q8—21no—
16C2×C5×C22⋊Q8—28no—
17C2×C5×C22⋊Q8C2212yes—
18C2×C5×C22⋊Q8C2212yes—
19C2×C5×#117C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4—21no—
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4—21no—
24C5×#485—28no—
25C2×C5×#107C2212yescomplemented
26C2×C5×#106C2212yescomplemented
27C2×C5×#103C2212yescomplemented
28C2×C5×#103C2212yescomplemented
29C2×C5×#103C2212yescomplemented
30C2×C5×#103C2212yescomplemented
31C2×C5×C22⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×C22⋊C8C2212yes—
34C2×C5×C22⋊C8C2212yes—
35C5×#381—21no—
36C5×#380C2211yescharacteristic
37C5×#380C2211yescharacteristic
38C5×#380C2211yescharacteristic
39C5×#380C2211yescharacteristic
40C5×#379—21no—
41C4×C5×C22⋊C4—21no—
42C4×C5×C22⋊C4—21no—
43C5×#340C2212yescomplemented
44C5×#340C2212yescomplemented
45#24010C511yesmaximal, characteristic, direct product factor, Sylow
46C25×C5D411yescharacteristic
47C22×C5×Q8—24no—
48C22×C5×Q8—21no—
49C22×C5×Q8—22no—
50C22×C5×Q8—22no—
51C22×C5×Q8—42no—
52C22×C5×Q8C2312yes—
53C23×C4×C5—21no—
54C23×C4×C5—21no—
55C23×C4×C5—24no—
56C23×C4×C5—22no—
57C23×C4×C5—22no—
58C23×C4×C5—42no—
59C23×C4×C5D411yescharacteristic
60C23×C4×C5D411yescharacteristic
61C23×C4×C5D411yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C22×C5×C8C2312yes—
66C22×C5×C8C2312yes—
67C5×C22⋊Q8—28no—
68C5×C22⋊Q8—28no—
69C5×C22⋊Q8—24no—
70C5×C22⋊Q8—24no—
71C5×C22⋊Q8—24no—
72C5×C22⋊Q8D418yes—
73C5×#117—24no—
74C5×#117—42no—
75C2×C5×C4⋊C4—28no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2312yes—
85C2×C5×C22⋊C4—28no—
86C2×C5×C22⋊C4—22no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C42×C5—21no—
95C2×C42×C5—21no—
96C5×#107—24no—
97C5×#106—24no—
98C5×#103—24no—
99C5×#103—24no—
100C5×#103—42no—
101C5×#103—42no—
102C5×C22⋊C8—24no—
103C5×C22⋊C8—22no—
104C5×C22⋊C8—22no—
105C5×C22⋊C8—42no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110C22×C22⋊Q8C2×C511yescharacteristic
111C2×#485C2×C512yescomplemented
112#2280C2×C511yescharacteristic
113#2036C2×C512yescomplemented
114#2035C2×C512yescomplemented
115#1873C2×C512yescomplemented
116#1853C2×C511yescharacteristic, complemented
117#1852C2×C511yescharacteristic, complemented
118#1787C2×C511yescharacteristic, complemented
119#1787C2×C511yescharacteristic, complemented
120#1779C2×C511yescharacteristic
121C24×C5—22no—
122C24×C5—22no—
123C24×C5—22no—
124C24×C5—22no—
125C24×C5—22no—
126C24×C5—41no—
127C24×C5—41no—
128C24×C5C2×D411yescharacteristic
129C24×C5C2×D411yescharacteristic
130C24×C5C2×D411yescharacteristic
131C2×C5×Q8—24no—
132C2×C5×Q8—22no—
133C2×C5×Q8—22no—
134C2×C5×Q8—22no—
135C2×C5×Q8—22no—
136C2×C5×Q8—22no—
137C2×C5×Q8—48no—
138C2×C5×Q8—48no—
139C2×C5×Q8—42no—
140C2×C5×Q8—42no—
141C2×C5×Q8C2×D414yes—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—24no—
148C22×C4×C5—24no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—41no—
166C22×C4×C5—41no—
167C22×C4×C5—41no—
168C22×C4×C5—48no—
169C22×C4×C5—48no—
170C22×C4×C5—42no—
171C22×C4×C5—42no—
172C22×C4×C5—42no—
173C22×C4×C5—42no—
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5C2×D414yes—
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5#4112yes—
179C22×C4×C5#4112yes—
180C22×C4×C5C2411yescharacteristic
181C2×C5×C8—22no—
182C2×C5×C8—22no—
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C5×C4⋊C4—24no—
188C5×C4⋊C4—28no—
189C5×C4⋊C4—28no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4C2×D414yes—
196C5×C22⋊C4—28no—
197C5×C22⋊C4—28no—
198C5×C22⋊C4—42no—
199C5×C22⋊C4—42no—
200C5×C22⋊C4—42no—
201C5×C22⋊C4—42no—
202C5×C22⋊C4—42no—
203C5×C22⋊C4—42no—
204C42×C5—42no—
205C42×C5—42no—
206C23×Q8C22×C511yescharacteristic
207C24×C4C22×C511yescharacteristic
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—28no—
