Finite Group Databasebeta

← C5×#18258 #11940978

Subgroups — C5×#18258 #11940978

Order 1280.

1276 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3538C211yesmaximal, characteristic, complemented
2C5×#3003C211yesmaximal, characteristic
3C2×C5×#450C211yesmaximal, characteristic, complemented
4C5×#2435C211yesmaximal, characteristic, complemented
5C5×#1599C214yesmaximal, complemented
6C5×#1597C214yesmaximal, complemented
7C5×#1508C211yesmaximal, characteristic, complemented
8C5×#1501C211yesmaximal, characteristic, complemented
9C5×#1472C211yesmaximal, characteristic, complemented
10C23×C5×D4C2211yescharacteristic
11C2×C5×AGL(1,ℤ/8)—21no—
12C22×C5×SD16—21no—
13C5×#563—22no—
14C5×#552—21no—
15C5×#552—21no—
16C5×#551—22no—
17C5×D4×Q8—21no—
18C5×D4×Q8—21no—
19C5×#544—21no—
20C5×#544C2212yescomplemented
21C5×#541—21no—
22C5×#539—21no—
23C5×#539C2212yescomplemented
24C5×#536—21no—
25C2×C5×#124—21no—
26C5×#525C2211yescharacteristic
27C2×C5×C22⋊Q8C2211yescharacteristic
28C2×C5×C22⋊Q8C2211yescharacteristic
29C5×#450—22no—
30C5×#450—21no—
31C5×#450C2214yes—
32C5×#450C2212yes—
33C5×#447—21no—
34C5×#447C2212yes—
35C5×#418—21no—
36C2×C5×#102—21no—
37C5×#407C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C5×#394C2214yes—
40C5×#390—21no—
41C5×#379—22no—
42C4×C5×C22⋊C4C2211yescharacteristic
43C5×#328C2212yescomplemented
44C5×#328C2214yescomplemented
45C5×#327C2212yescomplemented
46C5×#324C2214yescomplemented
47#18258C511yesmaximal, characteristic, direct product factor, Sylow
48C25×C5—21no—
49C2×C5×#41D411yescharacteristic
50C22×C5×Q8—21no—
51C22×C5×Q8D411yescharacteristic
52C22×C5×Q8D411yescharacteristic
53C22×C5×D4—21no—
54C22×C5×D4—21no—
55C22×C5×D4—21no—
56C22×C5×D4—21no—
57C22×C5×D4—21no—
58C22×C5×D4—44no—
59C22×C5×D4C2312yes—
60C23×C4×C5C2311yescharacteristic
61C5×AGL(1,ℤ/8)—44no—
62C2×C5×SD16—24no—
63C2×C5×SD16—22no—
64C2×C5×SD16—44no—
65C2×C5×D8—22no—
66C2×C5×M16—21no—
67C22×C5×C8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—22no—
70C5×C4⋊Q8—22no—
71C5×C4⋊Q8—22no—
72C5×#126—22no—
73C5×#126—22no—
74C5×#126—22no—
75C5×#126—22no—
76C5×#125—21no—
77C5×#125—22no—
78C5×#125—22no—
79C5×#125—22no—
80C5×#125—22no—
81C5×#124—22no—
82C5×#124—44no—
83C5×#123—22no—
84C5×#123—22no—
85C5×#123—22no—
86C5×#123—21no—
87C5×#123—22no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—21no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—21no—
96C5×C22⋊Q8—21no—
97C5×C22⋊Q8—21no—
98C5×C22⋊Q8—21no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8D412yes—
101C5×C22⋊Q8D411yescharacteristic
102C5×C22⋊Q8C2312yes—
103C5×C22⋊Q8C2311yescharacteristic
104C5×#121D411yescharacteristic
105C5×#121C2311yescharacteristic
106C5×#120—21no—
107C4×C5×Q8—21no—
108C4×C5×Q8—21no—
109C4×C5×D4—22no—
110C4×C5×D4—21no—
111C4×C5×D4—21no—
112C4×C5×D4—22no—
113C5×#117—21no—
114C5×#117—22no—
115C5×#117—22no—
116C5×#117D411yescharacteristic
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4D411yescharacteristic
120C2×C5×C4⋊C4C2312yes—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—24no—
124C2×C5×C22⋊C4—24no—
