Finite Group Databasebeta

← C5×#12762 #11935482

Subgroups — C5×#12762 #11935482

Order 1280.

944 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#560C211yesmaximal, characteristic
2C2×C5×#353C211yesmaximal, characteristic, complemented
3C2×C5×#352C211yesmaximal, characteristic, complemented
4C2×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C5×#1890C211yesmaximal, characteristic, complemented
6C5×#1889C211yesmaximal, characteristic, complemented
7C5×#1887C211yesmaximal, characteristic, complemented
8C5×#560—22no—
9C5×#560—22no—
10C5×#560—22no—
11C5×#560C414yescomplemented
12C2×C5×#127C2211yescharacteristic
13C2×C5×#126—21no—
14C2×C5×#123—21no—
15C2×C5×#123C2211yescharacteristic
16C2×C5×#121—21no—
17C2×C5×#121—21no—
18C2×C5×#121—21no—
19C2×C5×#120—21no—
20C2×C5×#120C2211yescharacteristic
21C5×#518C2211yescharacteristic
22C5×#418—21no—
23C2×C5×#100C2211yescharacteristic
24C2×C5×#99C2211yescharacteristic
25C2×C5×#99C2211yescharacteristic
26C5×#381—21no—
27C5×#379—21no—
28C5×#353—22no—
29C5×#352—22no—
30C5×AΣL(1,𝔽16)—22no—
31C5×#342—21no—
32C5×#342—21no—
33C5×#339—21no—
34#12762C511yesmaximal, characteristic, direct product factor, Sylow
35C25×C5D411yescharacteristic
36C22×C5×D4—21no—
37C22×C5×D4—21no—
38C22×C5×D4—21no—
39C22×C5×D4—21no—
40C22×C5×D4—21no—
41C22×C5×D4D411yescharacteristic
42C22×C5×D4C2311yescharacteristic
43C23×C4×C5—21no—
44C23×C4×C5D411yescharacteristic
45C2×C5×M16—21no—
46C5×#127—21no—
47C5×#127—21no—
48C5×#127C2×C412yes—
49C5×#127D412yes—
50C5×#126—24no—
51C5×#126—24no—
52C5×#123—24no—
53C5×#123—21no—
54C5×#123—21no—
55C5×#123—24no—
56C5×#123C2×C412yes—
57C5×#123D412yes—
58C5×#121—24no—
59C5×#121—24no—
60C5×#121—24no—
61C5×#121—24no—
62C5×#121—24no—
63C5×#121—24no—
64C5×#120—24no—
65C5×#120—24no—
66C5×#120—21no—
67C5×#120—21no—
68C5×#120C2×C412yes—
69C5×#120D412yes—
70C4×C5×D4—42no—
71C5×#117—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—42no—
85C2×C5×C22⋊C4D411yescharacteristic
86C2×C5×C22⋊C4D411yescharacteristic
87C2×C42×C5D411yescharacteristic
88C5×#102—42no—
89C5×#100—21no—
90C5×#100—21no—
91C5×#99—21no—
92C5×#99—21no—
93C5×#99—21no—
94C5×#99—21no—
95C5×#95—42no—
96C2×#560C2×C511yescharacteristic
97C2×#353C2×C511yescharacteristic, complemented
98C2×#352C2×C511yescharacteristic, complemented
99C2×AΣL(1,𝔽16)C2×C511yescharacteristic, complemented
100#1890C2×C511yescharacteristic, complemented
101#1889C2×C511yescharacteristic, complemented
102#1887C2×C511yescharacteristic, complemented
103C24×C5—21no—
104C24×C5—21no—
105C24×C5—21no—
106C24×C5—41no—
107C24×C5—41no—
108C24×C5—82no—
109C24×C5C22⋊C412yes—
110C24×C5C2×D411yescharacteristic
111C24×C5C2×D411yescharacteristic
112C2×C5×D4—24no—
113C2×C5×D4—24no—
114C2×C5×D4—22no—
115C2×C5×D4—22no—
116C2×C5×D4—22no—
117C2×C5×D4—22no—
118C2×C5×D4—22no—
119C2×C5×D4—22no—
120C2×C5×D4—21no—
121C2×C5×D4—41no—
122C2×C5×D4—41no—
123C2×C5×D4—41no—
124C2×C5×D4—41no—
125C2×C5×D4—82no—
126C2×C5×D4—82no—
127C2×C5×D4—82no—
128C2×C5×D4—82no—
129C2×C5×D4—81no—
130C2×C5×D4—81no—
131C2×C5×D4C22⋊C412yescomplemented
132C2×C5×D4C22×C411yescharacteristic
133C2×C5×D4C2×D411yescharacteristic
134C2×C5×D4C2×D411yescharacteristic
135C2×C5×D4C2×D411yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—24no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—82no—
149C22×C4×C5C22⋊C412yescomplemented
150C22×C4×C5C2×D411yescharacteristic
151C5×M16—41no—
152C5×M16—41no—
153C2×C5×C8—41no—
154C5×C4⋊C4—24no—
155C5×C4⋊C4—24no—