211C2×C22⋊Q8C22×C512yes—
212C2×C22⋊Q8C22×C512yes—
213C2×#117C22×C511yescharacteristic
214C2×#117C22×C511yescharacteristic
215C22×C4⋊C4—21no—
216C22×C4⋊C4C22×C511yescharacteristic
217C22×C22⋊C4—21no—
218#485—28no—
219C2×#107C22×C512yescomplemented
220C2×#106C22×C512yescomplemented
221C2×#103C22×C512yescomplemented
222C2×#103C22×C512yescomplemented
223C2×#103C22×C512yescomplemented
224C2×#103C22×C512yescomplemented
225C2×C22⋊C8C22×C512yes—
226C2×C22⋊C8C22×C511yescharacteristic
227C2×C22⋊C8C22×C511yescharacteristic
228C2×C22⋊C8C22×C512yes—
229#381—21no—
230#380C22×C511yescharacteristic
231#380C22×C511yescharacteristic
232#380C22×C511yescharacteristic
233#380C22×C511yescharacteristic
234#379—21no—
235C4×C22⋊C4—21no—
236C4×C22⋊C4—21no—
237#340C22×C512yescomplemented
238#340C22×C512yescomplemented
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—21no—
242C23×C5—21no—
243C23×C5—28no—
244C23×C5—21no—
245C23×C5—21no—
246C23×C5—21no—
247C23×C5—21no—
248C23×C5—21no—
249C23×C5—21no—
250C23×C5—21no—
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—44no—
257C23×C5—44no—
258C23×C5—44no—
259C23×C5—44no—
260C23×C5—44no—
261C23×C5—44no—
262C23×C5#12012yes—
263C23×C5#12312yes—
264C23×C5#13512yes—
265C23×C5#13712yes—
266C23×C5#13712yes—
267C23×C5C22×D411yescharacteristic
268C5×Q8—24no—
269C5×Q8—24no—
270C5×Q8—48no—
271C5×Q8—42no—
272C5×Q8—42no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—24no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—44no—
287C2×C4×C5—44no—
288C2×C4×C5—44no—
289C2×C4×C5—48no—
290C2×C4×C5—48no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5#12012yes—
310C2×C4×C5#12312yes—
311C2×C4×C5C22×D412yes—
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5H(5,𝔽2)12yes—
315C5×C8—42no—
316C5×C8—42no—
317C25C5×D411yescharacteristic
318C22×Q8—24no—
319C22×Q8—21no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—42no—
323C22×Q8C23×C512yes—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—24no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4C5×D411yescharacteristic
331C23×C4C5×D411yescharacteristic
332C23×C4C5×D411yescharacteristic
333C23×C4C23×C511yescharacteristic
334C23×C4C23×C511yescharacteristic
335C23×C4C23×C511yescharacteristic
336C22×C8C23×C512yes—
337C22×C8C23×C512yes—
338C22⋊Q8—28no—
339C22⋊Q8—28no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343C22⋊Q8C5×D418yes—
344#117—24no—
345#117—42no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4C23×C511yescharacteristic
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C4⋊C4C23×C511yescharacteristic
355C2×C4⋊C4C23×C512yes—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C42—21no—
366C2×C42—21no—
367#107—24no—
368#106—24no—
369#103—24no—
370#103—24no—
371#103—42no—
372#103—42no—
373C22⋊C8—24no—
374C22⋊C8—22no—
375C22⋊C8—22no—
376C22⋊C8—42no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—22no—
387C22×C5—22no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5—22no—
393C22×C5—416no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5#48514yescomplemented
403C22×C5C2×#12011yescharacteristic
404C22×C5C2×#12311yescharacteristic
405C22×C5#53411yescharacteristic
406C22×C5C2×#13511yescharacteristic
407C22×C5C2×#13711yescharacteristic
408C22×C5C2×#13711yescharacteristic
409C22×C5#57511yescharacteristic
410C4×C5—22no—
411C4×C5—22no—
412C4×C5—41no—
413C4×C5—44no—
414C4×C5—44no—
415C4×C5—81no—
416C4×C5—81no—
417C4×C5—81no—
418C4×C5—81no—
419C4×C5#54612yes—
420C4×C5#54612yes—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—41no—
427C24—41no—
428C24C2×C5×D411yescharacteristic
429C24C2×C5×D411yescharacteristic
430C24C2×C5×D411yescharacteristic
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—48no—