125C2×C5×C22⋊C4D412yes—
126C2×C42×C5—21no—
127C5×#102—24no—
128C5×#102—22no—
129C5×#102—22no—
130C5×C22⋊C8—21no—
131C5×C22⋊C8—21no—
132C5×C22⋊C8C2312yes—
133C5×C22⋊C8C2312yes—
134C5×#95C2312yes—
135#3538C2×C511yescharacteristic, complemented
136#3003C2×C511yescharacteristic
137C2×#450C2×C511yescharacteristic, complemented
138#2435C2×C511yescharacteristic, complemented
139#1599C2×C514yescomplemented
140#1597C2×C514yescomplemented
141#1508C2×C511yescharacteristic, complemented
142#1501C2×C511yescharacteristic, complemented
143#1472C2×C511yescharacteristic, complemented
144C24×C5—22no—
145C24×C5—44no—
146C24×C5—44no—
147C24×C5—41no—
148C24×C5—41no—
149C24×C5—82no—
150C24×C5C2×D411yescharacteristic
151C5×#41—42no—
152C2×C5×Q8—22no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—42no—
157C2×C5×Q8—42no—
158C2×C5×Q8—82no—
159C2×C5×Q8C2×D412yes—
160C2×C5×Q8C2×D411yescharacteristic
161C2×C5×D4—24no—
162C2×C5×D4—24no—
163C2×C5×D4—24no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—22no—
168C2×C5×D4—22no—
169C2×C5×D4—42no—
170C2×C5×D4—42no—
171C2×C5×D4—42no—
172C2×C5×D4—44no—
173C2×C5×D4—44no—
174C2×C5×D4—44no—
175C2×C5×D4—41no—
176C2×C5×D4—41no—
177C2×C5×D4C2×D411yescharacteristic
178C22×C4×C5—21no—
179C22×C4×C5—22no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—22no—
183C22×C4×C5—42no—
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D412yes—
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2411yescharacteristic
192C5×SD16—48no—
193C5×SD16—44no—
194C5×D8—44no—
195C5×M16—42no—
196C2×C5×C8—22no—
197C2×C5×C8—22no—
198C2×C5×C8—42no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C4⋊C4—22no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C2×D412yes—
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C4⋊C4C2×D411yescharacteristic
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—48no—
233C5×C22⋊C4—84no—
234C42×C5—22no—
235C42×C5—22no—
236C42×C5—22no—
237C42×C5—21no—
238C42×C5—42no—
239C23×D4C22×C511yescharacteristic
240C2×AGL(1,ℤ/8)—21no—
241C22×SD16—21no—
242#563—22no—
243#552—21no—
244#552—21no—
245#551—22no—
246D4×Q8—21no—
247D4×Q8—21no—
248#544—21no—
249#544C22×C512yescomplemented
250#541—21no—
251#539—21no—
252#539C22×C512yescomplemented
253#536—21no—
254C2×#124—21no—
255#525C22×C511yescharacteristic
256C2×C22⋊Q8C22×C511yescharacteristic
257C2×C22⋊Q8C22×C511yescharacteristic
258#450—22no—
259#450—21no—
260#450C22×C514yes—
261#450C22×C512yes—
262#447—21no—
263#447C22×C512yes—
264#418—21no—
265C2×#102—21no—
266#407C22×C511yescharacteristic
267C2×C22⋊C8C22×C511yescharacteristic
268#394C22×C514yes—
269#390—21no—
270#379—22no—
271C4×C22⋊C4C22×C511yescharacteristic
272#328C22×C514yescomplemented
273#328C22×C512yescomplemented
274#327C22×C512yescomplemented
275#324C22×C514yescomplemented
276C23×C5—22no—
277C23×C5—22no—
278C23×C5—24no—
279C23×C5—21no—
280C23×C5—41no—
281C23×C5—44no—
282C23×C5—44no—
283C23×C5—42no—
284C23×C5—44no—
285C23×C5—42no—
286C23×C5—44no—
287C23×C5—82no—
288C23×C5—82no—
289C23×C5—82no—
290C23×C5—816no—
291C23×C5—82no—
292C23×C5#12011yescharacteristic
