Finite Group Databasebeta

← C5×#13088 #11935808

Subgroups — C5×#13088 #11935808

Order 1280.

1040 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×#99C211yesmaximal, characteristic, complemented
2C5×#2433C211yesmaximal, characteristic
3C2×C5×#353C212yesmaximal, complemented
4C5×#1781C211yesmaximal, characteristic, complemented
5C5×#1393C212yesmaximal, complemented
6C23×C5×D4C2211yescharacteristic
7C2×C5×#127C411yescharacteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×C5×#121C411yescharacteristic, complemented
10C2×C5×#120—21no—
11C2×C5×#120—21no—
12C22×C5×C22⋊C4—21no—
13C2×C5×#99—24no—
14C2×C5×#99—21no—
15C2×C5×#99—21no—
16C2×C5×#99C2212yes—
17C2×C5×#99C2212yes—
18C5×#392—21no—
19C5×#392—21no—
20C5×#390C411yescharacteristic, complemented
21C5×#390C2211yescharacteristic
22C5×#379—21no—
23C4×C5×C22⋊C4C411yescharacteristic, complemented
24C5×#353—24no—
25#13088C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5D411yescharacteristic
27C25×C5D411yescharacteristic
28C22×C5×D4—22no—
29C22×C5×D4—22no—
30C22×C5×D4—21no—
31C22×C5×D4—21no—
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×D4C2×C411yescharacteristic
39C22×C5×D4C2×C411yescharacteristic, complemented
40C22×C5×D4D411yescharacteristic
41C22×C5×D4D411yescharacteristic
42C22×C5×D4C2311yescharacteristic
43C23×C4×C5—41no—
44C23×C4×C5C2×C411yescharacteristic
45C5×#127—22no—
46C5×#127—22no—
47C5×#127—42no—
48C5×#121—41no—
49C5×#121—41no—
50C5×#120—44no—
51C5×#120—44no—
52C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—24no—
55C2×C5×C22⋊C4—22no—
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—41no—
63C2×C5×C22⋊C4—42no—
64C2×C5×C22⋊C4—41no—
65C2×C5×C22⋊C4—41no—
66C2×C42×C5C2×C411yescharacteristic, complemented
67C2×C42×C5C2×C411yescharacteristic, complemented
68C5×#99—24no—
69C5×#99—22no—
70C5×#99—22no—
71C5×#99—22no—
72C5×#99—42no—
73C5×#99D414yescomplemented
74C5×#95—21no—
75C22×#99C2×C511yescharacteristic, complemented
76#2433C2×C511yescharacteristic
77C2×#353C2×C512yescomplemented
78#1781C2×C511yescharacteristic, complemented
79#1393C2×C512yescomplemented
80C24×C5—21no—
81C24×C5—22no—
82C24×C5—21no—
83C24×C5—21no—
84C24×C5—21no—
85C24×C5—21no—
86C24×C5—21no—
87C24×C5—22no—
88C24×C5—21no—
89C24×C5—41no—
90C24×C5—42no—
91C24×C5—42no—
92C24×C5—81no—
93C24×C5—81no—
94C24×C5C22⋊C411yescharacteristic
95C24×C5C22⋊C411yescharacteristic
96C24×C5C22⋊C411yescharacteristic
97C24×C5C2×D411yescharacteristic
98C24×C5C2×D411yescharacteristic
99C2×C5×D4—22no—
100C2×C5×D4—22no—
101C2×C5×D4—21no—
102C2×C5×D4—22no—
103C2×C5×D4—21no—
104C2×C5×D4—22no—
105C2×C5×D4—22no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4—41no—
110C2×C5×D4—41no—
111C2×C5×D4—41no—
112C2×C5×D4—41no—
113C2×C5×D4—41no—
114C2×C5×D4—42no—
115C2×C5×D4—42no—
116C2×C5×D4—42no—
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—41no—
126C2×C5×D4—41no—
127C2×C5×D4—42no—
128C2×C5×D4—41no—
129C2×C5×D4—42no—
130C2×C5×D4—41no—
131C2×C5×D4—81no—
132C2×C5×D4—81no—
133C2×C5×D4—81no—
134C2×C5×D4—81no—
135C2×C5×D4C2×D412yes—
136C2×C5×D4#4112yes—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—21no—
143C22×C4×C5—41no—
144C22×C4×C5—44no—
145C22×C4×C5—42no—
146C22×C4×C5—42no—
147C22×C4×C5—82no—
148C22×C4×C5—82no—
149C22×C4×C5C22⋊C411yescharacteristic
150C22×C4×C5C22×C411yescharacteristic
151C5×C4⋊C4—41no—
152C5×C22⋊C4—24no—
153C5×C22⋊C4—24no—
154C5×C22⋊C4—42no—
155C5×C22⋊C4—42no—
156C5×C22⋊C4—42no—
157C5×C22⋊C4—42no—
158C5×C22⋊C4—42no—
159C5×C22⋊C4—44no—
160C5×C22⋊C4—42no—
161C5×C22⋊C4—42no—
162C5×C22⋊C4—42no—
163C5×C22⋊C4—82no—
164C5×C22⋊C4—82no—
165C42×C5—22no—
166C42×C5—41no—
167C23×D4C22×C511yescharacteristic
168C2×#127C4×C511yescharacteristic, complemented
169C2×#127C22×C511yescharacteristic
