Finite Group Databasebeta

← C5×#16514 #11939234

Subgroups — C5×#16514 #11939234

Order 1280.

1774 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#396C212yesmaximal, complemented
2C2×C5×#394C211yesmaximal, characteristic
3C2×C5×#394C212yesmaximal
4C2×C5×#388C212yesmaximal, complemented
5C2×C5×#384C211yesmaximal, characteristic, complemented
6C5×#1441C211yesmaximal, characteristic, complemented
7C5×#1441C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×#1439C212yesmaximal, complemented
10C23×C5×D4C2211yescharacteristic
11C22×C5×C4⋊C4C2212yes—
12C22×C5×C4⋊C4C2212yes—
13C22×C5×C4⋊C4C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C22⋊C4C2212yes—
18C22×C5×C22⋊C4C2212yes—
19C22×C5×C22⋊C4C2212yes—
20C22×C5×C22⋊C4C2212yes—
21C22×C5×C22⋊C4C2212yes—
22C22×C5×C22⋊C4C2212yes—
23C22×C42×C5C2211yescharacteristic
24C5×#396—28no—
25C5×#394—24no—
26C5×#394—28no—
27C5×#388—28no—
28C5×#384—24no—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2212yes—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2212yes—
36#16514C511yesmaximal, characteristic, direct product factor, Sylow
37C25×C5C2312yes—
38C22×C5×D4—24no—
39C22×C5×D4—22no—
40C22×C5×D4—42no—
41C22×C5×D4—41no—
42C22×C5×D4—41no—
43C23×C4×C5C2312yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2312yes—
51C2×C5×C4⋊C4—24no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—24no—
55C2×C5×C4⋊C4—24no—
56C2×C5×C4⋊C4—24no—
57C2×C5×C4⋊C4—24no—
58C2×C5×C4⋊C4—24no—
59C2×C5×C4⋊C4—24no—
60C2×C5×C4⋊C4—41no—
61C2×C5×C4⋊C4—41no—
62C2×C5×C4⋊C4—42no—
63C2×C5×C4⋊C4—42no—
64C2×C5×C4⋊C4—41no—
65C2×C5×C4⋊C4—41no—
66C2×C5×C4⋊C4—41no—
67C2×C5×C4⋊C4D414yes—
68C2×C5×C22⋊C4—24no—
69C2×C5×C22⋊C4—24no—
70C2×C5×C22⋊C4—24no—
71C2×C5×C22⋊C4—24no—
72C2×C5×C22⋊C4—24no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—24no—
75C2×C5×C22⋊C4—24no—
76C2×C5×C22⋊C4—24no—
77C2×C5×C22⋊C4—24no—
78C2×C5×C22⋊C4—24no—
79C2×C5×C22⋊C4—24no—
80C2×C5×C22⋊C4—24no—
81C2×C5×C22⋊C4—42no—
82C2×C5×C22⋊C4—42no—
83C2×C5×C22⋊C4—42no—
84C2×C5×C22⋊C4—42no—
85C2×C5×C22⋊C4D418yes—
86C2×C42×C5—22no—
87C2×C42×C5—22no—
88C2×C42×C5D414yescomplemented
89C5×#95—24no—
90C5×#95—24no—
91C5×#95—24no—
92C5×#95—22no—
93C5×#95—24no—
94C5×#95—41no—
95C5×#95—42no—
96C2×#396C2×C512yescomplemented
97C2×#394C2×C511yescharacteristic
98C2×#394C2×C512yes—
99C2×#388C2×C512yescomplemented
100C2×#384C2×C511yescharacteristic, complemented
101#1441C2×C512yescomplemented
102#1441C2×C511yescharacteristic, complemented
103#1439C2×C512yescomplemented
104#1439C2×C512yescomplemented
105C24×C5—22no—
106C24×C5—22no—
107C24×C5—22no—
108C24×C5—22no—
109C24×C5—22no—
110C24×C5—22no—
111C24×C5—22no—
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—22no—
115C24×C5—22no—
116C24×C5—22no—
117C24×C5—22no—
118C24×C5—22no—
119C24×C5C2×D414yes—
120C24×C5C2411yescharacteristic
121C2×C5×D4—48no—
122C2×C5×D4—44no—
123C2×C5×D4—44no—
124C2×C5×D4—48no—
125C2×C5×D4—44no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—22no—
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—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5C2×D412yes—
170C22×C4×C5C2×D414yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D414yes—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D414yes—
176C22×C4×C5#4112yes—
177C22×C4×C5#4114yes—
178C5×C4⋊C4—44no—
179C5×C4⋊C4—48no—
180C5×C4⋊C4—48no—
181C5×C4⋊C4—44no—
182C5×C4⋊C4—44no—
