Finite Group Databasebeta

← C5×#13082 #11935802

Subgroups — C5×#13082 #11935802

Order 1280.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#100C211yesmaximal, characteristic, complemented
2C5×#2403C211yesmaximal, characteristic
3C2×C5×AΣL(1,𝔽16)C212yesmaximal, complemented
4C5×#1781C211yesmaximal, characteristic, complemented
5C5×#1390C212yesmaximal, complemented
6C23×C5×D4C411yescharacteristic, complemented
7C23×C5×D4C2211yescharacteristic
8C22×C5×M16—21no—
9C2×C5×#120—21no—
10C2×C5×#120C411yescharacteristic, complemented
11C2×C5×#120C2211yescharacteristic
12C2×C5×#100—24no—
13C2×C5×#100—21no—
14C2×C5×#100C2212yes—
15C2×C5×#99—21no—
16C2×C5×#99C2212yes—
17C5×#392—21no—
18C5×#392—21no—
19C5×#386—21no—
20C5×#386C411yescharacteristic, complemented
21C5×#386C2211yescharacteristic
22C5×#379—21no—
23C5×#379C411yescharacteristic, complemented
24C5×AΣL(1,𝔽16)—24no—
25#13082C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5C2×C411yescharacteristic
27C25×C5C2×C411yescharacteristic
28C25×C5D411yescharacteristic
29C22×C5×D4—21no—
30C22×C5×D4—22no—
31C22×C5×D4—22no—
32C22×C5×D4—21no—
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4—42no—
36C22×C5×D4—41no—
37C22×C5×D4—41no—
38C22×C5×D4—44no—
39C22×C5×D4—41no—
40C22×C5×D4—41no—
41C22×C5×D4C2×C411yescharacteristic
42C22×C5×D4D411yescharacteristic
43C22×C5×D4D411yescharacteristic
44C22×C5×D4C2311yescharacteristic
45C23×C4×C5C2×C411yescharacteristic
46C23×C4×C5D411yescharacteristic
47C2×C5×M16—24no—
48C2×C5×M16—22no—
49C2×C5×M16—41no—
50C2×C5×M16—42no—
51C22×C5×C8—41no—
52C5×#120—22no—
53C5×#120—22no—
54C5×#120—44no—
55C5×#120—42no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—22no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—41no—
64C2×C5×C22⋊C4—41no—
65C2×C5×C22⋊C4C2×C411yescharacteristic
66C2×C5×C22⋊C4C2×C411yescharacteristic
67C5×#100—24no—
68C5×#100—22no—
69C5×#100D414yescomplemented
70C5×#99—22no—
71C5×#99—22no—
72C5×#99—42no—
73C5×#95—21no—
74C5×#95—21no—
75C22×#100C2×C511yescharacteristic, complemented
76#2403C2×C511yescharacteristic
77C2×AΣL(1,𝔽16)C2×C512yescomplemented
78#1781C2×C511yescharacteristic, complemented
79#1390C2×C512yescomplemented
80C24×C5—21no—
81C24×C5—21no—
82C24×C5—21no—
83C24×C5—21no—
84C24×C5—21no—
85C24×C5—22no—
86C24×C5—22no—
87C24×C5—22no—
88C24×C5—41no—
89C24×C5—41no—
90C24×C5—42no—
91C24×C5—41no—
92C24×C5—42no—
93C24×C5—42no—
94C24×C5—41no—
95C24×C5—81no—
96C24×C5—81no—
97C24×C5—81no—
98C24×C5C22⋊C411yescharacteristic
99C24×C5C22⋊C411yescharacteristic
100C24×C5C22⋊C411yescharacteristic
101C24×C5C22×C411yescharacteristic
102C24×C5C2×D411yescharacteristic
103C2×C5×D4—24no—
104C2×C5×D4—22no—
105C2×C5×D4—22no—
106C2×C5×D4—22no—
107C2×C5×D4—22no—
108C2×C5×D4—21no—
109C2×C5×D4—21no—
110C2×C5×D4—41no—
111C2×C5×D4—41no—
112C2×C5×D4—41no—
113C2×C5×D4—41no—
114C2×C5×D4—41no—
115C2×C5×D4—41no—
116C2×C5×D4—44no—
117C2×C5×D4—44no—
118C2×C5×D4—44no—
119C2×C5×D4—44no—
120C2×C5×D4—42no—
121C2×C5×D4—42no—
122C2×C5×D4—42no—
123C2×C5×D4—42no—
124C2×C5×D4—44no—
125C2×C5×D4—44no—
126C2×C5×D4—44no—
127C2×C5×D4—41no—
128C2×C5×D4—41no—
129C2×C5×D4—44no—
130C2×C5×D4—42no—
131C2×C5×D4—42no—
132C2×C5×D4—42no—
133C2×C5×D4—42no—
134C2×C5×D4—81no—
135C2×C5×D4—81no—
136C2×C5×D4C2×D412yes—
137C2×C5×D4#4112yes—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—42no—
147C22×C4×C5—41no—
148C22×C4×C5—42no—
149C22×C4×C5C22⋊C411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C5×M16—24no—
152C5×M16—44no—
153C5×M16—42no—
