Finite Group Databasebeta

← C5×#25229 #11947949

Subgroups — C5×#25229 #11947949

Order 1280.

808 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#484C211yesmaximal, characteristic
2C2×C5×#470C211yesmaximal, characteristic
3C5×#2503C211yesmaximal, characteristic
4C5×#2362C211yesmaximal, characteristic
5C5×#2085C211yesmaximal, characteristic, complemented
6C5×#2074C211yesmaximal, characteristic, complemented
7C5×#2068C211yesmaximal, characteristic, complemented
8C5×#2056C211yesmaximal, characteristic, complemented
9C5×#1949C211yesmaximal, characteristic, complemented
10C5×#1928C211yesmaximal, characteristic, complemented
11C5×#1878C211yesmaximal, characteristic, complemented
12C5×#1873C211yesmaximal, characteristic
13C5×#1851C211yesmaximal, characteristic
14C5×#1805C211yesmaximal, characteristic, complemented
15C5×#1736C211yesmaximal, characteristic
16C22×C5×Q16C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#484—24no—
24C5×#470—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#400—21no—
38C5×#400—21no—
39C5×#391C2211yescharacteristic
40C5×#391C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#388—21no—
44C5×#388—21no—
45C5×#387—21no—
46C5×#382C2211yescharacteristic
47C5×#382C2211yescharacteristic
48C5×#381—21no—
49C5×#381—21no—
50C4×C5×C4⋊C4—21no—
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25229C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5C2311yescharacteristic
66C2×C5×Q16—22no—
67C2×C5×Q16—22no—
68C2×C5×Q16—41no—
69C2×C5×M16—22no—
70C2×C5×M16—22no—
71C2×C5×M16—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—22no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8D414yes—
80C4×C5×Q8—22no—
81C4×C5×Q8—41no—
82C5×#117—22no—
83C5×#117—41no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4D411yescharacteristic
101C2×C5×C22⋊C4D411yescharacteristic
102C2×C42×C5—21no—
103C2×C42×C5—21no—
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C2×C42×C5C2311yescharacteristic
107C5×#107—22no—
108C5×#107—22no—
109C5×#106—22no—
110C5×C4⋊C8—22no—
111C5×C4⋊C8—41no—
112C5×#103—22no—
113C5×#103—22no—
114C5×#103—22no—
115C5×#103—22no—
116C5×#103—22no—
117C5×#103—41no—
118C5×C22⋊C8—22no—
119C5×#95—21no—
120C5×#95—21no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95D411yescharacteristic
132C5×#95D411yescharacteristic
133C2×#484C2×C511yescharacteristic
134C2×#470C2×C511yescharacteristic
135#2503C2×C511yescharacteristic
136#2362C2×C511yescharacteristic
137#2085C2×C511yescharacteristic, complemented
138#2074C2×C511yescharacteristic, complemented
139#2068C2×C511yescharacteristic, complemented
140#2056C2×C511yescharacteristic, complemented
141#1949C2×C511yescharacteristic, complemented
142#1928C2×C511yescharacteristic, complemented
143#1878C2×C511yescharacteristic, complemented
144#1873C2×C511yescharacteristic
145#1851C2×C511yescharacteristic
146#1805C2×C511yescharacteristic, complemented
147#1736C2×C511yescharacteristic
148C24×C5C2×D411yescharacteristic
149C2×C5×Q8—21no—
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8C2×D412yes—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—42no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5C2×D411yescharacteristic
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D412yes—
182C22×C4×C5#4112yes—
183C22×C4×C5C2411yescharacteristic
184C5×Q16—44no—
185C5×M16—44no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8#4112yes—
198C5×C4⋊C4—24no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—42no—
