Finite Group Databasebeta

← C5×#14551 #11937271

Subgroups — C5×#14551 #11937271

Order 1280.

1642 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2C2×C5×#389C212yesmaximal, complemented
3C2×C5×#385C212yesmaximal
4C5×#1445C212yesmaximal, complemented
5C5×#1441C212yesmaximal, complemented
6C5×#1439C211yesmaximal, characteristic
7C5×#1437C212yesmaximal
8C5×#1436C212yesmaximal, complemented
9C5×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C5C2211yescharacteristic
11C22×C5×C4⋊C4C2212yes—
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C22⋊C4C2212yes—
17C22×C5×C22⋊C4C2212yes—
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C42×C5C2212yes—
21C5×#399C418yescomplemented
22C5×#389—28no—
23C5×#385—28no—
24C2×C5×#95C2212yes—
25C2×C5×#95C2212yes—
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34#14551C511yesmaximal, characteristic, direct product factor, Sylow
35C25×C5C2311yescharacteristic
36C23×C4×C5—22no—
37C23×C4×C5—24no—
38C23×C4×C5—41no—
39C23×C4×C5—41no—
40C23×C4×C5—42no—
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2312yes—
48C23×C4×C5C2312yes—
49C2×C5×C4⋊C4—24no—
50C2×C5×C4⋊C4—24no—
51C2×C5×C4⋊C4—24no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—41no—
55C2×C5×C4⋊C4—41no—
56C2×C5×C4⋊C4—42no—
57C2×C5×C4⋊C4—42no—
58C2×C5×C4⋊C4—41no—
59C2×C5×C4⋊C4—42no—
60C2×C5×C4⋊C4C2×C418yescomplemented
61C2×C5×C4⋊C4C2×C414yescomplemented
62C2×C5×C4⋊C4D418yes—
63C2×C5×C22⋊C4—24no—
64C2×C5×C22⋊C4—24no—
65C2×C5×C22⋊C4—24no—
66C2×C5×C22⋊C4—24no—
67C2×C5×C22⋊C4—41no—
68C2×C5×C22⋊C4—41no—
69C2×C5×C22⋊C4—41no—
70C2×C5×C22⋊C4—41no—
71C2×C5×C22⋊C4—42no—
72C2×C5×C22⋊C4C2×C418yes—
73C2×C5×C22⋊C4C2×C414yes—
74C2×C5×C22⋊C4Q814yes—
75C2×C42×C5—24no—
76C2×C42×C5—42no—
77C2×C42×C5—42no—
78C5×#95—24no—
79C5×#95—24no—
80C5×#95—24no—
81C5×#95—24no—
82C5×#95—24no—
83C5×#95—42no—
84C5×#95—42no—
85C5×#95—41no—
86C5×#95—42no—
87C5×#95C2×C414yescomplemented
88C2×#399C2×C511yescharacteristic
89C2×#389C2×C512yescomplemented
90C2×#385C2×C512yes—
91#1445C2×C512yescomplemented
92#1441C2×C512yescomplemented
93#1439C2×C511yescharacteristic
94#1437C2×C512yes—
95#1436C2×C512yescomplemented
96C22⋊#95C2×C511yescharacteristic
97C24×C5—22no—
98C24×C5—22no—
99C24×C5—21no—
100C24×C5—21no—
101C24×C5—21no—
102C24×C5—22no—
103C24×C5—21no—
104C24×C5—22no—
105C24×C5C22×C412yes—
106C24×C5C2×Q812yes—
107C24×C5#4112yes—
108C24×C5C2411yescharacteristic
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—44no—
153C22×C4×C5—48no—
154C22×C4×C5—48no—
155C22×C4×C5—44no—
156C22×C4×C5—44no—
157C22×C4×C5C22×C414yes—
158C22×C4×C5C22×C412yes—
159C22×C4×C5C22×C412yes—
160C22×C4×C5C22×C414yes—
161C22×C4×C5C2×D414yes—
162C22×C4×C5C2×D414yes—
163C22×C4×C5C2×D414yes—
164C22×C4×C5C2×Q814yes—
165C22×C4×C5#4114yes—
166C5×C4⋊C4—216no—
167C5×C4⋊C4—44no—
168C5×C4⋊C4—48no—
169C5×C4⋊C4—44no—
170C5×C4⋊C4—48no—
171C5×C22⋊C4—216no—
172C5×C22⋊C4—44no—
173C5×C22⋊C4—44no—
174C5×C22⋊C4—48no—
175C42×C5—48no—
176C24×C4C22×C511yescharacteristic
177C22×C4⋊C4C22×C511yescharacteristic
178C22×C4⋊C4C22×C512yes—
179C22×C4⋊C4C22×C512yes—
180C22×C4⋊C4C22×C511yescharacteristic
181C22×C4⋊C4C22×C512yes—
182C22×C22⋊C4C22×C512yes—
183C22×C22⋊C4C22×C512yes—
184C22×C22⋊C4C22×C511yescharacteristic
185C22×C22⋊C4C22×C511yescharacteristic
186C22×C42C22×C512yes—
187#399C4×C518yescomplemented
188#389—28no—
189#385—28no—