183C5×C4⋊C4—48no—
184C5×C22⋊C4—216no—
185C5×C22⋊C4—48no—
186C5×C22⋊C4—48no—
187C5×C22⋊C4—48no—
188C5×C22⋊C4—48no—
189C5×C22⋊C4—48no—
190C42×C5—28no—
191C23×D4C22×C511yescharacteristic
192C22×C4⋊C4C22×C512yes—
193C22×C4⋊C4C22×C512yes—
194C22×C4⋊C4C22×C511yescharacteristic
195C22×C4⋊C4C22×C512yes—
196C22×C4⋊C4C22×C511yescharacteristic
197C22×C4⋊C4C22×C511yescharacteristic
198C22×C22⋊C4C22×C512yes—
199C22×C22⋊C4C22×C512yes—
200C22×C22⋊C4C22×C512yes—
201C22×C22⋊C4C22×C512yes—
202C22×C22⋊C4C22×C512yes—
203C22×C22⋊C4C22×C512yes—
204C22×C42C22×C511yescharacteristic
205#396—28no—
206#394—24no—
207#394—28no—
208#388—28no—
209#384—24no—
210C2×#95C22×C511yescharacteristic
211C2×#95C22×C512yes—
212C2×#95C22×C512yes—
213C2×#95C22×C512yes—
214C2×#95C22×C512yes—
215C2×#95C22×C512yes—
216C2×#95C22×C511yescharacteristic
217C23×C5—24no—
218C23×C5—24no—
219C23×C5—24no—
220C23×C5—24no—
221C23×C5—24no—
222C23×C5—24no—
223C23×C5—24no—
224C23×C5—42no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5—42no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—42no—
234C23×C5—42no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5—42no—
244C23×C5—42no—
245C23×C5—42no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—42no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5C22×D411yescharacteristic
253C23×C5C22×D411yescharacteristic
254C23×C5C22×D412yes—
255C23×C5C2×#4111yescharacteristic
256C23×C5C2×#4112yes—
257C23×C5H(5,𝔽2)11yescharacteristic
258C23×C5H(5,𝔽2)11yescharacteristic
259C23×C5H(5,𝔽2)12yes—
260C23×C52−1+411yescharacteristic
261C23×C52−1+411yescharacteristic
262C23×C52−1+412yes—
263C5×D4—416no—
264C2×C4×C5—24no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—42no—
290C2×C4×C5—42no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—42no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5—42no—
306C2×C4×C5—42no—
307C2×C4×C5—42no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5#12114yes—
315C2×C4×C5#12118yes—
316C25C23×C512yes—
317C22×D4—24no—
318C22×D4—22no—
319C22×D4—42no—
320C22×D4—41no—
321C22×D4—41no—
322C23×C4C23×C512yes—
323C23×C4C23×C512yes—
324C23×C4C23×C512yes—
325C23×C4C23×C511yescharacteristic
326C23×C4C23×C512yes—
327C23×C4C23×C511yescharacteristic
328C23×C4C23×C512yes—
329C23×C4C23×C511yescharacteristic
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4C5×D414yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4C5×D418yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42C5×D414yescomplemented
368#95—24no—
369#95—24no—
370#95—24no—
371#95—22no—
372#95—24no—
373#95—41no—
374#95—42no—
375C22×C5—44no—
376C22×C5—44no—
377C22×C5—44no—
378C22×C5—44no—
379C22×C5—44no—
380C22×C5—44no—
381C22×C5—44no—
382C22×C5—82no—
383C22×C5—82no—
384C22×C5—82no—
385C22×C5—82no—
386C22×C5—82no—
387C22×C5—82no—
388C22×C5—82no—
389C22×C5—82no—
390C22×C5C2×#12111yescharacteristic
391C22×C5C2×#12112yes—
392C22×C5#53411yescharacteristic
393C22×C5#53512yes—
394C22×C5#53611yescharacteristic
395C22×C5#53612yes—
396C22×C5#53711yescharacteristic
397C22×C5#53712yes—
398C22×C5#53711yescharacteristic
399C22×C5#53911yescharacteristic
400C22×C5#53911yescharacteristic
401C22×C5#54212yes—
402C22×C5#54212yes—
403C22×C5D4212yes—
404C22×C5D4211yescharacteristic
405C22×C5#54712yes—
406C22×C5#54712yes—
407C22×C5#54812yes—
408C22×C5#55312yes—
409C22×C5#55511yescharacteristic
410C22×C5#56011yescharacteristic
