Finite Group Databasebeta

← C5×#26367 #11949087

Subgroups — C5×#26367 #11949087

Order 1280.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#479C211yesmaximal, characteristic, complemented
2C2×C5×#428C211yesmaximal, characteristic
3C5×#2442C211yesmaximal, characteristic
4C5×#2362C211yesmaximal, characteristic
5C5×#2097C211yesmaximal, characteristic, complemented
6C5×#2087C211yesmaximal, characteristic, complemented
7C5×#2068C211yesmaximal, characteristic, complemented
8C5×#2059C211yesmaximal, characteristic, complemented
9C5×#1949C211yesmaximal, characteristic, complemented
10C5×#1919C211yesmaximal, characteristic, complemented
11C5×#1894C211yesmaximal, characteristic
12C5×#1872C211yesmaximal, characteristic
13C5×#1865C211yesmaximal, characteristic, complemented
14C5×#1854C211yesmaximal, characteristic
15C5×#1851C211yesmaximal, characteristic
16C22×C5×M16C2211yescharacteristic
17C2×C5×#125C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C5×#479—24no—
23C5×#428—24no—
24C2×C5×#107C2211yescharacteristic
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#400—21no—
38C5×#398—21no—
39C5×#391C2211yescharacteristic
40C5×#389C2211yescharacteristic
41C5×#389C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#388—21no—
44C5×#388—21no—
45C5×#387—21no—
46C5×#385—21no—
47C5×#382C2211yescharacteristic
48C5×#380—21no—
49C5×#380C2211yescharacteristic
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#26367C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C23×C4×C5—21no—
64C23×C4×C5C2311yescharacteristic
65C2×C5×M16—22no—
66C2×C5×M16—22no—
67C2×C5×M16—22no—
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C5×#125—22no—
73C5×#125—41no—
74C5×C22⋊Q8—22no—
75C5×C22⋊Q8Q814yes—
76C4×C5×Q8—22no—
77C4×C5×Q8—41no—
78C5×#117—22no—
79C5×#117—41no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
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—41no—
90C2×C5×C4⋊C4C2311yescharacteristic
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×#107—22no—
110C5×#106—22no—
111C5×#106—41no—
112C5×#106D414yes—
113C5×C4⋊C8—22no—
114C5×C4⋊C8—22no—
115C5×#103—22no—
116C5×#103—22no—
117C5×#103—22no—
118C5×#103—41no—
119C5×C22⋊C8—22no—
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×#95D411yescharacteristic
130C5×#95D411yescharacteristic
131C2×#479C2×C511yescharacteristic, complemented
132C2×#428C2×C511yescharacteristic
133#2442C2×C511yescharacteristic
134#2362C2×C511yescharacteristic
135#2097C2×C511yescharacteristic, complemented
136#2087C2×C511yescharacteristic, complemented
137#2068C2×C511yescharacteristic, complemented
138#2059C2×C511yescharacteristic, complemented
139#1949C2×C511yescharacteristic, complemented
140#1919C2×C511yescharacteristic, complemented
141#1894C2×C511yescharacteristic
142#1872C2×C511yescharacteristic
143#1865C2×C511yescharacteristic, complemented
144#1854C2×C511yescharacteristic
145#1851C2×C511yescharacteristic
146C24×C5C2×D411yescharacteristic
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8C2×Q812yes—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—42no—
166C22×C4×C5—42no—
167C22×C4×C5—81no—
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×Q812yes—
174C22×C4×C5#4112yes—
175C22×C4×C5C2411yescharacteristic
176C5×M16—28no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8C2×D412yes—
188C2×C5×C8#4112yes—
189C5×C4⋊C4—24no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—42no—
202C5×C4⋊C4—42no—
203C5×C4⋊C4—42no—
204C5×C4⋊C4—42no—
205C5×C4⋊C4—42no—
206C5×C4⋊C4—81no—
207C5×C4⋊C4—81no—
208C5×C4⋊C4C2×D412yes—