293C23×C5#12011yescharacteristic
294C23×C5C22×D411yescharacteristic
295C5×Q8—42no—
296C5×Q8—41no—
297C5×Q8—42no—
298C5×Q8—42no—
299C5×Q8—81no—
300C5×Q8—82no—
301C5×D4—24no—
302C5×D4—24no—
303C5×D4—41no—
304C5×D4—42no—
305C5×D4—42no—
306C5×D4—44no—
307C5×D4—42no—
308C5×D4—42no—
309C5×D4—44no—
310C5×D4—81no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—21no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—24no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—81no—
332C2×C4×C5—82no—
333C2×C4×C5#12011yescharacteristic
334C2×C4×C5#12011yescharacteristic
335C2×C4×C5C22×D411yescharacteristic
336C2×C4×C5C22×D411yescharacteristic
337C5×C8—42no—
338C5×C8—42no—
339C25—21no—
340C2×#41C5×D411yescharacteristic
341C22×Q8—21no—
342C22×Q8C5×D411yescharacteristic
343C22×Q8C5×D411yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—44no—
350C22×D4C23×C512yes—
351C23×C4C23×C511yescharacteristic
352AGL(1,ℤ/8)—44no—
353C2×SD16—24no—
354C2×SD16—22no—
355C2×SD16—44no—
356C2×D8—22no—
357C2×M16—21no—
358C22×C8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363#126—22no—
364#126—22no—
365#126—22no—
366#126—22no—
367#125—21no—
368#125—22no—
369#125—22no—
370#125—22no—
371#125—22no—
372#124—22no—
373#124—44no—
374#123—22no—
375#123—22no—
376#123—22no—
377#123—21no—
378#123—22no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8C5×D412yes—
392C22⋊Q8C5×D411yescharacteristic
393C22⋊Q8C23×C512yes—
394C22⋊Q8C23×C511yescharacteristic
395#121C5×D411yescharacteristic
396#121C23×C511yescharacteristic
397#120—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—22no—
404#117—21no—
405#117—22no—
406#117—22no—
407#117C5×D411yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4C5×D411yescharacteristic
410C2×C4⋊C4C5×D411yescharacteristic
411C2×C4⋊C4C23×C512yes—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4C5×D412yes—
417C2×C42—21no—
418#102—24no—
419#102—22no—
420#102—22no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8C23×C512yes—
424C22⋊C8C23×C512yes—
425#95C23×C512yes—
426C22×C5—21no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—21no—
430C22×C5—21no—
431C22×C5—21no—
432C22×C5—21no—
433C22×C5—44no—
434C22×C5—48no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—44no—
439C22×C5—84no—
440C22×C5—88no—
441C22×C5—88no—
442C22×C5—82no—
443C22×C5—82no—
444C22×C5#45412yes—
445C22×C5C2×#12011yescharacteristic
446C22×C5#57712yes—
447C4×C5—21no—
448C4×C5—21no—
449C4×C5—21no—
450C4×C5—42no—
451C4×C5—41no—
452C4×C5—42no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—42no—
456C4×C5—42no—
457C4×C5—82no—
458C4×C5B(4,𝔽2)12yes—
459C24—22no—
460C24—44no—
461C24—44no—
462C24—41no—
463C24—41no—
464C24—82no—
465C24C2×C5×D411yescharacteristic
466#41—42no—
467C2×Q8—22no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—82no—
474C2×Q8C2×C5×D412yes—
475C2×Q8C2×C5×D411yescharacteristic
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4C2×C5×D411yescharacteristic
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—42no—
499C22×C4C2×C5×D412yes—
500C22×C4C2×C5×D411yescharacteristic
