Finite Group Databasebeta

← C5×#11094 #11933814

Subgroups — C5×#11094 #11933814

Order 1280.

868 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2905C211yesmaximal, characteristic, complemented
2C2×C5×#421C211yesmaximal, characteristic
3C2×C5×#421C211yesmaximal, characteristic
4C2×C5×#410C211yesmaximal, characteristic
5C5×#1740C211yesmaximal, characteristic, complemented
6C5×#1733C211yesmaximal, characteristic, complemented
7C5×#1733C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×M16C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C2×C5×#117C2211yescharacteristic
12C2×C5×#117C2211yescharacteristic
13C2×C5×#117C2211yescharacteristic
14C2×C5×#117C2211yescharacteristic
15C5×#424—22no—
16C5×#424—22no—
17C5×#423—22no—
18C5×#421—22no—
19C5×#421—22no—
20C5×#421—22no—
21C5×#421—22no—
22C2×C5×#104—22no—
23C2×C5×#104—22no—
24C5×#410—22no—
25C5×#410C414yescomplemented
26C2×C5×#99—22no—
27C5×#342—22no—
28C5×#339—22no—
29C5×#339—22no—
30#11094C511yesmaximal, 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×M16—21no—
57C2×C5×M16—21no—
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×#117C2×C412yes—
75C5×#117C2×C412yes—
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×C5D412yes—
90C5×C4⋊C8—28no—
91C5×#104—28no—
92C5×#104—28no—
93C5×#99—28no—
94#2905C2×C511yescharacteristic, complemented
95C2×#421C2×C511yescharacteristic
96C2×#421C2×C511yescharacteristic
97C2×#410C2×C511yescharacteristic
98#1740C2×C511yescharacteristic, complemented
99#1733C2×C511yescharacteristic, complemented
100#1733C2×C511yescharacteristic, complemented
101C24×C5—21no—
102C24×C5C2×D411yescharacteristic
103C5×#41—22no—
104C5×#41—22no—
105C5×#41—22no—
106C5×#41—22no—
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—41no—
112C5×#41—41no—
113C5×#41—41no—
114C5×#41—41no—
115C5×#41—41no—
116C5×#41—41no—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8—21no—
120C2×C5×Q8—21no—
121C2×C5×Q8—21no—
122C2×C5×Q8—21no—
123C2×C5×Q8—21no—
124C2×C5×Q8C4⋊C412yes—
125C2×C5×D4—22no—
126C2×C5×D4—22no—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—41no—
133C2×C5×D4—41no—
134C2×C5×D4—41no—
135C2×C5×D4—41no—
136C2×C5×D4C4⋊C412yes—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×Q811yescharacteristic
156C22×C4×C5#4111yescharacteristic
157C22×C4×C5#4111yescharacteristic
158C22×C4×C5#4111yescharacteristic
159C22×C4×C5#4111yescharacteristic
160C22×C4×C5#4111yescharacteristic
161C22×C4×C5#4111yescharacteristic
162C5×M16—22no—
163C5×M16—22no—
164C5×M16—22no—
165C5×M16—22no—
166C5×M16—41no—
167C5×M16—41no—
168C5×M16—41no—
169C5×M16—41no—
170C2×C5×C8—22no—
171C2×C5×C8—22no—
172C2×C5×C8—41no—
173C2×C5×C8—41no—
174C2×C5×C8—41no—
175C2×C5×C8—41no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—41no—
181C5×C4⋊C4—41no—
182C5×C4⋊C4—41no—
183C5×C4⋊C4—41no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—41no—
188C5×C22⋊C4—41no—
189C5×C22⋊C4—41no—
190C5×C22⋊C4—41no—
191C5×C22⋊C4C22⋊C414yes—
192C42×C5—22no—
193C42×C5—22no—
194C42×C5—22no—
195C42×C5—22no—
196C42×C5—22no—
197C42×C5—22no—
198C42×C5—41no—
199C42×C5—41no—
200C22×#41C22×C511yescharacteristic
201C22×M16C22×C511yescharacteristic
202C22×M16C22×C511yescharacteristic
203C2×#117C22×C511yescharacteristic
204C2×#117C22×C511yescharacteristic
205C2×#117C22×C511yescharacteristic
206C2×#117C22×C511yescharacteristic
207#424—22no—
208#424—22no—
209#423—22no—
210#421—22no—
211#421—22no—
212#421—22no—
213#421—22no—
214C2×#104—22no—
215C2×#104—22no—
216#410—22no—
217#410C4×C514yescomplemented
218C2×#99—22no—
