Finite Group Databasebeta

← C5×#11115 #11933835

Subgroups — C5×#11115 #11933835

Order 1280.

864 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2911C211yesmaximal, characteristic, complemented
2C2×C5×#421C211yesmaximal, characteristic
3C2×C5×#421C211yesmaximal, characteristic
4C2×C5×#410C211yesmaximal, characteristic
5C5×#1742C211yesmaximal, characteristic, complemented
6C5×#1740C211yesmaximal, characteristic, complemented
7C2×C5×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×M16C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C2×C5×#117C2211yescharacteristic
12C2×C5×#117C2211yescharacteristic
13C2×C5×#117C2211yescharacteristic
14C2×C5×#117C2211yescharacteristic
15C5×#428—22no—
16C5×#428—22no—
17C5×#427—22no—
18C5×#421—22no—
19C5×#421—22no—
20C5×#421—22no—
21C5×#421—22no—
22C2×C5×#104—22no—
23C2×C5×#104C414yescomplemented
24C5×#410—22no—
25C5×#410—22no—
26C2×C5×#99—22no—
27C5×#343—22no—
28C5×#342—22no—
29C5×H(3,ℤ/4)—22no—
30#11115C511yesmaximal, characteristic, direct product factor, Sylow
31C2×C5×#41—21no—
32C2×C5×#41—21no—
33C2×C5×#41—21no—
34C2×C5×#41—21no—
35C2×C5×#41—21no—
36C2×C5×#41—21no—
37C2×C5×#41—21no—
38C2×C5×#41—21no—
39C2×C5×#41—21no—
40C2×C5×#41—21no—
41C2×C5×#41C2×C412yes—
42C2×C5×#41D412yes—
43C22×C5×Q8Q811yescharacteristic
44C22×C5×D4—21no—
45C22×C5×D4Q811yescharacteristic
46C23×C4×C5—21no—
47C23×C4×C5C2311yescharacteristic
48C2×C5×M16—21no—
49C2×C5×M16—21no—
50C2×C5×M16—21no—
51C2×C5×M16—21no—
52C2×C5×M16—21no—
53C2×C5×M16—21no—
54C2×C5×M16—21no—
55C2×C5×M16—21no—
56C2×C5×M16C2×C412yes—
57C2×C5×M16D412yes—
58C2×C5×M16D412yes—
59C2×C5×M16D412yes—
60C22×C5×C8—21no—
61C22×C5×C8—21no—
62C5×#117—21no—
63C5×#117—21no—
64C5×#117—21no—
65C5×#117—21no—
66C5×#117—21no—
67C5×#117—21no—
68C5×#117—21no—
69C5×#117—21no—
70C5×#117—21no—
71C5×#117—21no—
72C5×#117—21no—
73C5×#117—21no—
74C5×#117—21no—
75C5×#117—21no—
76C5×#117D412yes—
77C5×#117D412yes—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4D412yes—
86C2×C42×C5—21no—
87C2×C42×C5—21no—
88C2×C42×C5—21no—
89C2×C42×C5C2×C412yes—
90C5×#107—24no—
91C5×#106—24no—
92C5×#104—28no—
93C5×#104—28no—
94C5×#99—28no—
95#2911C2×C511yescharacteristic, complemented
96C2×#421C2×C511yescharacteristic
97C2×#421C2×C511yescharacteristic
98C2×#410C2×C511yescharacteristic
99#1742C2×C511yescharacteristic, complemented
100#1740C2×C511yescharacteristic, complemented
101C2×H(3,ℤ/4)C2×C511yescharacteristic, complemented
102C24×C5—21no—
103C24×C5C2×D411yescharacteristic
104C5×#41—22no—
105C5×#41—22no—
106C5×#41—22no—
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—22no—
112C5×#41—41no—
113C5×#41—41no—
114C5×#41—41no—
115C5×#41—41no—
116C5×#41—41no—
117C5×#41—41no—
118C5×#41—41no—
119C5×#41—41no—
120C2×C5×Q8—21no—
121C2×C5×Q8—21no—
122C2×C5×Q8—21no—
123C2×C5×Q8—21no—
124C2×C5×Q8—21no—
125C2×C5×Q8C4⋊C412yes—
126C2×C5×D4—22no—
127C2×C5×D4—22no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—41no—
