Finite Group Databasebeta

← C5×#14306 #11937026

Subgroups — C5×#14306 #11937026

Order 1280.

1406 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic
3C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C5×#1445C211yesmaximal, characteristic, complemented
5C5×#1444C211yesmaximal, characteristic, complemented
6C5×#1442C212yesmaximal, complemented
7C5×#1439C212yesmaximal
8C5×#1439C211yesmaximal, characteristic
9C5×#1437C212yesmaximal
10C5×#1436C212yesmaximal, complemented
11C5×#1434C211yesmaximal, characteristic, complemented
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C22⋊C4C2211yescharacteristic
17C22×C5×C22⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2212yes—
20C22×C5×C22⋊C4C2212yes—
21C22×C42×C5C2211yescharacteristic
22C22×C42×C5C2212yes—
23C5×#397C418yescomplemented
24C5×#388—24no—
25C4×C5×C4⋊C4—24no—
26C2×C5×#95C2212yes—
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2212yes—
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38#14306C511yesmaximal, characteristic, direct product factor, Sylow
39C25×C5C2311yescharacteristic
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2312yes—
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—22no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4—24no—
56C2×C5×C4⋊C4—42no—
57C2×C5×C4⋊C4—42no—
58C2×C5×C4⋊C4—42no—
59C2×C5×C4⋊C4C2×C414yes—
60C2×C5×C22⋊C4—22no—
61C2×C5×C22⋊C4—22no—
62C2×C5×C22⋊C4—22no—
63C2×C5×C22⋊C4—22no—
64C2×C5×C22⋊C4—24no—
65C2×C5×C22⋊C4—24no—
66C2×C5×C22⋊C4—42no—
67C2×C5×C22⋊C4—42no—
68C2×C5×C22⋊C4—42no—
69C2×C5×C22⋊C4—42no—
70C2×C5×C22⋊C4—42no—
71C2×C5×C22⋊C4C2×C414yes—
72C2×C5×C22⋊C4C2×C418yes—
73C2×C42×C5—24no—
74C2×C42×C5—24no—
75C2×C42×C5—42no—
76C2×C42×C5—42no—
77C2×C42×C5D414yes—
78C5×#95—24no—
79C5×#95—22no—
80C5×#95—22no—
81C5×#95—24no—
82C5×#95—22no—
83C5×#95—42no—
84C5×#95—42no—
85C5×#95—42no—
86C5×#95—42no—
87C5×#95—42no—
88C5×#95C2×C418yes—
89C5×#95C2×C414yes—
90C2×#397C2×C511yescharacteristic
91C2×#388C2×C511yescharacteristic
92C2×C4×C4⋊C4C2×C511yescharacteristic, complemented
93#1445C2×C511yescharacteristic, complemented
94#1444C2×C511yescharacteristic, complemented
95#1442C2×C512yescomplemented
96#1439C2×C511yescharacteristic
97#1439C2×C512yes—
98#1437C2×C512yes—
99#1436C2×C512yescomplemented
100#1434C2×C511yescharacteristic, complemented
101C24×C5—21no—
102C24×C5—21no—
103C24×C5—22no—
104C24×C5—22no—
105C24×C5—21no—
106C24×C5—21no—
107C24×C5—22no—
108C24×C5—21no—
109C24×C5—22no—
110C24×C5—21no—
111C24×C5C22×C412yes—
112C24×C5C2411yescharacteristic
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—21no—
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—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
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—21no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
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—22no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5C22×C414yes—
162C22×C4×C5C22×C412yes—
163C22×C4×C5C22×C414yes—
164C22×C4×C5C22×C412yes—
165C22×C4×C5C2×D412yes—
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2×D412yes—
168C22×C4×C5#4114yes—
169C22×C4×C5#4112yes—
170C22×C4×C5#4114yes—
171C5×C4⋊C4—28no—
172C5×C4⋊C4—28no—
173C5×C4⋊C4—44no—
174C5×C4⋊C4—48no—
175C5×C22⋊C4—28no—
176C5×C22⋊C4—48no—
177C5×C22⋊C4—44no—
178C5×C22⋊C4—48no—
179C5×C22⋊C4—44no—
180C42×C5—28no—
181C42×C5—48no—
182C22×C4⋊C4C22×C511yescharacteristic
183C22×C4⋊C4C22×C511yescharacteristic
184C22×C4⋊C4C22×C512yes—
185C22×C4⋊C4C22×C511yescharacteristic