219#342—22no—
220#339—22no—
221#339—22no—
222C23×C5—22no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—81no—
226C23×C5—82no—
227C23×C5C2×C22⋊C411yescharacteristic
228C23×C5#12111yescharacteristic
229C23×C5#12111yescharacteristic
230C23×C5#12111yescharacteristic
231C23×C5#12111yescharacteristic
232C23×C5#12111yescharacteristic
233C23×C5C22⋊Q811yescharacteristic
234C5×Q8—22no—
235C5×Q8—22no—
236C5×Q8—41no—
237C5×Q8—41no—
238C5×D4—22no—
239C5×D4—22no—
240C5×D4—42no—
241C5×D4—42no—
242C5×D4—42no—
243C5×D4—42no—
244C5×D4—41no—
245C5×D4—41no—
246C2×C4×C5—22no—
247C2×C4×C5—24no—
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—82no—
258C2×C4×C5—82no—
259C2×C4×C5—82no—
260C2×C4×C5—82no—
261C2×C4×C5C2×C4⋊C411yescharacteristic
262C2×C4×C5#11711yescharacteristic
263C2×C4×C5C4×D411yescharacteristic
264C2×C4×C5C4×D411yescharacteristic
265C2×C4×C5C4×D411yescharacteristic
266C2×C4×C5C4×D411yescharacteristic
267C2×C4×C5#12011yescharacteristic
268C2×C4×C5#12011yescharacteristic
269C2×C4×C5#12011yescharacteristic
270C2×C4×C5#12111yescharacteristic
271C2×C4×C5#12111yescharacteristic
272C2×C4×C5#12111yescharacteristic
273C2×C4×C5C22⋊Q811yescharacteristic
274C2×C4×C5C22⋊Q811yescharacteristic
275C2×C4×C5C22⋊Q811yescharacteristic
276C2×C4×C5C22⋊Q811yescharacteristic
277C2×C4×C5C22⋊Q811yescharacteristic
278C2×C4×C5#12311yescharacteristic
279C2×C4×C5#12311yescharacteristic
280C2×C4×C5#12311yescharacteristic
281C2×C4×C5#12311yescharacteristic
282C2×C4×C5#12311yescharacteristic
283C2×C4×C5#12411yescharacteristic
284C2×C4×C5#12411yescharacteristic
285C2×C4×C5#12411yescharacteristic
286C2×C4×C5#12611yescharacteristic
287C2×C4×C5#12611yescharacteristic
288C2×C4×C5#12711yescharacteristic
289C5×C8—42no—
290C5×C8—42no—
291C2×#41—21no—
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×#41C2×C4×C512yes—
302C2×#41C5×D412yes—
303C22×Q8C5×Q811yescharacteristic
304C22×D4—21no—
305C22×D4C5×Q811yescharacteristic
306C23×C4—21no—
307C23×C4C23×C511yescharacteristic
308C2×M16—21no—
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×M16—21no—
318C2×M16C5×D412yes—
319C2×M16C5×D412yes—
320C22×C8—21no—
321C22×C8—21no—
322#117—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#117C2×C4×C512yes—
335#117C2×C4×C512yes—
336#117C5×D412yes—
337#117C5×D412yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4C5×D412yes—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42C5×D412yes—
350C4⋊C8—28no—
351#104—28no—
352#104—28no—
353#99—28no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5—41no—
361C22×C5—42no—
362C22×C5—82no—
363C22×C5—82no—
364C22×C5—82no—
365C22×C5#38011yescharacteristic
366C22×C5#38611yescharacteristic
367C22×C5#39011yescharacteristic
368C22×C5#39411yescharacteristic
369C22×C5#39411yescharacteristic
370C22×C5#39611yescharacteristic
371C22×C5#39611yescharacteristic
372C4×C5—44no—
373C4×C5—42no—
374C4×C5—82no—
375C4×C5—82no—
376C4×C5—82no—
377C4×C5#38511yescharacteristic
378C4×C5#38511yescharacteristic
379C4×C5#38811yescharacteristic
380C4×C5#38811yescharacteristic
381C4×C5#39211yescharacteristic
382C4×C5#39311yescharacteristic
383C4×C5#39711yescharacteristic
384C4×C5#39911yescharacteristic
385C24—21no—
386C24C2×C5×D411yescharacteristic
387#41—22no—
388#41—22no—
389#41—22no—
390#41—22no—
391#41—22no—
392#41—22no—
393#41—22no—
394#41—22no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C5×C4⋊C412yes—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4C5×C4⋊C412yes—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C22×C4×C511yescharacteristic