134C2×C5×D4—41no—
135C2×C5×D4—41no—
136C2×C5×D4—41no—
137C2×C5×D4C4⋊C412yes—
138C22×C4×C5—21no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5C22×C411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×Q811yescharacteristic
157C22×C4×C5#4111yescharacteristic
158C22×C4×C5#4111yescharacteristic
159C22×C4×C5#4111yescharacteristic
160C22×C4×C5#4111yescharacteristic
161C22×C4×C5#4111yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C5×M16—22no—
164C5×M16—22no—
165C5×M16—22no—
166C5×M16—22no—
167C5×M16—22no—
168C5×M16—41no—
169C5×M16—41no—
170C5×M16C22⋊C414yes—
171C2×C5×C8—22no—
172C2×C5×C8—22no—
173C2×C5×C8—22no—
174C2×C5×C8—22no—
175C2×C5×C8—41no—
176C2×C5×C8—41no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—41no—
180C5×C4⋊C4—41no—
181C5×C4⋊C4—41no—
182C5×C4⋊C4—41no—
183C5×C4⋊C4—41no—
184C5×C4⋊C4—41no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—41no—
190C5×C22⋊C4—41no—
191C5×C22⋊C4—41no—
192C5×C22⋊C4—41no—
193C42×C5—22no—
194C42×C5—22no—
195C42×C5—22no—
196C42×C5—22no—
197C42×C5—41no—
198C42×C5—41no—
199C42×C5—41no—
200C42×C5—41no—
201C22×#41C22×C511yescharacteristic
202C22×M16C22×C511yescharacteristic
203C22×M16C22×C511yescharacteristic
204C2×#117C22×C511yescharacteristic
205C2×#117C22×C511yescharacteristic
206C2×#117C22×C511yescharacteristic
207C2×#117C22×C511yescharacteristic
208#428—22no—
209#428—22no—
210#427—22no—
211#421—22no—
212#421—22no—
213#421—22no—
214#421—22no—
215C2×#104—22no—
216C2×#104C4×C514yescomplemented
217#410—22no—
218#410—22no—
219C2×#99—22no—
220#343—22no—
221#342—22no—
222H(3,ℤ/4)—22no—
223C23×C5—22no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5—81no—
227C23×C5—82no—
228C23×C5C4×D411yescharacteristic
229C23×C5#12011yescharacteristic
230C23×C5#12111yescharacteristic
231C23×C5#12111yescharacteristic
232C23×C5C22⋊Q811yescharacteristic
233C23×C5#12311yescharacteristic
234C23×C5#12711yescharacteristic
235C5×Q8—22no—
236C5×Q8—22no—
237C5×Q8—41no—
238C5×Q8—41no—
239C5×D4—22no—
240C5×D4—22no—
241C5×D4—42no—
242C5×D4—42no—
243C5×D4—42no—
244C5×D4—42no—
245C5×D4—41no—
246C5×D4—41no—
247C2×C4×C5—22no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—42no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—82no—
259C2×C4×C5—82no—
260C2×C4×C5—82no—
261C2×C4×C5—82no—
262C2×C4×C5C2×C22⋊C411yescharacteristic
263C2×C4×C5C2×C4⋊C411yescharacteristic
264C2×C4×C5#11711yescharacteristic
265C2×C4×C5C4×D411yescharacteristic
266C2×C4×C5C4×D411yescharacteristic
267C2×C4×C5C4×D411yescharacteristic
268C2×C4×C5#12011yescharacteristic
269C2×C4×C5#12011yescharacteristic
270C2×C4×C5#12111yescharacteristic
271C2×C4×C5#12111yescharacteristic
272C2×C4×C5#12111yescharacteristic
273C2×C4×C5#12111yescharacteristic
274C2×C4×C5#12111yescharacteristic
275C2×C4×C5#12111yescharacteristic
276C2×C4×C5C22⋊Q811yescharacteristic
277C2×C4×C5C22⋊Q811yescharacteristic
278C2×C4×C5C22⋊Q811yescharacteristic
279C2×C4×C5C22⋊Q811yescharacteristic
