Finite Group Databasebeta

← C5×#13086 #11935806

Subgroups — C5×#13086 #11935806

Order 1280.

1118 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#99C211yesmaximal, characteristic, complemented
2C5×#2403C211yesmaximal, characteristic
3C2×C5×AΣL(1,𝔽16)C212yesmaximal, complemented
4C5×#1783C211yesmaximal, characteristic, complemented
5C5×#1390C212yesmaximal, complemented
6C23×C5×D4C411yescharacteristic, complemented
7C23×C5×D4C2211yescharacteristic
8C2×C5×#120—21no—
9C2×C5×#120C411yescharacteristic, complemented
10C2×C5×#120C2211yescharacteristic
11C22×C5×C22⋊C4—21no—
12C2×C5×#100—21no—
13C2×C5×#100C2212yes—
14C2×C5×#99—24no—
15C2×C5×#99—21no—
16C2×C5×#99C2212yes—
17C5×#407—21no—
18C5×#392—21no—
19C5×#392—21no—
20C5×#386—21no—
21C5×#386C411yescharacteristic, complemented
22C5×#386C2211yescharacteristic
23C5×#379C411yescharacteristic, complemented
24C5×AΣL(1,𝔽16)—24no—
25#13086C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5C2×C411yescharacteristic
27C25×C5C2×C411yescharacteristic, complemented
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—41no—
36C22×C5×D4—41no—
37C22×C5×D4—42no—
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×C5—41no—
46C23×C4×C5C2×C411yescharacteristic, complemented
47C23×C4×C5D411yescharacteristic
48C2×C5×M16—22no—
49C5×#120—22no—
50C5×#120—22no—
51C5×#120—44no—
52C5×#120—42no—
53C2×C5×C22⋊C4—24no—
54C2×C5×C22⋊C4—22no—
55C2×C5×C22⋊C4—21no—
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—41no—
62C2×C5×C22⋊C4—42no—
63C2×C5×C22⋊C4C2×C411yescharacteristic, complemented
64C2×C5×C22⋊C4C2×C411yescharacteristic, complemented
65C5×#100—22no—
66C5×#100—22no—
67C5×#100—42no—
68C5×#99—24no—
69C5×#99—22no—
70C5×#99D414yescomplemented
71C5×C22⋊C8—41no—
72C5×C22⋊C8—41no—
73C5×#95—21no—
74C5×#95—21no—
75C22×#99C2×C511yescharacteristic, complemented
76#2403C2×C511yescharacteristic
77C2×AΣL(1,𝔽16)C2×C512yescomplemented
78#1783C2×C511yescharacteristic, complemented
79#1390C2×C512yescomplemented
80C24×C5—21no—
81C24×C5—22no—
82C24×C5—21no—
83C24×C5—21no—
84C24×C5—21no—
85C24×C5—21no—
86C24×C5—21no—
87C24×C5—21no—
88C24×C5—22no—
89C24×C5—22no—
90C24×C5—41no—
91C24×C5—42no—
92C24×C5—41no—
93C24×C5—42no—
94C24×C5—42no—
95C24×C5—41no—
96C24×C5—81no—
97C24×C5—81no—
98C24×C5—81no—
99C24×C5C22⋊C411yescharacteristic
100C24×C5C22⋊C411yescharacteristic
101C24×C5C22⋊C411yescharacteristic
102C24×C5C22×C411yescharacteristic
103C24×C5C2×D411yescharacteristic
104C2×C5×D4—24no—
105C2×C5×D4—22no—
106C2×C5×D4—22no—
107C2×C5×D4—22no—
108C2×C5×D4—21no—
109C2×C5×D4—21no—
110C2×C5×D4—22no—
111C2×C5×D4—41no—
112C2×C5×D4—41no—
113C2×C5×D4—41no—
114C2×C5×D4—41no—
115C2×C5×D4—41no—
116C2×C5×D4—41no—
117C2×C5×D4—42no—
118C2×C5×D4—44no—
119C2×C5×D4—44no—
120C2×C5×D4—44no—
121C2×C5×D4—44no—
122C2×C5×D4—42no—
123C2×C5×D4—42no—
124C2×C5×D4—42no—
125C2×C5×D4—44no—
126C2×C5×D4—44no—
127C2×C5×D4—44no—
128C2×C5×D4—41no—
129C2×C5×D4—41no—
130C2×C5×D4—44no—
131C2×C5×D4—42no—
132C2×C5×D4—42no—
133C2×C5×D4—42no—
134C2×C5×D4—41no—
135C2×C5×D4—41no—
136C2×C5×D4—81no—
137C2×C5×D4—81no—
138C2×C5×D4C2×D412yes—
139C2×C5×D4#4112yes—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—41no—
147C22×C4×C5—42no—
148C22×C4×C5—41no—
149C22×C4×C5—44no—
150C22×C4×C5—42no—
151C22×C4×C5—82no—
152C22×C4×C5—82no—
153C22×C4×C5C22⋊C411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C5×M16—42no—
156C5×M16—42no—
157C2×C5×C8—42no—
158C5×C22⋊C4—22no—
159C5×C22⋊C4—24no—
160C5×C22⋊C4—42no—
161C5×C22⋊C4—42no—
162C5×C22⋊C4—42no—
163C5×C22⋊C4—44no—
164C5×C22⋊C4—42no—
165C5×C22⋊C4—42no—
166C5×C22⋊C4—42no—
167C5×C22⋊C4—41no—
168C5×C22⋊C4—81no—
169C23×D4C4×C511yescharacteristic, complemented
170C23×D4C22×C511yescharacteristic
171C2×#120—21no—
172C2×#120C4×C511yescharacteristic, complemented