209C5×C4⋊C4C2×D412yes—
210C5×C4⋊C4C2×Q812yes—
211C5×C22⋊C4—24no—
212C5×C22⋊C4—41no—
213C5×C22⋊C4—41no—
214C5×C22⋊C4—42no—
215C5×C22⋊C4—42no—
216C42×C5—21no—
217C42×C5—21no—
218C42×C5—21no—
219C42×C5—21no—
220C42×C5—42no—
221C42×C5—42no—
222C42×C5—42no—
223C22×M16C22×C511yescharacteristic
224C2×#125C22×C511yescharacteristic
225C2×C22⋊Q8C22×C511yescharacteristic
226C2×C4×Q8C22×C511yescharacteristic
227C2×#117C22×C511yescharacteristic
228C22×C4⋊C4C22×C511yescharacteristic
229#479—24no—
230#428—24no—
231C2×#107C22×C511yescharacteristic
232C2×#107C22×C511yescharacteristic
233C2×#107C22×C511yescharacteristic
234C2×#106C22×C511yescharacteristic
235C2×#106C22×C511yescharacteristic
236C2×#106C22×C511yescharacteristic
237C2×C4⋊C8C22×C511yescharacteristic
238C2×C4⋊C8C22×C511yescharacteristic
239C2×#103C22×C511yescharacteristic
240C2×#103C22×C511yescharacteristic
241C2×#103C22×C511yescharacteristic
242C2×#103C22×C511yescharacteristic
243C2×C22⋊C8C22×C511yescharacteristic
244#400—21no—
245#398—21no—
246#391C22×C511yescharacteristic
247#389C22×C511yescharacteristic
248#389C22×C511yescharacteristic
249#389C22×C511yescharacteristic
250#388—21no—
251#388—21no—
252#387—21no—
253#385—21no—
254#382C22×C511yescharacteristic
255#380—21no—
256#380C22×C511yescharacteristic
257C4×C4⋊C4—21no—
258C4×C4⋊C4C22×C511yescharacteristic
259C4×C22⋊C4C22×C511yescharacteristic
260#340C22×C511yescharacteristic
261#340C22×C511yescharacteristic
262#340C22×C511yescharacteristic
263#340C22×C511yescharacteristic
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#336C22×C511yescharacteristic
267#336C22×C511yescharacteristic
268C23×C5—21no—
269C23×C5—21no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5C22⋊Q812yes—
275C23×C5C22×D411yescharacteristic
276C5×Q8—22no—
277C5×Q8—22no—
278C5×Q8—41no—
279C5×Q8—41no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
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—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—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—84no—
323C2×C4×C5C22⋊Q812yes—
324C2×C4×C5C22×D411yescharacteristic
325C2×C4×C5C22×Q811yescharacteristic
326C2×C4×C5C2×#4111yescharacteristic
327C2×C4×C5C2×#4111yescharacteristic
328C2×C4×C5H(5,𝔽2)11yescharacteristic
329C2×C4×C52−1+411yescharacteristic
330C5×C8—22no—
331C5×C8—22no—
332C5×C8—41no—
333C5×C8—41no—
334C22×Q8C23×C511yescharacteristic
335C23×C4—21no—
336C23×C4C23×C511yescharacteristic
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C22×C8C23×C511yescharacteristic
341C22×C8C23×C511yescharacteristic
342C22×C8C23×C511yescharacteristic
343C22×C8C23×C511yescharacteristic
344#125—22no—
345#125—41no—
346C22⋊Q8—22no—
347C22⋊Q8C5×Q814yes—
348C4×Q8—22no—
349C4×Q8—41no—
350#117—22no—
351#117—41no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4C23×C511yescharacteristic
363C2×C4⋊C4C23×C511yescharacteristic
364C2×C4⋊C4C23×C511yescharacteristic
365C2×C4⋊C4C23×C511yescharacteristic
366C2×C4⋊C4C23×C511yescharacteristic
367C2×C4⋊C4C23×C511yescharacteristic
368C2×C4⋊C4C23×C511yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4C5×D411yescharacteristic
373C2×C22⋊C4C5×D411yescharacteristic
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42C23×C511yescharacteristic
378C2×C42C23×C511yescharacteristic
379#107—22no—
380#107—22no—
381#107—22no—
382#106—22no—
383#106—41no—
384#106C5×D414yes—
385C4⋊C8—22no—
386C4⋊C8—22no—
387#103—22no—
388#103—22no—
389#103—22no—
390#103—41no—
391C22⋊C8—22no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95C5×D411yescharacteristic
402#95C5×D411yescharacteristic