210C5×C4⋊C4—42no—
211C5×C4⋊C4—42no—
212C5×C4⋊C4—42no—
213C5×C4⋊C4C2×D412yes—
214C5×C4⋊C4#4112yes—
215C5×C22⋊C4—24no—
216C5×C22⋊C4—41no—
217C5×C22⋊C4—41no—
218C5×C22⋊C4—42no—
219C5×C22⋊C4—42no—
220C42×C5—21no—
221C42×C5—21no—
222C42×C5—21no—
223C42×C5—21no—
224C42×C5—42no—
225C42×C5—42no—
226C42×C5—42no—
227C22×Q16C22×C511yescharacteristic
228C22×M16C22×C511yescharacteristic
229C2×C22⋊Q8C22×C511yescharacteristic
230C2×C22⋊Q8C22×C511yescharacteristic
231C2×C4×Q8C22×C511yescharacteristic
232C2×#117C22×C511yescharacteristic
233C22×C4⋊C4C22×C511yescharacteristic
234#484—24no—
235#470—24no—
236C2×#107C22×C511yescharacteristic
237C2×#107C22×C511yescharacteristic
238C2×#106C22×C511yescharacteristic
239C2×C4⋊C8C22×C511yescharacteristic
240C2×C4⋊C8C22×C511yescharacteristic
241C2×#103C22×C511yescharacteristic
242C2×#103C22×C511yescharacteristic
243C2×#103C22×C511yescharacteristic
244C2×#103C22×C511yescharacteristic
245C2×#103C22×C511yescharacteristic
246C2×#103C22×C511yescharacteristic
247C2×C22⋊C8C22×C511yescharacteristic
248#400—21no—
249#400—21no—
250#391C22×C511yescharacteristic
251#391C22×C511yescharacteristic
252#391C22×C511yescharacteristic
253#389C22×C511yescharacteristic
254#388—21no—
255#388—21no—
256#387—21no—
257#382C22×C511yescharacteristic
258#382C22×C511yescharacteristic
259#381—21no—
260#381—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4C22×C511yescharacteristic
263C4×C22⋊C4C22×C511yescharacteristic
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#336C22×C511yescharacteristic
271#336C22×C511yescharacteristic
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5#12112yes—
279C23×C5C22×D411yescharacteristic
280C5×Q8—22no—
281C5×Q8—22no—
282C5×Q8—41no—
283C5×Q8—41no—
284C5×Q8—41no—
285C5×Q8—41no—
286C5×Q8—41no—
287C5×Q8—41no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—84no—
331C2×C4×C5#12112yes—
332C2×C4×C5C22×D411yescharacteristic
333C2×C4×C5C2×#4111yescharacteristic
334C2×C4×C5C2×#4111yescharacteristic
335C2×C4×C5C2×#4111yescharacteristic
336C2×C4×C5H(5,𝔽2)11yescharacteristic
337C2×C4×C52−1+411yescharacteristic
338C5×C8—22no—
339C5×C8—41no—
340C5×C8—41no—
341C5×C8—41no—
342C22×Q8C23×C511yescharacteristic
343C22×Q8C23×C511yescharacteristic
344C23×C4—21no—
345C23×C4C23×C511yescharacteristic
346C2×Q16—22no—
347C2×Q16—22no—
348C2×Q16—41no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—41no—
352C22×C8C23×C511yescharacteristic
353C22×C8C23×C511yescharacteristic
354C22×C8C23×C511yescharacteristic
355C22×C8C23×C511yescharacteristic
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8C5×D414yes—
360C4×Q8—22no—
361C4×Q8—41no—
362#117—22no—
363#117—41no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C511yescharacteristic
372C2×C4⋊C4C23×C511yescharacteristic
373C2×C4⋊C4C23×C511yescharacteristic
374C2×C4⋊C4C23×C511yescharacteristic
375C2×C4⋊C4C23×C511yescharacteristic
376C2×C4⋊C4C23×C511yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4C5×D411yescharacteristic
381C2×C22⋊C4C5×D411yescharacteristic
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42C23×C511yescharacteristic
386C2×C42C23×C511yescharacteristic
387#107—22no—
388#107—22no—
389#106—22no—
390C4⋊C8—22no—
391C4⋊C8—41no—
392#103—22no—
393#103—22no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—41no—
398C22⋊C8—22no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95C5×D411yescharacteristic
412#95C5×D411yescharacteristic
413C22×C5—22no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5C2×#12111yescharacteristic