173C2×#120C22×C511yescharacteristic
174C22×C22⋊C4—21no—
175C2×#100—21no—
176C2×#100C22×C512yes—
177C2×#99—21no—
178C2×#99—24no—
179C2×#99C22×C512yes—
180#407—21no—
181#392—21no—
182#392—21no—
183#386—21no—
184#386C4×C511yescharacteristic, complemented
185#386C22×C511yescharacteristic
186#379C4×C511yescharacteristic, complemented
187AΣL(1,𝔽16)—24no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—22no—
191C23×C5—22no—
192C23×C5—22no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—21no—
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—21no—
199C23×C5—21no—
200C23×C5—21no—
201C23×C5—22no—
202C23×C5—21no—
203C23×C5—21no—
204C23×C5—21no—
205C23×C5—41no—
206C23×C5—42no—
207C23×C5—42no—
208C23×C5—41no—
209C23×C5—41no—
210C23×C5—42no—
211C23×C5—41no—
212C23×C5—41no—
213C23×C5—41no—
214C23×C5—41no—
215C23×C5—41no—
216C23×C5—42no—
217C23×C5—41no—
218C23×C5—41no—
219C23×C5—41no—
220C23×C5—41no—
221C23×C5—42no—
222C23×C5—42no—
223C23×C5—42no—
224C23×C5—42no—
225C23×C5—41no—
226C23×C5—41no—
227C23×C5—41no—
228C23×C5—81no—
229C23×C5—81no—
230C23×C5—81no—
231C23×C5—81no—
232C23×C5—82no—
233C23×C5—84no—
234C23×C5—82no—
235C23×C5—82no—
236C23×C5—84no—
237C23×C5—84no—
238C23×C5—84no—
239C23×C5—84no—
240C23×C5—82no—
241C23×C5#9911yescharacteristic
242C23×C5#9911yescharacteristic
243C23×C5#9912yes—
244C23×C5C2×C22⋊C411yescharacteristic
245C23×C5C4×D412yes—
246C23×C5#12011yescharacteristic
247C23×C5#12311yescharacteristic
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—44no—
251C5×D4—44no—
252C5×D4—44no—
253C5×D4—42no—
254C5×D4—42no—
255C5×D4—48no—
256C5×D4—44no—
257C5×D4—84no—
258C5×D4—82no—
259C5×D4—82no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—41no—
269C2×C4×C5—42no—
270C2×C4×C5—41no—
271C2×C4×C5—42no—
272C2×C4×C5—44no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—88no—
280C2×C4×C5—82no—
281C2×C4×C5—82no—
282C2×C4×C5#12112yes—
283C5×C8—82no—
284C25C2×C4×C511yescharacteristic
285C25C2×C4×C511yescharacteristic, complemented
286C25C5×D411yescharacteristic
287C22×D4—21no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—41no—
294C22×D4—41no—
295C22×D4—42no—
296C22×D4—44no—
297C22×D4—41no—
298C22×D4—41no—
299C22×D4C2×C4×C511yescharacteristic
300C22×D4C5×D411yescharacteristic
301C22×D4C5×D411yescharacteristic
302C22×D4C23×C511yescharacteristic
303C23×C4—41no—
304C23×C4C2×C4×C511yescharacteristic, complemented
305C23×C4C5×D411yescharacteristic
306C2×M16—22no—
307#120—22no—
308#120—22no—
309#120—44no—
310#120—42no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4C2×C4×C511yescharacteristic, complemented
322C2×C22⋊C4C2×C4×C511yescharacteristic, complemented
323#100—22no—
324#100—22no—
325#100—42no—
326#99—24no—
327#99—22no—
328#99C5×D414yescomplemented
329C22⋊C8—41no—
330C22⋊C8—41no—
331#95—21no—
332#95—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—21no—
339C22×C5—21no—
340C22×C5—21no—
341C22×C5—22no—
342C22×C5—21no—
343C22×C5—22no—
344C22×C5—42no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—42no—
350C22×C5—44no—
351C22×C5—44no—
352C22×C5—42no—
353C22×C5—42no—
354C22×C5—42no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5—41no—
361C22×C5—42no—
362C22×C5—41no—
363C22×C5—41no—
364C22×C5—41no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5—84no—
368C22×C5—81no—
369C22×C5—81no—
370C22×C5—81no—
371C22×C5—81no—
372C22×C5—82no—
373C22×C5—82no—
374C22×C5—84no—
375C22×C5—84no—
376C22×C5—84no—
377C22×C5—81no—
378C22×C5—81no—
379C22×C5AΣL(1,𝔽16)12yescomplemented
380C22×C5#38611yescharacteristic
381C22×C5C2×#9911yescharacteristic
382C22×C5C2×#9911yescharacteristic
383C4×C5—22no—
384C4×C5—42no—
385C4×C5—41no—
386C4×C5—81no—
387C4×C5—81no—
388C4×C5—84no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—41no—