186C22×C22⋊C4C22×C511yescharacteristic
187C22×C22⋊C4C22×C511yescharacteristic
188C22×C22⋊C4C22×C512yes—
189C22×C22⋊C4C22×C511yescharacteristic
190C22×C22⋊C4C22×C512yes—
191C22×C42C22×C511yescharacteristic
192C22×C42C22×C512yes—
193#397C4×C518yescomplemented
194#388—24no—
195C4×C4⋊C4—24no—
196C2×#95C22×C512yes—
197C2×#95C22×C511yescharacteristic
198C2×#95C22×C511yescharacteristic
199C2×#95C22×C512yes—
200C2×#95C22×C511yescharacteristic
201C2×#95C22×C512yes—
202C2×#95C22×C512yes—
203C2×#95C22×C512yes—
204C2×#95C22×C512yes—
205C2×#95C22×C512yes—
206C2×#95C22×C511yescharacteristic
207C2×#95C22×C512yes—
208C23×C5—22no—
209C23×C5—24no—
210C23×C5—22no—
211C23×C5—22no—
212C23×C5—24no—
213C23×C5—41no—
214C23×C5—41no—
215C23×C5—42no—
216C23×C5—41no—
217C23×C5—41no—
218C23×C5—41no—
219C23×C5—41no—
220C23×C5—42no—
221C23×C5—42no—
222C23×C5—42no—
223C23×C5—42no—
224C23×C5—41no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5—41no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5C23×C411yescharacteristic
232C23×C5C22×D411yescharacteristic
233C23×C5C2×#4111yescharacteristic
234C23×C5C2×#4112yes—
235C23×C5C2×#4112yes—
236C23×C5H(5,𝔽2)11yescharacteristic
237C23×C5H(5,𝔽2)11yescharacteristic
238C23×C5H(5,𝔽2)11yescharacteristic
239C23×C5H(5,𝔽2)12yes—
240C23×C52−1+412yes—
241C23×C52−1+411yescharacteristic
242C2×C4×C5—24no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—24no—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—22no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—24no—
256C2×C4×C5—24no—
257C2×C4×C5—24no—
258C2×C4×C5—22no—
259C2×C4×C5—24no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—24no—
263C2×C4×C5—24no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—41no—
267C2×C4×C5—42no—
268C2×C4×C5—41no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—42no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—42no—
289C2×C4×C5—42no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—42no—
298C2×C4×C5C4×D414yes—
299C2×C4×C5#12314yes—
300C25C23×C511yescharacteristic
301C23×C4C23×C511yescharacteristic
302C23×C4C23×C511yescharacteristic
303C23×C4C23×C512yes—
304C23×C4C23×C511yescharacteristic
305C23×C4C23×C512yes—
306C23×C4C23×C512yes—
307C23×C4C23×C511yescharacteristic
308C23×C4C23×C512yes—
309C23×C4C23×C511yescharacteristic
310C23×C4C23×C511yescharacteristic
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4C2×C4×C514yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4C2×C4×C514yes—
333C2×C22⋊C4C2×C4×C518yes—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42C5×D414yes—
339#95—24no—
340#95—22no—
341#95—22no—
342#95—24no—
343#95—22no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95C2×C4×C518yes—
350#95C2×C4×C514yes—
351C22×C5—42no—
352C22×C5—42no—
353C22×C5—44no—
354C22×C5—44no—
355C22×C5—42no—
356C22×C5—81no—
357C22×C5—81no—
358C22×C5—81no—
359C22×C5—81no—
360C22×C5—82no—
361C22×C5—82no—
362C22×C5C2×C4×D411yescharacteristic
363C22×C5C4×#4112yes—
364C22×C5#51811yescharacteristic
365C22×C5#52011yescharacteristic
366C22×C5#52012yes—
367C22×C5C2×#12311yescharacteristic
368C22×C5#52511yescharacteristic
369C22×C5#52912yes—
370C22×C5#53511yescharacteristic
371C22×C5#53511yescharacteristic
372C22×C5#53611yescharacteristic
373C22×C5#53711yescharacteristic
374C22×C5#53812yes—
375C22×C5#53812yes—
376C22×C5#53912yes—
377C22×C5#53912yes—
378C22×C5#54011yescharacteristic
379C22×C5#54012yes—
380C22×C5#54112yes—
381C22×C5#54211yescharacteristic
382C22×C5#54212yes—
383C22×C5#54212yes—
384C22×C5#54212yes—
385C4×C5—24no—