156C5×C4⋊C4—22no—
157C5×C4⋊C4—22no—
158C5×C4⋊C4—22no—
159C5×C22⋊C4—24no—
160C5×C22⋊C4—24no—
161C5×C22⋊C4—24no—
162C5×C22⋊C4—22no—
163C5×C22⋊C4—22no—
164C5×C22⋊C4—21no—
165C5×C22⋊C4—21no—
166C5×C22⋊C4—22no—
167C5×C22⋊C4—22no—
168C5×C22⋊C4—41no—
169C5×C22⋊C4—41no—
170C5×C22⋊C4—41no—
171C5×C22⋊C4—41no—
172C5×C22⋊C4—41no—
173C5×C22⋊C4—41no—
174C5×C22⋊C4—41no—
175C5×C22⋊C4—84no—
176C5×C22⋊C4C22⋊C412yes—
177C5×C22⋊C4C22⋊C412yescomplemented
178C42×C5—21no—
179C42×C5—41no—
180C42×C5C22⋊C412yescomplemented
181#560—22no—
182#560—22no—
183#560—22no—
184#560C4×C514yescomplemented
185C2×#127C22×C511yescharacteristic
186C2×#126—21no—
187C2×#123—21no—
188C2×#123C22×C511yescharacteristic
189C2×#121—21no—
190C2×#121—21no—
191C2×#121—21no—
192C2×#120—21no—
193C2×#120C22×C511yescharacteristic
194#518C22×C511yescharacteristic
195#418—21no—
196C2×#100C22×C511yescharacteristic
197C2×#99C22×C511yescharacteristic
198C2×#99C22×C511yescharacteristic
199#381—21no—
200#379—21no—
201#353—22no—
202#352—22no—
203AΣL(1,𝔽16)—22no—
204#342—21no—
205#342—21no—
206#339—21no—
207C23×C5—21no—
208C23×C5—21no—
209C23×C5—21no—
210C23×C5—21no—
211C23×C5—22no—
212C23×C5—22no—
213C23×C5—42no—
214C23×C5—42no—
215C23×C5—42no—
216C23×C5—42no—
217C23×C5—42no—
218C23×C5—42no—
219C23×C5—42no—
220C23×C5—44no—
221C23×C5—41no—
222C23×C5—41no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—81no—
226C23×C5—82no—
227C23×C5—82no—
228C23×C5—82no—
229C23×C5—84no—
230C23×C5C2×C22⋊C411yescharacteristic
231C23×C5C2×C22⋊C411yescharacteristic
232C23×C5#12011yescharacteristic
233C23×C5#12011yescharacteristic
234C23×C5#12011yescharacteristic
235C5×D4—41no—
236C5×D4—41no—
237C5×D4—41no—
238C5×D4—41no—
239C5×D4—42no—
240C5×D4—81no—
241C5×D4—82no—
242C5×D4—82no—
243C5×D4—84no—
244C5×D4—82no—
245C5×D4—82no—
246C5×D4—82no—
247C5×D4—82no—
248C5×D4—84no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—81no—
263C2×C4×C5—84no—
264C2×C4×C5—82no—
265C2×C4×C5—82no—
266C2×C4×C5—81no—
267C2×C4×C5—81no—
268C2×C4×C5—82no—
269C2×C4×C5—82no—
270C2×C4×C5C2×C22⋊C411yescharacteristic
271C2×C4×C5#12011yescharacteristic
272C5×C8—81no—
273C25C5×D411yescharacteristic
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4C5×D411yescharacteristic
280C22×D4C23×C511yescharacteristic
281C23×C4—21no—
282C23×C4C5×D411yescharacteristic
283C2×M16—21no—
284#127—21no—
285#127—21no—
286#127C2×C4×C512yes—
287#127C5×D412yes—
288#126—24no—
289#126—24no—
290#123—24no—
291#123—21no—
292#123—21no—
293#123—24no—
294#123C2×C4×C512yes—
295#123C5×D412yes—
296#121—24no—
297#121—24no—
298#121—24no—
299#121—24no—
300#121—24no—
301#121—24no—
302#120—24no—
303#120—24no—
304#120—21no—
305#120—21no—
306#120C2×C4×C512yes—
307#120C5×D412yes—
308C4×D4—42no—
309#117—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
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—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4C5×D411yescharacteristic
324C2×C22⋊C4C5×D411yescharacteristic
325C2×C42C5×D411yescharacteristic
326#102—42no—
327#100—21no—
328#100—21no—
329#99—21no—
330#99—21no—
331#99—21no—
332#99—21no—
333#95—42no—
334C22×C5—22no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—21no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5—42no—
349C22×C5—44no—
350C22×C5—42no—
351C22×C5—42no—
352C22×C5—81no—
353C22×C5—81no—
354C22×C5—82no—
355C22×C5—82no—
356C22×C5—82no—
357C22×C5—84no—
358C22×C5—82no—
359C22×C5—82no—
360C22×C5#37911yescharacteristic
361C22×C5B(4,𝔽2)11yescharacteristic