421C22×C5#54611yescharacteristic
422C22×C5#54711yescharacteristic
423C22×C5#57511yescharacteristic
424C22×C5#57511yescharacteristic
425C22×C5#57811yescharacteristic
426C22×C5#57811yescharacteristic
427C4×C5—22no—
428C4×C5—41no—
429C4×C5—41no—
430C4×C5—42no—
431C4×C5—42no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5—41no—
435C4×C5—81no—
436C4×C5—81no—
437C4×C5—81no—
438C4×C5—81no—
439C4×C5—81no—
440C4×C5#52911yescharacteristic
441C4×C5#53911yescharacteristic
442C4×C5#54611yescharacteristic
443C4×C5#54711yescharacteristic
444C24C2×C5×D411yescharacteristic
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×C5×D412yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4C2×C5×D411yescharacteristic
473C22×C4C2×C5×D411yescharacteristic
474C22×C4C2×C5×D411yescharacteristic
475C22×C4C2×C5×D411yescharacteristic
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D412yes—
478C22×C4C5×#4112yes—
479C22×C4C24×C511yescharacteristic
480Q16—44no—
481M16—44no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8C5×#4112yes—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4C2×C5×D412yes—
510C4⋊C4C5×#4112yes—
511C22⋊C4—24no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—42no—
522C42—42no—
523C2×C5—42no—
524C2×C5#242511yescharacteristic
525C2×C5#304011yescharacteristic
526C2×C5#304411yescharacteristic
527C2×C5#331511yescharacteristic
528C2×C5#332711yescharacteristic
529C2×C5#334911yescharacteristic
530C2×C5#335211yescharacteristic
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23C5×#12112yes—
538C23C22×C5×D411yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
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×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4C5×#12112yes—
591C2×C4C22×C5×D411yescharacteristic
592C2×C4C2×C5×#4111yescharacteristic
593C2×C4C2×C5×#4111yescharacteristic
594C2×C4C2×C5×#4111yescharacteristic
595C2×C4C5×H(5,𝔽2)11yescharacteristic
596C2×C4C5×2−1+411yescharacteristic
597C8—22no—
598C8—41no—
599C8—41no—
600C8—41no—
601C5#2522911yescharacteristic, direct product factor, Sylow
602C22—22no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22C2×C5×#12111yescharacteristic
610C22C5×#54611yescharacteristic
611C22C5×#54711yescharacteristic
612C22C5×#57511yescharacteristic
613C22C5×#57511yescharacteristic
614C22C5×#57811yescharacteristic
615C22C5×#57811yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4C5×#52911yescharacteristic
630C4C5×#53911yescharacteristic
631C4C5×#54611yescharacteristic
632C4C5×#54711yescharacteristic
633C2—42no—
634C2C5×#242511yescharacteristic
635C2C5×#304011yescharacteristic
636C2C5×#304411yescharacteristic
637C2C5×#331511yescharacteristic
638C2C5×#332711yescharacteristic
639C2C5×#334911yescharacteristic
640C2C5×#335211yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
5. C5×#2085C2semidirect
6. C5×#2074C2semidirect
7. C5×#2068C2semidirect
8. C5×#2056C2semidirect
9. C5×#1949C2semidirect
10. C5×#1928C2semidirect
11. C5×#1878C2semidirect
14. C5×#1805C2semidirect
61. #25229C5direct (N × H)
137. #2085C2×C5semidirect
138. #2074C2×C5semidirect
139. #2068C2×C5semidirect
140. #2056C2×C5semidirect
141. #1949C2×C5semidirect
142. #1928C2×C5semidirect
143. #1878C2×C5semidirect
146. #1805C2×C5semidirect
601. C5#25229direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4842
C2×C5×#4702
C5×#25032
C5×#23622
C5×#20852
C5×#20742
C5×#20682
C5×#20562
C5×#19492
C5×#19282
C5×#18782
C5×#18732
C5×#18512
C5×#18052
C5×#17362
#252295