Finite Group Databasebeta

← C5×#26829 #11949549

Subgroups — C5×#26829 #11949549

Order 1280.

806 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#491C211yesmaximal, characteristic, complemented
2C2×C4×C5×SD16C211yesmaximal, characteristic
3C5×#2454C211yesmaximal, characteristic
4C5×#2446C211yesmaximal, characteristic, complemented
5C5×#2066C211yesmaximal, characteristic, complemented
6C5×#2059C211yesmaximal, characteristic, complemented
7C5×#2055C211yesmaximal, characteristic
8C5×#2013C211yesmaximal, characteristic
9C5×#1973C211yesmaximal, characteristic
10C5×#1936C211yesmaximal, characteristic
11C5×#1935C211yesmaximal, characteristic, complemented
12C5×#1933C211yesmaximal, characteristic, complemented
13C5×#1877C211yesmaximal, characteristic
14C5×#1863C211yesmaximal, characteristic, complemented
15C5×#1771C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×#125C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C5×#491—24no—
23C4×C5×SD16—24no—
24C2×C5×#107C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#97C2211yescharacteristic
36C2×C5×#97C2211yescharacteristic
37C2×C4×C5×C8C2211yescharacteristic
38C5×#400—21no—
39C5×#399—21no—
40C5×#398—21no—
41C5×#396—21no—
42C5×#391C2211yescharacteristic
43C5×#391C2211yescharacteristic
44C5×#391C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#390C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#387—21no—
51C5×#387—21no—
52C5×#385—21no—
53C5×#380—21no—
54C4×C5×C4⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26829C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C2×C5×SD16—22no—
67C2×C5×SD16—22no—
68C2×C5×SD16—22no—
69C2×C5×SD16—22no—
70C2×C5×SD16—22no—
71C2×C5×SD16—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8—41no—
78C5×#125—22no—
79C5×#125—41no—
80C4×C5×Q8—22no—
81C4×C5×Q8—41no—
82C4×C5×D4—22no—
83C4×C5×D4—41no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C2×C42×C5C2311yescharacteristic
107C2×C42×C5C2311yescharacteristic
108C5×#107—41no—
109C5×#106—22no—
110C5×C4⋊C8—22no—
111C5×#103—22no—
112C5×#103—22no—
113C5×#103—22no—
114C5×#103—22no—
115C5×#103—22no—
116C5×#103D414yes—
117C5×#102—22no—
118C5×#102—22no—
119C5×#97—22no—
120C5×#97—22no—
121C4×C5×C8—22no—
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×#491C2×C511yescharacteristic, complemented
134C2×C4×SD16C2×C511yescharacteristic
135#2454C2×C511yescharacteristic
136#2446C2×C511yescharacteristic, complemented
137#2066C2×C511yescharacteristic, complemented
138#2059C2×C511yescharacteristic, complemented
139#2055C2×C511yescharacteristic
140#2013C2×C511yescharacteristic
141#1973C2×C511yescharacteristic
142#1936C2×C511yescharacteristic
143#1935C2×C511yescharacteristic, complemented
144#1933C2×C511yescharacteristic, complemented
145#1877C2×C511yescharacteristic
146#1863C2×C511yescharacteristic, complemented
147#1771C2×C511yescharacteristic, complemented
148C24×C5—21no—
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—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4#4112yes—
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—21no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5—81no—
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2411yescharacteristic
184C5×SD16—28no—
185C5×SD16—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×C8C2×D412yes—
196C2×C5×C8#4112yes—
197C2×C5×C8#4112yes—
198C5×C4⋊C4—22no—
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—41no—
209C5×C4⋊C4—42no—
210C5×C4⋊C4—42no—
211C5×C4⋊C4—42no—
212C5×C4⋊C4—42no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—81no—
216C5×C4⋊C4—81no—
217C5×C4⋊C4C2×D412yes—