501C22×C4C2×C5×D411yescharacteristic
502C22×C4C2×C5×D411yescharacteristic
503C22×C4C2×C5×D412yes—
504C22×C4C2×C5×D411yescharacteristic
505C22×C4C2×C5×D411yescharacteristic
506C22×C4C24×C511yescharacteristic
507SD16—48no—
508SD16—44no—
509D8—44no—
510M16—42no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—42no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4C2×C5×D412yes—
532C4⋊C4C2×C5×D411yescharacteristic
533C4⋊C4C2×C5×D411yescharacteristic
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—48no—
547C22⋊C4—42no—
548C22⋊C4—84no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—21no—
553C42—42no—
554C2×C5—22no—
555C2×C5—22no—
556C2×C5—41no—
557C2×C5—81no—
558C2×C5—84no—
559C2×C5#301011yescharacteristic
560C2×C5C2×#45411yescharacteristic
561C2×C5C2×B(4,𝔽2)11yescharacteristic
562C23—22no—
563C23—22no—
564C23—24no—
565C23—21no—
566C23—41no—
567C23—44no—
568C23—44no—
569C23—42no—
570C23—44no—
571C23—42no—
572C23—44no—
573C23—82no—
574C23—82no—
575C23—82no—
576C23—816no—
577C23—82no—
578C23C5×#12011yescharacteristic
579C23C5×#12011yescharacteristic
580C23C22×C5×D411yescharacteristic
581Q8—42no—
582Q8—41no—
583Q8—42no—
584Q8—42no—
585Q8—81no—
586Q8—82no—
587D4—24no—
588D4—24no—
589D4—41no—
590D4—42no—
591D4—42no—
592D4—44no—
593D4—42no—
594D4—42no—
595D4—44no—
596D4—81no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—81no—
618C2×C4—82no—
619C2×C4C5×#12011yescharacteristic
620C2×C4C5×#12011yescharacteristic
621C2×C4C22×C5×D411yescharacteristic
622C2×C4C22×C5×D411yescharacteristic
623C8—42no—
624C8—42no—
625C5#1825811yescharacteristic, direct product factor, Sylow
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—44no—
634C22—48no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—44no—
639C22—84no—
640C22—88no—
641C22—88no—
642C22—82no—
643C22—82no—
644C22C5×#45412yes—
645C22C2×C5×#12011yescharacteristic
646C22C5×#57712yes—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4C5×B(4,𝔽2)12yes—
659C2—22no—
660C2—22no—
661C2—41no—
662C2—84no—
663C2—81no—
664C2C5×#301011yescharacteristic
665C2C2×C5×#45411yescharacteristic
666C2C2×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3538C2semidirect
3. C2×C5×#450C2semidirect
4. C5×#2435C2semidirect
5. C5×#1599C2semidirect
6. C5×#1597C2semidirect
7. C5×#1508C2semidirect
8. C5×#1501C2semidirect
9. C5×#1472C2semidirect
20. C5×#544C22semidirect
23. C5×#539C22semidirect
43. C5×#328C22semidirect
44. C5×#328C22semidirect
45. C5×#327C22semidirect
46. C5×#324C22semidirect
47. #18258C5direct (N × H)
135. #3538C2×C5semidirect
137. C2×#450C2×C5semidirect
138. #2435C2×C5semidirect
139. #1599C2×C5semidirect
140. #1597C2×C5semidirect
141. #1508C2×C5semidirect
142. #1501C2×C5semidirect
143. #1472C2×C5semidirect
249. #544C22×C5semidirect
252. #539C22×C5semidirect
272. #328C22×C5semidirect
273. #328C22×C5semidirect
274. #327C22×C5semidirect
275. #324C22×C5semidirect
625. C5#18258direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35382
C5×#30032
C2×C5×#4502
C5×#24352
C5×#15992
C5×#15972
C5×#15082
C5×#15012
C5×#14722
#182585