280C2×C4×C5C22⋊Q811yescharacteristic
281C2×C4×C5#12311yescharacteristic
282C2×C4×C5#12311yescharacteristic
283C2×C4×C5#12311yescharacteristic
284C2×C4×C5#12311yescharacteristic
285C2×C4×C5#12411yescharacteristic
286C2×C4×C5#12411yescharacteristic
287C2×C4×C5#12411yescharacteristic
288C2×C4×C5#12611yescharacteristic
289C2×C4×C5#12611yescharacteristic
290C5×C8—24no—
291C5×C8—42no—
292C2×#41—21no—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41C2×C4×C512yes—
303C2×#41C5×D412yes—
304C22×Q8C5×Q811yescharacteristic
305C22×D4—21no—
306C22×D4C5×Q811yescharacteristic
307C23×C4—21no—
308C23×C4C23×C511yescharacteristic
309C2×M16—21no—
310C2×M16—21no—
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16—21no—
316C2×M16—21no—
317C2×M16C2×C4×C512yes—
318C2×M16C5×D412yes—
319C2×M16C5×D412yes—
320C2×M16C5×D412yes—
321C22×C8—21no—
322C22×C8—21no—
323#117—21no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—21no—
331#117—21no—
332#117—21no—
333#117—21no—
334#117—21no—
335#117—21no—
336#117—21no—
337#117C5×D412yes—
338#117C5×D412yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4C5×D412yes—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42C2×C4×C512yes—
351#107—24no—
352#106—24no—
353#104—28no—
354#104—28no—
355#99—28no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5—41no—
361C22×C5—41no—
362C22×C5—41no—
363C22×C5—42no—
364C22×C5—82no—
365C22×C5—82no—
366C22×C5—82no—
367C22×C5#38511yescharacteristic
368C22×C5#38811yescharacteristic
369C22×C5#39011yescharacteristic
370C22×C5#39211yescharacteristic
371C22×C5#39411yescharacteristic
372C22×C5#39611yescharacteristic
373C22×C5#39911yescharacteristic
374C4×C5—42no—
375C4×C5—82no—
376C4×C5—82no—
377C4×C5—82no—
378C4×C5—82no—
379C4×C5#38011yescharacteristic
380C4×C5#38511yescharacteristic
381C4×C5#38611yescharacteristic
382C4×C5#38811yescharacteristic
383C4×C5#39311yescharacteristic
384C4×C5#39411yescharacteristic
385C4×C5#39611yescharacteristic
386C4×C5#39711yescharacteristic
387C24—21no—
388C24C2×C5×D411yescharacteristic
389#41—22no—
390#41—22no—
391#41—22no—
392#41—22no—
393#41—22no—
394#41—22no—
395#41—22no—
396#41—22no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C5×C4⋊C412yes—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4C5×C4⋊C412yes—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4C22×C4×C511yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C2×C5×D411yescharacteristic
440C22×C4C2×C5×D411yescharacteristic
441C22×C4C2×C5×Q811yescharacteristic
442C22×C4C5×#4111yescharacteristic
443C22×C4C5×#4111yescharacteristic
444C22×C4C5×#4111yescharacteristic
445C22×C4C5×#4111yescharacteristic
446C22×C4C5×#4111yescharacteristic
447C22×C4C5×#4111yescharacteristic
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16—41no—
454M16—41no—
455M16C5×C22⋊C414yes—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C42—22no—
479C42—22no—
480C42—22no—
481C42—22no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42—41no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—21no—