154C2×C5×C8—44no—
155C2×C5×C8—42no—
156C5×C22⋊C4—22no—
157C5×C22⋊C4—42no—
158C5×C22⋊C4—42no—
159C5×C22⋊C4—42no—
160C5×C22⋊C4—42no—
161C5×C22⋊C4—41no—
162C5×C22⋊C4—41no—
163C5×C22⋊C4—41no—
164C5×C22⋊C4—42no—
165C5×C22⋊C4—42no—
166C5×C22⋊C4—81no—
167C5×C22⋊C4—82no—
168C5×C22⋊C4—82no—
169C23×D4C4×C511yescharacteristic, complemented
170C23×D4C22×C511yescharacteristic
171C22×M16—21no—
172C2×#120—21no—
173C2×#120C4×C511yescharacteristic, complemented
174C2×#120C22×C511yescharacteristic
175C2×#100—21no—
176C2×#100—24no—
177C2×#100C22×C512yes—
178C2×#99—21no—
179C2×#99C22×C512yes—
180#392—21no—
181#392—21no—
182#386—21no—
183#386C4×C511yescharacteristic, complemented
184#386C22×C511yescharacteristic
185#379—21no—
186#379C4×C511yescharacteristic, complemented
187AΣL(1,𝔽16)—24no—
188C23×C5—22no—
189C23×C5—21no—
190C23×C5—21no—
191C23×C5—21no—
192C23×C5—21no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—22no—
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—21no—
199C23×C5—21no—
200C23×C5—21no—
201C23×C5—21no—
202C23×C5—41no—
203C23×C5—42no—
204C23×C5—42no—
205C23×C5—42no—
206C23×C5—42no—
207C23×C5—41no—
208C23×C5—41no—
209C23×C5—41no—
210C23×C5—41no—
211C23×C5—41no—
212C23×C5—41no—
213C23×C5—42no—
214C23×C5—41no—
215C23×C5—42no—
216C23×C5—41no—
217C23×C5—41no—
218C23×C5—41no—
219C23×C5—41no—
220C23×C5—42no—
221C23×C5—42no—
222C23×C5—42no—
223C23×C5—42no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5—41no—
227C23×C5—81no—
228C23×C5—81no—
229C23×C5—81no—
230C23×C5—81no—
231C23×C5—82no—
232C23×C5—84no—
233C23×C5—84no—
234C23×C5—84no—
235C23×C5—84no—
236C23×C5—84no—
237C23×C5—84no—
238C23×C5—82no—
239C23×C5#9911yescharacteristic
240C23×C5#9911yescharacteristic
241C23×C5C2×C22⋊C411yescharacteristic
242C23×C5C4×D412yes—
243C23×C5#12112yes—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—44no—
247C5×D4—44no—
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—44no—
251C5×D4—48no—
252C5×D4—44no—
253C5×D4—84no—
254C5×D4—84no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—22no—
264C2×C4×C5—41no—
265C2×C4×C5—42no—
266C2×C4×C5—41no—
267C2×C4×C5—42no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—82no—
275C2×C4×C5—82no—
276C2×C4×C5—82no—
277C2×C4×C5#9912yes—
278C2×C4×C5#12011yescharacteristic
279C2×C4×C5#12311yescharacteristic
280C5×C8—44no—
281C25C2×C4×C511yescharacteristic
282C25C2×C4×C511yescharacteristic
283C25C5×D411yescharacteristic
284C22×D4—21no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—42no—
291C22×D4—41no—
292C22×D4—41no—
293C22×D4—44no—
294C22×D4—41no—
295C22×D4—41no—
296C22×D4C2×C4×C511yescharacteristic
297C22×D4C5×D411yescharacteristic
298C22×D4C5×D411yescharacteristic
299C22×D4C23×C511yescharacteristic
300C23×C4C2×C4×C511yescharacteristic
301C23×C4C5×D411yescharacteristic
302C2×M16—24no—
303C2×M16—22no—
304C2×M16—41no—
305C2×M16—42no—
306C22×C8—41no—
307#120—22no—
308#120—22no—
309#120—44no—
310#120—42no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4C2×C4×C511yescharacteristic
321C2×C22⋊C4C2×C4×C511yescharacteristic
322#100—24no—
323#100—22no—
324#100C5×D414yescomplemented
325#99—22no—
326#99—22no—
327#99—42no—
328#95—21no—
329#95—21no—
330C22×C5—21no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—22no—
338C22×C5—22no—
339C22×C5—42no—
340C22×C5—42no—
341C22×C5—42no—
342C22×C5—42no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5—42no—
352C22×C5—41no—
353C22×C5—41no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—81no—