170C2×#121C4×C511yescharacteristic, complemented
171C2×#120—21no—
172C2×#120—21no—
173C22×C22⋊C4—21no—
174C2×#99—21no—
175C2×#99—24no—
176C2×#99—21no—
177C2×#99C22×C512yes—
178C2×#99C22×C512yes—
179#392—21no—
180#392—21no—
181#390C4×C511yescharacteristic, complemented
182#390C22×C511yescharacteristic
183#379—21no—
184C4×C22⋊C4C4×C511yescharacteristic, complemented
185#353—24no—
186C23×C5—22no—
187C23×C5—22no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—22no—
191C23×C5—21no—
192C23×C5—21no—
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—21no—
202C23×C5—41no—
203C23×C5—42no—
204C23×C5—42no—
205C23×C5—42no—
206C23×C5—41no—
207C23×C5—41no—
208C23×C5—41no—
209C23×C5—41no—
210C23×C5—41no—
211C23×C5—41no—
212C23×C5—41no—
213C23×C5—41no—
214C23×C5—42no—
215C23×C5—41no—
216C23×C5—41no—
217C23×C5—41no—
218C23×C5—41no—
219C23×C5—42no—
220C23×C5—42no—
221C23×C5—41no—
222C23×C5—41no—
223C23×C5—41no—
224C23×C5—81no—
225C23×C5—81no—
226C23×C5—81no—
227C23×C5—81no—
228C23×C5—84no—
229C23×C5—82no—
230C23×C5—82no—
231C23×C5—84no—
232C23×C5—84no—
233C23×C5#9911yescharacteristic
234C23×C5#9911yescharacteristic
235C23×C5#9912yes—
236C23×C5C2×C22⋊C411yescharacteristic
237C23×C5#12011yescharacteristic
238C23×C5#12112yes—
239C23×C5#12311yescharacteristic
240C5×D4—42no—
241C5×D4—42no—
242C5×D4—44no—
243C5×D4—44no—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—82no—
247C5×D4—84no—
248C5×D4—82no—
249C5×D4—84no—
250C5×D4—82no—
251C5×D4—84no—
252C5×D4—82no—
253C5×D4—82no—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—44no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—88no—
272C2×C4×C5—82no—
273C2×C4×C5—82no—
274C2×C4×C5—82no—
275C2×C4×C5—82no—
276C2×C4×C5—82no—
277C2×C4×C5C4×D412yes—
278C25C5×D411yescharacteristic
279C25C5×D411yescharacteristic
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—41no—
288C22×D4—41no—
289C22×D4—42no—
290C22×D4C2×C4×C511yescharacteristic
291C22×D4C2×C4×C511yescharacteristic, complemented
292C22×D4C5×D411yescharacteristic
293C22×D4C5×D411yescharacteristic
294C22×D4C23×C511yescharacteristic
295C23×C4—41no—
296C23×C4C2×C4×C511yescharacteristic
297#127—22no—
298#127—22no—
299#127—42no—
300#121—41no—
301#121—41no—
302#120—44no—
303#120—44no—
304C2×C4⋊C4C2×C4×C511yescharacteristic, complemented
305C2×C22⋊C4—21no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C42C2×C4×C511yescharacteristic, complemented
319C2×C42C2×C4×C511yescharacteristic, complemented
320#99—24no—
321#99—22no—
322#99—22no—
323#99—22no—
324#99—42no—
325#99C5×D414yescomplemented
326#95—21no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—21no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—22no—
336C22×C5—22no—
337C22×C5—21no—
338C22×C5—42no—
339C22×C5—42no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5—42no—
343C22×C5—41no—
344C22×C5—44no—
345C22×C5—44no—
346C22×C5—42no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5—41no—
352C22×C5—41no—
353C22×C5—41no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—81no—
357C22×C5—81no—
358C22×C5—81no—
359C22×C5—84no—
360C22×C5—81no—
361C22×C5—81no—
362C22×C5—81no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—82no—
366C22×C5—82no—
367C22×C5—84no—
368C22×C5—81no—
369C22×C5—81no—
370C22×C5—81no—
371C22×C5#35312yescomplemented
372C22×C5#38611yescharacteristic
373C22×C5C2×#9911yescharacteristic
374C22×C5C2×#9911yescharacteristic
375C4×C5—22no—
376C4×C5—42no—
377C4×C5—42no—
378C4×C5—41no—
379C4×C5—84no—
380C4×C5—81no—
381C4×C5—162no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—22no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—21no—
391C24—41no—
392C24—42no—
393C24—42no—
394C24—81no—
395C24—81no—
396C24C5×C22⋊C411yescharacteristic
397C24C5×C22⋊C411yescharacteristic
398C24C5×C22⋊C411yescharacteristic