190C2×#95C22×C512yes—
191C2×#95C22×C512yes—
192C2×#95C22×C512yes—
193C2×#95C22×C512yes—
194C2×#95C22×C512yes—
195C2×#95C22×C512yes—
196C2×#95C22×C512yes—
197C2×#95C22×C512yes—
198C2×#95C22×C511yescharacteristic
199C2×#95C22×C511yescharacteristic
200C23×C5—24no—
201C23×C5—22no—
202C23×C5—22no—
203C23×C5—24no—
204C23×C5—22no—
205C23×C5—22no—
206C23×C5—22no—
207C23×C5—22no—
208C23×C5—24no—
209C23×C5—24no—
210C23×C5—24no—
211C23×C5—24no—
212C23×C5—42no—
213C23×C5—42no—
214C23×C5—42no—
215C23×C5—42no—
216C23×C5—41no—
217C23×C5—42no—
218C23×C5—41no—
219C23×C5—41no—
220C23×C5—42no—
221C23×C5—41no—
222C23×C5C4×Q814yes—
223C23×C5C23×C411yescharacteristic
224C23×C5C22×D412yes—
225C23×C5C22×Q811yescharacteristic
226C23×C5C2×#4112yes—
227C23×C5C2×#4111yescharacteristic
228C23×C5H(5,𝔽2)11yescharacteristic
229C23×C5H(5,𝔽2)11yescharacteristic
230C23×C5H(5,𝔽2)11yescharacteristic
231C23×C5H(5,𝔽2)12yes—
232C23×C52−1+411yescharacteristic
233C23×C52−1+412yes—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—24no—
237C2×C4×C5—24no—
238C2×C4×C5—24no—
239C2×C4×C5—24no—
240C2×C4×C5—24no—
241C2×C4×C5—24no—
242C2×C4×C5—24no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—24no—
246C2×C4×C5—24no—
247C2×C4×C5—24no—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—24no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—24no—
256C2×C4×C5—416no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—41no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—41no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5C4×D418yes—
287C25C23×C511yescharacteristic
288C23×C4—22no—
289C23×C4—24no—
290C23×C4—42no—
291C23×C4—41no—
292C23×C4—41no—
293C23×C4C23×C512yes—
294C23×C4C23×C512yes—
295C23×C4C23×C511yescharacteristic
296C23×C4C23×C511yescharacteristic
297C23×C4C23×C512yes—
298C23×C4C23×C512yes—
299C23×C4C23×C512yes—
300C23×C4C23×C512yes—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4C2×C4×C518yescomplemented
313C2×C4⋊C4C2×C4×C514yescomplemented
314C2×C4⋊C4C5×D418yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4C2×C4×C518yes—
325C2×C22⋊C4C2×C4×C514yes—
326C2×C22⋊C4C5×Q814yes—
327C2×C42—24no—
328C2×C42—42no—
329C2×C42—42no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—41no—
339#95C2×C4×C514yescomplemented
340C22×C5—24no—
341C22×C5—28no—
342C22×C5—44no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—44no—
348C22×C5—44no—
349C22×C5—42no—
350C22×C5—42no—
351C22×C5C2×C4×D412yes—
352C22×C5C2×C4×Q811yescharacteristic
353C22×C5#51811yescharacteristic
354C22×C5#52011yescharacteristic
355C22×C5#52012yes—
356C22×C5#53412yes—
357C22×C5#53612yes—
358C22×C5#53811yescharacteristic
359C22×C5#53912yes—
360C22×C5#53912yes—
361C22×C5#53911yescharacteristic
362C22×C5#54311yescharacteristic
363C22×C5#54411yescharacteristic
364C22×C5D4211yescharacteristic
365C22×C5#54612yes—
366C22×C5D4×Q812yes—
367C22×C5#55012yes—
368C22×C5#55212yes—
369C22×C5#55412yes—
370C22×C5#55911yescharacteristic
371C22×C5#56011yescharacteristic
372C22×C5#56212yes—
373C22×C5#56311yescharacteristic
374C4×C5—28no—
375C4×C5—44no—
376C4×C5—42no—
377C4×C5—42no—
378C4×C5—44no—
379C4×C5—44no—
380C4×C5—44no—
381C4×C5—82no—
382C24—22no—
383C24—22no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—22no—
390C24C22×C4×C512yes—
391C24C2×C5×Q812yes—
392C24C5×#4112yes—
393C24C24×C511yescharacteristic