489C2×C5—21no—
490C2×C5—21no—
491C2×C5—21no—
492C2×C5—21no—
493C2×C5—82no—
494C2×C5#143911yescharacteristic
495C23—22no—
496C23—41no—
497C23—41no—
498C23—81no—
499C23—82no—
500C23C4×C5×D411yescharacteristic
501C23C5×#12011yescharacteristic
502C23C5×#12111yescharacteristic
503C23C5×#12111yescharacteristic
504C23C5×C22⋊Q811yescharacteristic
505C23C5×#12311yescharacteristic
506C23C5×#12711yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511D4—22no—
512D4—22no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4C2×C5×C22⋊C411yescharacteristic
535C2×C4C2×C5×C4⋊C411yescharacteristic
536C2×C4C5×#11711yescharacteristic
537C2×C4C4×C5×D411yescharacteristic
538C2×C4C4×C5×D411yescharacteristic
539C2×C4C4×C5×D411yescharacteristic
540C2×C4C5×#12011yescharacteristic
541C2×C4C5×#12011yescharacteristic
542C2×C4C5×#12111yescharacteristic
543C2×C4C5×#12111yescharacteristic
544C2×C4C5×#12111yescharacteristic
545C2×C4C5×#12111yescharacteristic
546C2×C4C5×#12111yescharacteristic
547C2×C4C5×#12111yescharacteristic
548C2×C4C5×C22⋊Q811yescharacteristic
549C2×C4C5×C22⋊Q811yescharacteristic
550C2×C4C5×C22⋊Q811yescharacteristic
551C2×C4C5×C22⋊Q811yescharacteristic
552C2×C4C5×C22⋊Q811yescharacteristic
553C2×C4C5×#12311yescharacteristic
554C2×C4C5×#12311yescharacteristic
555C2×C4C5×#12311yescharacteristic
556C2×C4C5×#12311yescharacteristic
557C2×C4C5×#12411yescharacteristic
558C2×C4C5×#12411yescharacteristic
559C2×C4C5×#12411yescharacteristic
560C2×C4C5×#12611yescharacteristic
561C2×C4C5×#12611yescharacteristic
562C8—24no—
563C8—42no—
564C5#1111511yescharacteristic, direct product factor, Sylow
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—82no—
576C22C5×#38511yescharacteristic
577C22C5×#38811yescharacteristic
578C22C5×#39011yescharacteristic
579C22C5×#39211yescharacteristic
580C22C5×#39411yescharacteristic
581C22C5×#39611yescharacteristic
582C22C5×#39911yescharacteristic
583C4—42no—
584C4—82no—
585C4—82no—
586C4—82no—
587C4—82no—
588C4C5×#38011yescharacteristic
589C4C5×#38511yescharacteristic
590C4C5×#38611yescharacteristic
591C4C5×#38811yescharacteristic
592C4C5×#39311yescharacteristic
593C4C5×#39411yescharacteristic
594C4C5×#39611yescharacteristic
595C4C5×#39711yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—82no—
604C2C5×#143911yescharacteristic
subgroupG/H
centerC4×C5#388
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
socleC2×C5#1439
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2911C2semidirect
5. C5×#1742C2semidirect
6. C5×#1740C2semidirect
7. C2×C5×H(3,ℤ/4)C2semidirect
23. C2×C5×#104C4semidirect
30. #11115C5direct (N × H)
95. #2911C2×C5semidirect
99. #1742C2×C5semidirect
100. #1740C2×C5semidirect
101. C2×H(3,ℤ/4)C2×C5semidirect
216. C2×#104C4×C5semidirect
564. C5#11115direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29112
C2×C5×#4212
C2×C5×#4102
C5×#17422
C5×#17402
C2×C5×H(3,ℤ/4)2
#111155