386C4×C5—24no—
387C4×C5—44no—
388C4×C5—42no—
389C4×C5—44no—
390C4×C5—42no—
391C4×C5—44no—
392C4×C5—81no—
393C4×C5—81no—
394C4×C5—82no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—21no—
403C24—22no—
404C24—21no—
405C24C22×C4×C512yes—
406C24C24×C511yescharacteristic
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
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—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4C22×C4×C512yes—
456C22×C4C22×C4×C514yes—
457C22×C4C22×C4×C514yes—
458C22×C4C22×C4×C512yes—
459C22×C4C2×C5×D412yes—
460C22×C4C2×C5×D412yes—
461C22×C4C2×C5×D412yes—
462C22×C4C5×#4114yes—
463C22×C4C5×#4112yes—
464C22×C4C5×#4114yes—
465C4⋊C4—28no—
466C4⋊C4—28no—
467C4⋊C4—44no—
468C4⋊C4—48no—
469C22⋊C4—28no—
470C22⋊C4—48no—
471C22⋊C4—44no—
472C22⋊C4—48no—
473C22⋊C4—44no—
474C42—28no—
475C42—48no—
476C2×C5—82no—
477C2×C5C4×#12311yescharacteristic
478C2×C5#232411yescharacteristic
479C2×C5#232611yescharacteristic
480C2×C5#233412yes—
481C2×C5#233512yes—
482C2×C5#262311yescharacteristic
483C2×C5#262411yescharacteristic
484C2×C5#263111yescharacteristic
485C2×C5#263711yescharacteristic
486C2×C5#265012yes—
487C2×C5#265112yes—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C23×C4×C511yescharacteristic
512C23C22×C5×D411yescharacteristic
513C23C2×C5×#4111yescharacteristic
514C23C2×C5×#4112yes—
515C23C2×C5×#4112yes—
516C23C5×H(5,𝔽2)11yescharacteristic
517C23C5×H(5,𝔽2)11yescharacteristic
518C23C5×H(5,𝔽2)11yescharacteristic
519C23C5×H(5,𝔽2)12yes—
520C23C5×2−1+412yes—
521C23C5×2−1+411yescharacteristic
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4C4×C5×D414yes—
579C2×C4C5×#12314yes—
580C5#1430611yescharacteristic, direct product factor, Sylow
581C22—42no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—44no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—82no—
591C22—82no—
592C22C2×C4×C5×D411yescharacteristic
593C22C4×C5×#4112yes—
594C22C5×#51811yescharacteristic
595C22C5×#52011yescharacteristic
596C22C5×#52012yes—
597C22C2×C5×#12311yescharacteristic
598C22C5×#52511yescharacteristic
599C22C5×#52912yes—
600C22C5×#53511yescharacteristic
601C22C5×#53511yescharacteristic
602C22C5×#53611yescharacteristic
603C22C5×#53711yescharacteristic
604C22C5×#53812yes—
605C22C5×#53812yes—
606C22C5×#53912yes—
607C22C5×#53912yes—
608C22C5×#54011yescharacteristic
609C22C5×#54012yes—
610C22C5×#54112yes—
611C22C5×#54211yescharacteristic
612C22C5×#54212yes—
613C22C5×#54212yes—
614C22C5×#54212yes—
615C4—24no—
616C4—24no—
617C4—44no—
618C4—42no—
619C4—44no—
620C4—42no—
621C4—44no—
622C4—81no—
623C4—81no—
624C4—82no—
625C2—82no—
626C2C4×C5×#12311yescharacteristic
627C2C5×#232411yescharacteristic
628C2C5×#232611yescharacteristic
629C2C5×#233412yes—
630C2C5×#233512yes—
631C2C5×#262311yescharacteristic
632C2C5×#262411yescharacteristic
633C2C5×#263111yescharacteristic
634C2C5×#263711yescharacteristic
635C2C5×#265012yes—
636C2C5×#265112yes—
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
3. C2×C4×C5×C4⋊C4C2semidirect
4. C5×#1445C2semidirect
5. C5×#1444C2semidirect
6. C5×#1442C2semidirect
10. C5×#1436C2semidirect
11. C5×#1434C2semidirect
23. C5×#397C4semidirect
38. #14306C5direct (N × H)
92. C2×C4×C4⋊C4C2×C5semidirect
93. #1445C2×C5semidirect
94. #1444C2×C5semidirect
95. #1442C2×C5semidirect
99. #1436C2×C5semidirect
100. #1434C2×C5semidirect
193. #397C4×C5semidirect
580. C5#14306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×C5×#3882
C2×C4×C5×C4⋊C42
C5×#14452
C5×#14442
C5×#14422
C5×#14392
C5×#14372
C5×#14362
C5×#14342
#143065