218C5×C22⋊C4—42no—
219C5×C22⋊C4—42no—
220C5×C22⋊C4—81no—
221C5×C22⋊C4—81no—
222C5×C22⋊C4—81no—
223C42×C5—21no—
224C42×C5—21no—
225C42×C5—21no—
226C42×C5—21no—
227C42×C5—21no—
228C42×C5—21no—
229C42×C5—42no—
230C22×SD16C22×C511yescharacteristic
231C22×SD16C22×C511yescharacteristic
232C2×C4⋊Q8C22×C511yescharacteristic
233C2×#125C22×C511yescharacteristic
234C2×C4×Q8C22×C511yescharacteristic
235C2×C4×D4C22×C511yescharacteristic
236#491—24no—
237C4×SD16—24no—
238C2×#107C22×C511yescharacteristic
239C2×#106C22×C511yescharacteristic
240C2×C4⋊C8C22×C511yescharacteristic
241C2×#103C22×C511yescharacteristic
242C2×#103C22×C511yescharacteristic
243C2×#103C22×C511yescharacteristic
244C2×#103C22×C511yescharacteristic
245C2×#103C22×C511yescharacteristic
246C2×#103C22×C511yescharacteristic
247C2×#102C22×C511yescharacteristic
248C2×#102C22×C511yescharacteristic
249C2×#97C22×C511yescharacteristic
250C2×#97C22×C511yescharacteristic
251C2×C4×C8C22×C511yescharacteristic
252#400—21no—
253#399—21no—
254#398—21no—
255#396—21no—
256#391C22×C511yescharacteristic
257#391C22×C511yescharacteristic
258#391C22×C511yescharacteristic
259#390C22×C511yescharacteristic
260#390C22×C511yescharacteristic
261#389C22×C511yescharacteristic
262#389C22×C511yescharacteristic
263#389C22×C511yescharacteristic
264#387—21no—
265#387—21no—
266#385—21no—
267#380—21no—
268C4×C4⋊C4C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#336C22×C511yescharacteristic
274#336C22×C511yescharacteristic
275C23×C5—22no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5C22×D411yescharacteristic
283C5×Q8—22no—
284C5×Q8—22no—
285C5×Q8—41no—
286C5×Q8—41no—
287C5×Q8—41no—
288C5×Q8—41no—
289C5×Q8—41no—
290C5×Q8—41no—
291C5×D4—22no—
292C5×D4—22no—
293C5×D4—41no—
294C5×D4—41no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
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—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—84no—
334C2×C4×C5#13712yes—
335C2×C4×C5C22×D411yescharacteristic
336C2×C4×C5C2×#4111yescharacteristic
337C2×C4×C5C2×#4111yescharacteristic
338C2×C4×C5C2×#4111yescharacteristic
339C2×C4×C5H(5,𝔽2)11yescharacteristic
340C2×C4×C52−1+411yescharacteristic
341C5×C8—22no—
342C5×C8—22no—
343C5×C8—22no—
344C5×C8—41no—
345C22×Q8C23×C511yescharacteristic
346C22×Q8C23×C511yescharacteristic
347C22×D4C23×C511yescharacteristic
348C23×C4—21no—
349C2×SD16—22no—
350C2×SD16—22no—
351C2×SD16—22no—
352C2×SD16—22no—
353C2×SD16—22no—
354C2×SD16—41no—
355C22×C8C23×C511yescharacteristic
356C22×C8C23×C511yescharacteristic
357C22×C8C23×C511yescharacteristic
358C22×C8C23×C511yescharacteristic
359C4⋊Q8—22no—
360C4⋊Q8—41no—
361#125—22no—
362#125—41no—
363C4×Q8—22no—
364C4×Q8—41no—
365C4×D4—22no—
366C4×D4—41no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C5×D411yescharacteristic
376C2×C4⋊C4C5×D411yescharacteristic
377C2×C4⋊C4C23×C511yescharacteristic
378C2×C4⋊C4C23×C511yescharacteristic
379C2×C4⋊C4C23×C511yescharacteristic
380C2×C4⋊C4C23×C511yescharacteristic
381C2×C4⋊C4C23×C511yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42C23×C511yescharacteristic
389C2×C42C23×C511yescharacteristic
390C2×C42C23×C511yescharacteristic
391#107—41no—
392#106—22no—
393C4⋊C8—22no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#103—22no—
399#103C5×D414yes—
400#102—22no—
401#102—22no—
402#97—22no—
403#97—22no—
404C4×C8—22no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95C5×D411yescharacteristic
415#95C5×D411yescharacteristic
416C22×C5—42no—
417C22×C5—42no—
418C22×C5—42no—
419C22×C5—81no—
420C22×C5—81no—
421C22×C5—81no—
422C22×C5—81no—