362C22×C5#45811yescharacteristic
363C4×C5—21no—
364C4×C5—21no—
365C4×C5—42no—
366C4×C5—42no—
367C4×C5—42no—
368C4×C5—42no—
369C4×C5—82no—
370C4×C5—161no—
371C4×C5—161no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—41no—
376C24—41no—
377C24—82no—
378C24C5×C22⋊C412yes—
379C24C2×C5×D411yescharacteristic
380C24C2×C5×D411yescharacteristic
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—82no—
395C2×D4—82no—
396C2×D4—82no—
397C2×D4—82no—
398C2×D4—81no—
399C2×D4—81no—
400C2×D4C5×C22⋊C412yescomplemented
401C2×D4C22×C4×C511yescharacteristic
402C2×D4C2×C5×D411yescharacteristic
403C2×D4C2×C5×D411yescharacteristic
404C2×D4C2×C5×D411yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—82no—
418C22×C4C5×C22⋊C412yescomplemented
419C22×C4C2×C5×D411yescharacteristic
420M16—41no—
421M16—41no—
422C2×C8—41no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—84no—
445C22⋊C4C5×C22⋊C412yes—
446C22⋊C4C5×C22⋊C412yescomplemented
447C42—21no—
448C42—41no—
449C42C5×C22⋊C412yescomplemented
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—41no—
453C2×C5—41no—
454C2×C5—41no—
455C2×C5—41no—
456C2×C5—82no—
457C2×C5—82no—
458C2×C5#179011yescharacteristic
459C2×C5#220012yes—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—44no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—81no—
479C23—82no—
480C23—82no—
481C23—82no—
482C23—84no—
483C23C2×C5×C22⋊C411yescharacteristic
484C23C2×C5×C22⋊C411yescharacteristic
485C23C5×#12011yescharacteristic
486C23C5×#12011yescharacteristic
487C23C5×#12011yescharacteristic
488D4—41no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—42no—
493D4—81no—
494D4—82no—
495D4—82no—
496D4—84no—
497D4—82no—
498D4—82no—
499D4—82no—
500D4—82no—
501D4—84no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—81no—
516C2×C4—84no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4C2×C5×C22⋊C411yescharacteristic
524C2×C4C5×#12011yescharacteristic
525C8—81no—
526C5#1276211yescharacteristic, direct product factor, Sylow
527C22—22no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—81no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—84no—
551C22—82no—
552C22—82no—
553C22C5×#37911yescharacteristic
554C22C5×B(4,𝔽2)11yescharacteristic
555C22C5×#45811yescharacteristic
556C4—21no—
557C4—21no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—82no—
563C4—161no—
564C4—161no—
565C2—21no—
566C2—21no—
567C2—41no—
568C2—41no—
569C2—41no—
570C2—41no—
571C2—82no—
572C2—82no—
573C2C5×#179011yescharacteristic
574C2C5×#220012yes—
subgroupG/H
center, socleC22×C5B(4,𝔽2)
commutatorC2×D4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC2×C5×#560C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#353C2semidirect
3. C2×C5×#352C2semidirect
4. C2×C5×AΣL(1,𝔽16)C2semidirect
5. C5×#1890C2semidirect
6. C5×#1889C2semidirect
7. C5×#1887C2semidirect
11. C5×#560C4semidirect
34. #12762C5direct (N × H)
97. C2×#353C2×C5semidirect
98. C2×#352C2×C5semidirect
99. C2×AΣL(1,𝔽16)C2×C5semidirect
100. #1890C2×C5semidirect
101. #1889C2×C5semidirect
102. #1887C2×C5semidirect
131. C2×C5×D4C22⋊C4semidirect
149. C22×C4×C5C22⋊C4semidirect
177. C5×C22⋊C4C22⋊C4semidirect
180. C42×C5C22⋊C4semidirect
184. #560C4×C5semidirect
400. C2×D4C5×C22⋊C4semidirect
418. C22×C4C5×C22⋊C4semidirect
446. C22⋊C4C5×C22⋊C4semidirect
449. C42C5×C22⋊C4semidirect
526. C5#12762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5602
C2×C5×#3532
C2×C5×#3522
C2×C5×AΣL(1,𝔽16)2
C5×#18902
C5×#18892
C5×#18872
#127625