433C22×C4C2×C5×D411yescharacteristic
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C2×C5×Q811yescharacteristic
440C22×C4C5×#4111yescharacteristic
441C22×C4C5×#4111yescharacteristic
442C22×C4C5×#4111yescharacteristic
443C22×C4C5×#4111yescharacteristic
444C22×C4C5×#4111yescharacteristic
445C22×C4C5×#4111yescharacteristic
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—41no—
451M16—41no—
452M16—41no—
453M16—41no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—41no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4C5×C22⋊C414yes—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—22no—
481C42—22no—
482C42—41no—
483C42—41no—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—21no—
489C2×C5—21no—
490C2×C5—21no—
491C2×C5—82no—
492C2×C5#143911yescharacteristic
493C23—22no—
494C23—41no—
495C23—41no—
496C23—81no—
497C23—82no—
498C23C2×C5×C22⋊C411yescharacteristic
499C23C5×#12111yescharacteristic
500C23C5×#12111yescharacteristic
501C23C5×#12111yescharacteristic
502C23C5×#12111yescharacteristic
503C23C5×#12111yescharacteristic
504C23C5×C22⋊Q811yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509D4—22no—
510D4—22no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—41no—
516D4—41no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4C2×C5×C4⋊C411yescharacteristic
533C2×C4C5×#11711yescharacteristic
534C2×C4C4×C5×D411yescharacteristic
535C2×C4C4×C5×D411yescharacteristic
536C2×C4C4×C5×D411yescharacteristic
537C2×C4C4×C5×D411yescharacteristic
538C2×C4C5×#12011yescharacteristic
539C2×C4C5×#12011yescharacteristic
540C2×C4C5×#12011yescharacteristic
541C2×C4C5×#12111yescharacteristic
542C2×C4C5×#12111yescharacteristic
543C2×C4C5×#12111yescharacteristic
544C2×C4C5×C22⋊Q811yescharacteristic
545C2×C4C5×C22⋊Q811yescharacteristic
546C2×C4C5×C22⋊Q811yescharacteristic
547C2×C4C5×C22⋊Q811yescharacteristic
548C2×C4C5×C22⋊Q811yescharacteristic
549C2×C4C5×#12311yescharacteristic
550C2×C4C5×#12311yescharacteristic
551C2×C4C5×#12311yescharacteristic
552C2×C4C5×#12311yescharacteristic
553C2×C4C5×#12311yescharacteristic
554C2×C4C5×#12411yescharacteristic
555C2×C4C5×#12411yescharacteristic
556C2×C4C5×#12411yescharacteristic
557C2×C4C5×#12611yescharacteristic
558C2×C4C5×#12611yescharacteristic
559C2×C4C5×#12711yescharacteristic
560C8—42no—
561C8—42no—
562C5#1109411yescharacteristic, direct product factor, Sylow
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22C5×#38011yescharacteristic
575C22C5×#38611yescharacteristic
576C22C5×#39011yescharacteristic
577C22C5×#39411yescharacteristic
578C22C5×#39411yescharacteristic
579C22C5×#39611yescharacteristic
580C22C5×#39611yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4—82no—
585C4—82no—
586C4C5×#38511yescharacteristic
587C4C5×#38511yescharacteristic
588C4C5×#38811yescharacteristic
589C4C5×#38811yescharacteristic
590C4C5×#39211yescharacteristic
591C4C5×#39311yescharacteristic
592C4C5×#39711yescharacteristic
593C4C5×#39911yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—82no—
602C2C5×#143911yescharacteristic
subgroupG/H
centerC4×C5#392
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×#2905C2semidirect
5. C5×#1740C2semidirect
6. C5×#1733C2semidirect
7. C5×#1733C2semidirect
25. C5×#410C4semidirect
30. #11094C5direct (N × H)
94. #2905C2×C5semidirect
98. #1740C2×C5semidirect
99. #1733C2×C5semidirect
100. #1733C2×C5semidirect
217. #410C4×C5semidirect
562. C5#11094direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29052
C2×C5×#4212
C2×C5×#4102
C5×#17402
C5×#17332
#110945