399C24C2×C5×D411yescharacteristic
400C24C2×C5×D411yescharacteristic
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—41no—
428C2×D4—42no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—42no—
433C2×D4—81no—
434C2×D4—81no—
435C2×D4—81no—
436C2×D4—81no—
437C2×D4C2×C5×D412yes—
438C2×D4C5×#4112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—44no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—82no—
450C22×C4—82no—
451C22×C4C5×C22⋊C411yescharacteristic
452C22×C4C22×C4×C511yescharacteristic
453C4⋊C4—41no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—42no—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C22⋊C4—44no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—82no—
466C22⋊C4—82no—
467C42—22no—
468C42—41no—
469C2×C5—21no—
470C2×C5—21no—
471C2×C5—22no—
472C2×C5—41no—
473C2×C5—42no—
474C2×C5—41no—
475C2×C5—42no—
476C2×C5—41no—
477C2×C5—81no—
478C2×C5—161no—
479C2×C5#189811yescharacteristic
480C2×C5C2×#35311yescharacteristic
481C2×C5#212711yescharacteristic
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
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—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—81no—
521C23—81no—
522C23—81no—
523C23—81no—
524C23—82no—
525C23—82no—
526C23—84no—
527C23—84no—
528C23—84no—
529C23C5×#9911yescharacteristic
530C23C5×#9911yescharacteristic
531C23C5×#9912yes—
532C23C2×C5×C22⋊C411yescharacteristic
533C23C5×#12011yescharacteristic
534C23C5×#12112yes—
535C23C5×#12311yescharacteristic
536D4—42no—
537D4—42no—
538D4—44no—
539D4—44no—
540D4—42no—
541D4—42no—
542D4—82no—
543D4—82no—
544D4—84no—
545D4—82no—
546D4—84no—
547D4—84no—
548D4—82no—
549D4—82no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—44no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—88no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4C4×C5×D412yes—
574C5#1308811yescharacteristic, direct product factor, Sylow
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—22no—
584C22—21no—
585C22—22no—
586C22—42no—
587C22—42no—
588C22—41no—
589C22—42no—
590C22—41no—
591C22—42no—
592C22—44no—
593C22—44no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—84no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—82no—
614C22—82no—
615C22—84no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C5×#35312yescomplemented
620C22C5×#38611yescharacteristic
621C22C2×C5×#9911yescharacteristic
622C22C2×C5×#9911yescharacteristic
623C4—22no—
624C4—42no—
625C4—42no—
626C4—41no—
627C4—84no—
628C4—81no—
629C4—162no—
630C2—21no—
631C2—21no—
632C2—22no—
633C2—41no—
634C2—42no—
635C2—41no—
636C2—41no—
637C2—42no—
638C2—81no—
639C2—161no—
640C2C5×#189811yescharacteristic
641C2C2×C5×#35311yescharacteristic
642C2C5×#212711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC5×#2433C2
LCSG ▷ C22×C4 ▷ 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×#353C2semidirect
4. C5×#1781C2semidirect
5. C5×#1393C2semidirect
7. C2×C5×#127C4semidirect
9. C2×C5×#121C4semidirect
20. C5×#390C4semidirect
23. C4×C5×C22⋊C4C4semidirect
25. #13088C5direct (N × H)
39. C22×C5×D4C2×C4semidirect
52. C2×C5×C4⋊C4C2×C4semidirect
66. C2×C42×C5C2×C4semidirect
67. C2×C42×C5C2×C4semidirect
73. C5×#99D4semidirect
75. C22×#99C2×C5semidirect
77. C2×#353C2×C5semidirect
78. #1781C2×C5semidirect
79. #1393C2×C5semidirect
168. C2×#127C4×C5semidirect
170. C2×#121C4×C5semidirect
181. #390C4×C5semidirect
184. C4×C22⋊C4C4×C5semidirect
291. C22×D4C2×C4×C5semidirect
304. C2×C4⋊C4C2×C4×C5semidirect
318. C2×C42C2×C4×C5semidirect
319. C2×C42C2×C4×C5semidirect
325. #99C5×D4semidirect
371. C22×C5#353semidirect
574. C5#13088direct (N × H)
619. C22C5×#353semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#992
C5×#24332
C2×C5×#3532
C5×#17812
C5×#13932
#130885