423C22×C5#53211yescharacteristic
424C22×C5D4211yescharacteristic
425C22×C5#54811yescharacteristic
426C22×C5C2×#13711yescharacteristic
427C22×C5#57511yescharacteristic
428C22×C5#57711yescharacteristic
429C22×C5#57711yescharacteristic
430C4×C5—22no—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5—41no—
435C4×C5—42no—
436C4×C5—41no—
437C4×C5—41no—
438C4×C5—81no—
439C4×C5—81no—
440C4×C5—81no—
441C4×C5—81no—
442C4×C5—81no—
443C4×C5#52511yescharacteristic
444C4×C5#54211yescharacteristic
445C4×C5#54711yescharacteristic
446C4×C5#55111yescharacteristic
447C24—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×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8C2×C5×D412yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4C5×#4112yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—81no—
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C2×C5×D411yescharacteristic
480C22×C4C2×C5×D411yescharacteristic
481C22×C4C2×C5×D411yescharacteristic
482C22×C4C24×C511yescharacteristic
483SD16—28no—
484SD16—44no—
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×C8—21no—
494C2×C8C2×C5×D412yes—
495C2×C8C5×#4112yes—
496C2×C8C5×#4112yes—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4C2×C5×D412yes—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—42no—
529C2×C5—82no—
530C2×C5#246111yescharacteristic
531C2×C5#317211yescharacteristic
532C2×C5#317411yescharacteristic
533C2×C5#326611yescharacteristic
534C2×C5#327111yescharacteristic
535C2×C5#337211yescharacteristic
536C2×C5#337611yescharacteristic
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C22×C5×D411yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553D4—22no—
554D4—22no—
555D4—41no—
556D4—41no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
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—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4C5×#13712yes—
597C2×C4C22×C5×D411yescharacteristic
598C2×C4C2×C5×#4111yescharacteristic
599C2×C4C2×C5×#4111yescharacteristic
600C2×C4C2×C5×#4111yescharacteristic
601C2×C4C5×H(5,𝔽2)11yescharacteristic
602C2×C4C5×2−1+411yescharacteristic
603C8—22no—
604C8—22no—
605C8—22no—
606C8—41no—
607C5#2682911yescharacteristic, direct product factor, Sylow
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22C5×#53211yescharacteristic
616C22C5×D4211yescharacteristic
617C22C5×#54811yescharacteristic
618C22C2×C5×#13711yescharacteristic
619C22C5×#57511yescharacteristic
620C22C5×#57711yescharacteristic
621C22C5×#57711yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4C5×#52511yescharacteristic
636C4C5×#54211yescharacteristic
637C4C5×#54711yescharacteristic
638C4C5×#55111yescharacteristic
639C2—82no—
640C2C5×#246111yescharacteristic
641C2C5×#317211yescharacteristic
642C2C5×#317411yescharacteristic
643C2C5×#326611yescharacteristic
644C2C5×#327111yescharacteristic
645C2C5×#337211yescharacteristic
646C2C5×#337611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#491C2semidirect
4. C5×#2446C2semidirect
5. C5×#2066C2semidirect
6. C5×#2059C2semidirect
11. C5×#1935C2semidirect
12. C5×#1933C2semidirect
14. C5×#1863C2semidirect
15. C5×#1771C2semidirect
61. #26829C5direct (N × H)
133. C2×#491C2×C5semidirect
136. #2446C2×C5semidirect
137. #2066C2×C5semidirect
138. #2059C2×C5semidirect
143. #1935C2×C5semidirect
144. #1933C2×C5semidirect
146. #1863C2×C5semidirect
147. #1771C2×C5semidirect
607. C5#26829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4912
C2×C4×C5×SD162
C5×#24542
C5×#24462
C5×#20662
C5×#20592
C5×#20552
C5×#20132
C5×#19732
C5×#19362
C5×#19352
C5×#19332
C5×#18772
C5×#18632
C5×#17712
#268295