403C22×C5—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—41no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5C2×C22⋊Q811yescharacteristic
411C22×C5D4211yescharacteristic
412C22×C5#54711yescharacteristic
413C22×C5#57511yescharacteristic
414C22×C5#57511yescharacteristic
415C22×C5#57711yescharacteristic
416C22×C5#57811yescharacteristic
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5—42no—
422C4×C5—41no—
423C4×C5—42no—
424C4×C5—41no—
425C4×C5—42no—
426C4×C5—81no—
427C4×C5—81no—
428C4×C5—81no—
429C4×C5—81no—
430C4×C5#52511yescharacteristic
431C4×C5#53911yescharacteristic
432C4×C5D4×Q811yescharacteristic
433C4×C5#55411yescharacteristic
434C24C2×C5×D411yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×C5×Q812yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—81no—
456C22×C4C2×C5×D411yescharacteristic
457C22×C4C2×C5×D411yescharacteristic
458C22×C4C2×C5×D411yescharacteristic
459C22×C4C2×C5×D411yescharacteristic
460C22×C4C2×C5×D411yescharacteristic
461C22×C4C2×C5×Q812yes—
462C22×C4C5×#4112yes—
463C22×C4C24×C511yescharacteristic
464M16—28no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×C5×D412yes—
476C2×C8C5×#4112yes—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4C2×C5×D412yes—
497C4⋊C4C2×C5×D412yes—
498C4⋊C4C2×C5×Q812yes—
499C22⋊C4—24no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—42no—
510C42—42no—
511C2×C5—42no—
512C2×C5#244911yescharacteristic
513C2×C5#308011yescharacteristic
514C2×C5#308211yescharacteristic
515C2×C5#326911yescharacteristic
516C2×C5#327511yescharacteristic
517C2×C5#334911yescharacteristic
518C2×C5#335111yescharacteristic
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23C5×C22⋊Q812yes—
526C23C22×C5×D411yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4C5×C22⋊Q812yes—
575C2×C4C22×C5×D411yescharacteristic
576C2×C4C22×C5×Q811yescharacteristic
577C2×C4C2×C5×#4111yescharacteristic
578C2×C4C2×C5×#4111yescharacteristic
579C2×C4C5×H(5,𝔽2)11yescharacteristic
580C2×C4C5×2−1+411yescharacteristic
581C8—22no—
582C8—22no—
583C8—41no—
584C8—41no—
585C5#2636711yescharacteristic, direct product factor, Sylow
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×C5×C22⋊Q811yescharacteristic
594C22C5×D4211yescharacteristic
595C22C5×#54711yescharacteristic
596C22C5×#57511yescharacteristic
597C22C5×#57511yescharacteristic
598C22C5×#57711yescharacteristic
599C22C5×#57811yescharacteristic
600C4—22no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C5×#52511yescharacteristic
614C4C5×#53911yescharacteristic
615C4C5×D4×Q811yescharacteristic
616C4C5×#55411yescharacteristic
617C2—42no—
618C2C5×#244911yescharacteristic
619C2C5×#308011yescharacteristic
620C2C5×#308211yescharacteristic
621C2C5×#326911yescharacteristic
622C2C5×#327511yescharacteristic
623C2C5×#334911yescharacteristic
624C2C5×#335111yescharacteristic
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
1. C2×C5×#479C2semidirect
5. C5×#2097C2semidirect
6. C5×#2087C2semidirect
7. C5×#2068C2semidirect
8. C5×#2059C2semidirect
9. C5×#1949C2semidirect
10. C5×#1919C2semidirect
13. C5×#1865C2semidirect
61. #26367C5direct (N × H)
131. C2×#479C2×C5semidirect
135. #2097C2×C5semidirect
136. #2087C2×C5semidirect
137. #2068C2×C5semidirect
138. #2059C2×C5semidirect
139. #1949C2×C5semidirect
140. #1919C2×C5semidirect
143. #1865C2×C5semidirect
585. C5#26367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4792
C2×C5×#4282
C5×#24422
C5×#23622
C5×#20972
C5×#20872
C5×#20682
C5×#20592
C5×#19492
C5×#19192
C5×#18942
C5×#18722
C5×#18652
C5×#18542
C5×#18512
#263675