438C2×Q8—48no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8C2×C5×D414yes—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—48no—
469C22×C4—48no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4C2×C5×D411yescharacteristic
475C22×C4C2×C5×D411yescharacteristic
476C22×C4C2×C5×D414yes—
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C5×#4112yes—
479C22×C4C5×#4112yes—
480C22×C4C24×C511yescharacteristic
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—24no—
488C4⋊C4—28no—
489C4⋊C4—28no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4C2×C5×D414yes—
496C22⋊C4—28no—
497C22⋊C4—28no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C42—42no—
505C42—42no—
506C2×C5—24no—
507C2×C5—42no—
508C2×C5—42no—
509C2×C5#240511yescharacteristic
510C2×C5#300211yescharacteristic
511C2×C5#300411yescharacteristic
512C2×C5C2×#48511yescharacteristic
513C2×C5#309511yescharacteristic
514C2×C5#319011yescharacteristic
515C2×C5#319611yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—28no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—44no—
534C23—44no—
535C23—44no—
536C23—44no—
537C23—44no—
538C23—44no—
539C23C5×#12012yes—
540C23C5×#12312yes—
541C23C5×#13512yes—
542C23C5×#13712yes—
543C23C5×#13712yes—
544C23C22×C5×D411yescharacteristic
545Q8—24no—
546Q8—24no—
547Q8—48no—
548Q8—42no—
549Q8—42no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4C5×#12012yes—
587C2×C4C5×#12312yes—
588C2×C4C22×C5×D412yes—
589C2×C4C2×C5×#4111yescharacteristic
590C2×C4C2×C5×#4111yescharacteristic
591C2×C4C5×H(5,𝔽2)12yes—
592C8—42no—
593C8—42no—
594C5#2401011yescharacteristic, direct product factor, Sylow
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—416no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22C5×#48514yescomplemented
617C22C2×C5×#12011yescharacteristic
618C22C2×C5×#12311yescharacteristic
619C22C5×#53411yescharacteristic
620C22C2×C5×#13511yescharacteristic
621C22C2×C5×#13711yescharacteristic
622C22C2×C5×#13711yescharacteristic
623C22C5×#57511yescharacteristic
624C4—22no—
625C4—22no—
626C4—44no—
627C4—41no—
628C4—44no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4C5×#54612yes—
634C4C5×#54612yes—
635C2—24no—
636C2—42no—
637C2—42no—
638C2C5×#240511yescharacteristic
639C2C5×#300211yescharacteristic
640C2C5×#300411yescharacteristic
641C2C2×C5×#48511yescharacteristic
642C2C5×#309511yescharacteristic
643C2C5×#319011yescharacteristic
644C2C5×#319611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC25×C5D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C24×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#485C2semidirect
4. C5×#2036C2semidirect
5. C5×#2035C2semidirect
6. C5×#1873C2semidirect
7. C5×#1853C2semidirect
8. C5×#1852C2semidirect
9. C5×#1787C2semidirect
10. C5×#1787C2semidirect
25. C2×C5×#107C22semidirect
26. C2×C5×#106C22semidirect
27. C2×C5×#103C22semidirect
28. C2×C5×#103C22semidirect
29. C2×C5×#103C22semidirect
30. C2×C5×#103C22semidirect
43. C5×#340C22semidirect
44. C5×#340C22semidirect
45. #24010C5direct (N × H)
111. C2×#485C2×C5semidirect
113. #2036C2×C5semidirect
114. #2035C2×C5semidirect
115. #1873C2×C5semidirect
116. #1853C2×C5semidirect
117. #1852C2×C5semidirect
118. #1787C2×C5semidirect
119. #1787C2×C5semidirect
219. C2×#107C22×C5semidirect
220. C2×#106C22×C5semidirect
221. C2×#103C22×C5semidirect
222. C2×#103C22×C5semidirect
223. C2×#103C22×C5semidirect
224. C2×#103C22×C5semidirect
237. #340C22×C5semidirect
238. #340C22×C5semidirect
402. C22×C5#485semidirect
594. C5#24010direct (N × H)
616. C22C5×#485semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×C5×#4852
C5×#22802
C5×#20362
C5×#20352
C5×#18732
C5×#18532
C5×#18522
C5×#17872
C5×#17792
#240105