411C22×C5#56312yes—
412C22×C5#56311yescharacteristic
413C4×C5—24no—
414C4×C5—28no—
415C4×C5—42no—
416C4×C5—42no—
417C4×C5—44no—
418C4×C5—82no—
419C4×C5—82no—
420C4×C5—82no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×C5×D414yes—
436C24C24×C511yescharacteristic
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—48no—
441C2×D4—44no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4C2×C5×D414yes—
486C22×C4C2×C5×D412yes—
487C22×C4C2×C5×D412yes—
488C22×C4C2×C5×D412yes—
489C22×C4C2×C5×D414yes—
490C22×C4C2×C5×D412yes—
491C22×C4C2×C5×D414yes—
492C22×C4C5×#4112yes—
493C22×C4C5×#4114yes—
494C4⋊C4—44no—
495C4⋊C4—48no—
496C4⋊C4—48no—
497C4⋊C4—44no—
498C4⋊C4—44no—
499C4⋊C4—48no—
500C22⋊C4—216no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C42—28no—
507C2×C5—84no—
508C2×C5#241612yes—
509C2×C5#253711yescharacteristic
510C2×C5#261811yescharacteristic
511C2×C5#262012yes—
512C2×C5#266911yescharacteristic
513C2×C5#267412yes—
514C2×C5#268011yescharacteristic
515C2×C5#271812yes—
516C2×C5#273111yescharacteristic
517C2×C5#279511yescharacteristic
518C2×C5#282311yescharacteristic
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23C22×C5×D411yescharacteristic
555C23C22×C5×D411yescharacteristic
556C23C22×C5×D412yes—
557C23C2×C5×#4111yescharacteristic
558C23C2×C5×#4112yes—
559C23C5×H(5,𝔽2)11yescharacteristic
560C23C5×H(5,𝔽2)11yescharacteristic
561C23C5×H(5,𝔽2)12yes—
562C23C5×2−1+411yescharacteristic
563C23C5×2−1+411yescharacteristic
564C23C5×2−1+412yes—
565D4—416no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4C5×#12114yes—
617C2×C4C5×#12118yes—
618C5#1651411yescharacteristic, direct product factor, Sylow
619C22—44no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22—82no—
634C22C2×C5×#12112yes—
635C22C2×C5×#12111yescharacteristic
636C22C5×#53411yescharacteristic
637C22C5×#53512yes—
638C22C5×#53611yescharacteristic
639C22C5×#53612yes—
640C22C5×#53711yescharacteristic
641C22C5×#53712yes—
642C22C5×#53711yescharacteristic
643C22C5×#53911yescharacteristic
644C22C5×#53911yescharacteristic
645C22C5×#54212yes—
646C22C5×#54212yes—
647C22C5×D4211yescharacteristic
648C22C5×D4212yes—
649C22C5×#54712yes—
650C22C5×#54712yes—
651C22C5×#54812yes—
652C22C5×#55312yes—
653C22C5×#55511yescharacteristic
654C22C5×#56011yescharacteristic
655C22C5×#56311yescharacteristic
656C22C5×#56312yes—
657C4—24no—
658C4—28no—
659C4—44no—
660C4—42no—
661C4—42no—
662C4—82no—
663C4—82no—
664C4—82no—
665C2—84no—
666C2C5×#241612yes—
667C2C5×#253711yescharacteristic
668C2C5×#261811yescharacteristic
669C2C5×#262012yes—
670C2C5×#266911yescharacteristic
671C2C5×#267412yes—
672C2C5×#268011yescharacteristic
673C2C5×#271812yes—
674C2C5×#273111yescharacteristic
675C2C5×#279511yescharacteristic
676C2C5×#282311yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#396C2semidirect
4. C2×C5×#388C2semidirect
5. C2×C5×#384C2semidirect
6. C5×#1441C2semidirect
7. C5×#1441C2semidirect
8. C5×#1439C2semidirect
9. C5×#1439C2semidirect
36. #16514C5direct (N × H)
88. C2×C42×C5D4semidirect
96. C2×#396C2×C5semidirect
99. C2×#388C2×C5semidirect
100. C2×#384C2×C5semidirect
101. #1441C2×C5semidirect
102. #1441C2×C5semidirect
103. #1439C2×C5semidirect
104. #1439C2×C5semidirect
367. C2×C42C5×D4semidirect
618. C5#16514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3962
C2×C5×#3942
C2×C5×#3882
C2×C5×#3842
C5×#14412
C5×#14392
#165145