400C24—42no—
401C24—41no—
402C24—42no—
403C24—42no—
404C24—41no—
405C24—81no—
406C24—81no—
407C24—81no—
408C24C5×C22⋊C411yescharacteristic
409C24C5×C22⋊C411yescharacteristic
410C24C5×C22⋊C411yescharacteristic
411C24C22×C4×C511yescharacteristic
412C24C2×C5×D411yescharacteristic
413C2×D4—24no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—44no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—42no—
445C2×D4—81no—
446C2×D4—81no—
447C2×D4C2×C5×D412yes—
448C2×D4C5×#4112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—42no—
457C22×C4—41no—
458C22×C4—44no—
459C22×C4—42no—
460C22×C4—82no—
461C22×C4—82no—
462C22×C4C5×C22⋊C411yescharacteristic
463C22×C4C2×C5×D411yescharacteristic
464M16—42no—
465M16—42no—
466C2×C8—42no—
467C22⋊C4—22no—
468C22⋊C4—24no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—44no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—41no—
477C22⋊C4—81no—
478C2×C5—21no—
479C2×C5—21no—
480C2×C5—22no—
481C2×C5—41no—
482C2×C5—41no—
483C2×C5—42no—
484C2×C5—41no—
485C2×C5—42no—
486C2×C5—82no—
487C2×C5—81no—
488C2×C5#189811yescharacteristic
489C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
490C2×C5#212111yescharacteristic
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—21no—
503C23—21no—
504C23—22no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—42no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—82no—
536C23—82no—
537C23—82no—
538C23—84no—
539C23—84no—
540C23—84no—
541C23—84no—
542C23—84no—
543C23—82no—
544C23C5×#9911yescharacteristic
545C23C5×#9911yescharacteristic
546C23C5×#9912yes—
547C23C2×C5×C22⋊C411yescharacteristic
548C23C4×C5×D412yes—
549C23C5×#12011yescharacteristic
550C23C5×#12311yescharacteristic
551D4—42no—
552D4—42no—
553D4—44no—
554D4—44no—
555D4—44no—
556D4—42no—
557D4—42no—
558D4—48no—
559D4—44no—
560D4—82no—
561D4—82no—
562D4—84no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—88no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4C5×#12112yes—
586C8—82no—
587C5#1308611yescharacteristic, direct product factor, Sylow
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—44no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—81no—
621C22—81no—
622C22—84no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—84no—
630C22—84no—
631C22—84no—
632C22—81no—
633C22—81no—
634C22C5×AΣL(1,𝔽16)12yescomplemented
635C22C5×#38611yescharacteristic
636C22C2×C5×#9911yescharacteristic
637C22C2×C5×#9911yescharacteristic
638C4—22no—
639C4—42no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—84no—
644C2—21no—
645C2—21no—
646C2—22no—
647C2—41no—
648C2—41no—
649C2—41no—
650C2—42no—
651C2—42no—
652C2—82no—
653C2—81no—
654C2C5×#189811yescharacteristic
655C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
656C2C5×#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×#99C2semidirect
3. C2×C5×AΣL(1,𝔽16)C2semidirect
4. C5×#1783C2semidirect
5. C5×#1390C2semidirect
6. C23×C5×D4C4semidirect
9. C2×C5×#120C4semidirect
21. C5×#386C4semidirect
23. C5×#379C4semidirect
25. #13086C5direct (N × H)
27. C25×C5C2×C4semidirect
46. C23×C4×C5C2×C4semidirect
63. C2×C5×C22⋊C4C2×C4semidirect
64. C2×C5×C22⋊C4C2×C4semidirect
70. C5×#99D4semidirect
75. C22×#99C2×C5semidirect
77. C2×AΣL(1,𝔽16)C2×C5semidirect
78. #1783C2×C5semidirect
79. #1390C2×C5semidirect
169. C23×D4C4×C5semidirect
172. C2×#120C4×C5semidirect
184. #386C4×C5semidirect
186. #379C4×C5semidirect
285. C25C2×C4×C5semidirect
304. C23×C4C2×C4×C5semidirect
321. C2×C22⋊C4C2×C4×C5semidirect
322. C2×C22⋊C4C2×C4×C5semidirect
328. #99C5×D4semidirect
379. C22×C5AΣL(1,𝔽16)semidirect
587. C5#13086direct (N × H)
634. 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×#992
C5×#24032
C2×C5×AΣL(1,𝔽16)2
C5×#17832
C5×#13902
#130865