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—44no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4C22×C4×C512yes—
443C22×C4C22×C4×C514yes—
444C22×C4C22×C4×C512yes—
445C22×C4C22×C4×C514yes—
446C22×C4C2×C5×D414yes—
447C22×C4C2×C5×D414yes—
448C22×C4C2×C5×D414yes—
449C22×C4C2×C5×Q814yes—
450C22×C4C5×#4114yes—
451C4⋊C4—216no—
452C4⋊C4—44no—
453C4⋊C4—48no—
454C4⋊C4—44no—
455C4⋊C4—48no—
456C22⋊C4—216no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—48no—
460C42—48no—
461C2×C5—44no—
462C2×C5#232212yes—
463C2×C5#232911yescharacteristic
464C2×C5#236012yes—
465C2×C5#236611yescharacteristic
466C2×C5#237611yescharacteristic
467C2×C5#266811yescharacteristic
468C2×C5#267711yescharacteristic
469C2×C5#269412yes—
470C2×C5#273212yes—
471C2×C5#277111yescharacteristic
472C2×C5#280711yescharacteristic
473C23—24no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—41no—
490C23—42no—
491C23—41no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23C4×C5×Q814yes—
496C23C23×C4×C511yescharacteristic
497C23C22×C5×D412yes—
498C23C22×C5×Q811yescharacteristic
499C23C2×C5×#4112yes—
500C23C2×C5×#4111yescharacteristic
501C23C5×H(5,𝔽2)11yescharacteristic
502C23C5×H(5,𝔽2)11yescharacteristic
503C23C5×H(5,𝔽2)11yescharacteristic
504C23C5×H(5,𝔽2)12yes—
505C23C5×2−1+411yescharacteristic
506C23C5×2−1+412yes—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—416no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4C4×C5×D418yes—
560C5#1455111yescharacteristic, direct product factor, Sylow
561C22—24no—
562C22—28no—
563C22—44no—
564C22—42no—
565C22—42no—
566C22—44no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—44no—
572C22C2×C4×C5×D412yes—
573C22C2×C4×C5×Q811yescharacteristic
574C22C5×#51811yescharacteristic
575C22C5×#52011yescharacteristic
576C22C5×#52012yes—
577C22C5×#53412yes—
578C22C5×#53612yes—
579C22C5×#53811yescharacteristic
580C22C5×#53912yes—
581C22C5×#53912yes—
582C22C5×#53911yescharacteristic
583C22C5×#54311yescharacteristic
584C22C5×#54411yescharacteristic
585C22C5×D4211yescharacteristic
586C22C5×#54612yes—
587C22C5×D4×Q812yes—
588C22C5×#55012yes—
589C22C5×#55212yes—
590C22C5×#55412yes—
591C22C5×#55911yescharacteristic
592C22C5×#56011yescharacteristic
593C22C5×#56212yes—
594C22C5×#56311yescharacteristic
595C4—28no—
596C4—44no—
597C4—44no—
598C4—42no—
599C4—42no—
600C4—44no—
601C4—44no—
602C4—82no—
603C2—44no—
604C2C5×#232212yes—
605C2C5×#232911yescharacteristic
606C2C5×#236012yes—
607C2C5×#236611yescharacteristic
608C2C5×#237611yescharacteristic
609C2C5×#266811yescharacteristic
610C2C5×#267711yescharacteristic
611C2C5×#269412yes—
612C2C5×#273212yes—
613C2C5×#277111yescharacteristic
614C2C5×#280711yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#389C2semidirect
4. C5×#1445C2semidirect
5. C5×#1441C2semidirect
8. C5×#1436C2semidirect
21. C5×#399C4semidirect
34. #14551C5direct (N × H)
60. C2×C5×C4⋊C4C2×C4semidirect
61. C2×C5×C4⋊C4C2×C4semidirect
87. C5×#95C2×C4semidirect
89. C2×#389C2×C5semidirect
91. #1445C2×C5semidirect
92. #1441C2×C5semidirect
95. #1436C2×C5semidirect
187. #399C4×C5semidirect
312. C2×C4⋊C4C2×C4×C5semidirect
313. C2×C4⋊C4C2×C4×C5semidirect
339. #95C2×C4×C5semidirect
560. C5#14551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3992
C2×C5×#3892
C2×C5×#3852
C5×#14452
C5×#14412
C5×#14392
C5×#14372
C5×#14362
C5×C22⋊#952
#145515