359C22×C5—84no—
360C22×C5—84no—
361C22×C5—81no—
362C22×C5—81no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—84no—
367C22×C5—84no—
368C22×C5—84no—
369C22×C5—84no—
370C22×C5—81no—
371C22×C5—81no—
372C22×C5AΣL(1,𝔽16)12yescomplemented
373C22×C5#38611yescharacteristic
374C22×C5C2×#9911yescharacteristic
375C22×C5C2×#9911yescharacteristic
376C4×C5—21no—
377C4×C5—22no—
378C4×C5—21no—
379C4×C5—42no—
380C4×C5—81no—
381C4×C5—81no—
382C4×C5—162no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—41no—
398C24—81no—
399C24—81no—
400C24—81no—
401C24C5×C22⋊C411yescharacteristic
402C24C5×C22⋊C411yescharacteristic
403C24C5×C22⋊C411yescharacteristic
404C24C22×C4×C511yescharacteristic
405C24C2×C5×D411yescharacteristic
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—81no—
438C2×D4—81no—
439C2×D4C2×C5×D412yes—
440C2×D4C5×#4112yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—42no—
452C22×C4C5×C22⋊C411yescharacteristic
453C22×C4C2×C5×D411yescharacteristic
454M16—24no—
455M16—44no—
456M16—42no—
457C2×C8—44no—
458C2×C8—42no—
459C22⋊C4—22no—
460C22⋊C4—42no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—42no—
466C22⋊C4—41no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C22⋊C4—82no—
471C22⋊C4—82no—
472C2×C5—21no—
473C2×C5—21no—
474C2×C5—22no—
475C2×C5—42no—
476C2×C5—41no—
477C2×C5—42no—
478C2×C5—81no—
479C2×C5—82no—
480C2×C5—81no—
481C2×C5#189811yescharacteristic
482C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
483C2×C5#212111yescharacteristic
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—21no—
491C23—22no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—41no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—82no—
528C23—84no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—82no—
535C23C5×#9911yescharacteristic
536C23C5×#9911yescharacteristic
537C23C2×C5×C22⋊C411yescharacteristic
538C23C4×C5×D412yes—
539C23C5×#12112yes—
540D4—42no—
541D4—42no—
542D4—44no—
543D4—44no—
544D4—42no—
545D4—42no—
546D4—44no—
547D4—48no—
548D4—44no—
549D4—84no—
550D4—84no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4C5×#9912yes—
574C2×C4C5×#12011yescharacteristic
575C2×C4C5×#12311yescharacteristic
576C8—44no—
577C5#1308211yescharacteristic, direct product factor, Sylow
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22C5×AΣL(1,𝔽16)12yescomplemented
621C22C5×#38611yescharacteristic
622C22C2×C5×#9911yescharacteristic
623C22C2×C5×#9911yescharacteristic
624C4—21no—
625C4—21no—
626C4—22no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C5×#189811yescharacteristic
641C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
642C2C5×#212111yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC5×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C23×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C5×#100C2semidirect
3. C2×C5×AΣL(1,𝔽16)C2semidirect
4. C5×#1781C2semidirect
5. C5×#1390C2semidirect
6. C23×C5×D4C4semidirect
10. C2×C5×#120C4semidirect
20. C5×#386C4semidirect
23. C5×#379C4semidirect
25. #13082C5direct (N × H)
69. C5×#100D4semidirect
75. C22×#100C2×C5semidirect
77. C2×AΣL(1,𝔽16)C2×C5semidirect
78. #1781C2×C5semidirect
79. #1390C2×C5semidirect
169. C23×D4C4×C5semidirect
173. C2×#120C4×C5semidirect
183. #386C4×C5semidirect
186. #379C4×C5semidirect
324. #100C5×D4semidirect
372. C22×C5AΣL(1,𝔽16)semidirect
577. C5#13082direct (N × H)
620. C22C5×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#1002
C5×#24032
C2×C5×AΣL(1,𝔽16)2
C5×#17812
C5×#13902
#130825