Finite Group Databasebeta

← C5×#14244 #11936964

Subgroups — C5×#14244 #11936964

Order 1280.

1362 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic
3C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
4C5×#1445C211yesmaximal, characteristic
5C5×#1444C211yesmaximal, characteristic
6C5×#1441C211yesmaximal, characteristic
7C5×#1436C212yesmaximal
8C5×#1436C212yesmaximal
9C5×#1436C212yesmaximal
10C5×C4⋊#95C212yesmaximal
11C4×C5×#95C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2212yes—
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2212yes—
18C22×C42×C5C2212yes—
19C22×C42×C5C2211yescharacteristic
20C22×C42×C5C2212yes—
21C5×#398C418yescomplemented
22C5×#387—24no—
23C4×C5×C4⋊C4—24no—
24C2×C5×#95C2212yes—
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38#14244C511yesmaximal, characteristic, direct product factor, Sylow
39C23×C4×C5C2311yescharacteristic
40C23×C4×C5C2311yescharacteristic
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2312yes—
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—22no—
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4—22no—
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4—24no—
58C2×C5×C4⋊C4—24no—
59C2×C5×C4⋊C4—24no—
60C2×C5×C4⋊C4—42no—
61C2×C5×C4⋊C4—42no—
62C2×C5×C4⋊C4—42no—
63C2×C5×C4⋊C4C2×C414yes—
64C2×C5×C4⋊C4C2×C414yes—
65C2×C5×C4⋊C4C2×C418yes—
66C2×C42×C5—24no—
67C2×C42×C5—24no—
68C2×C42×C5—24no—
69C2×C42×C5—24no—
70C2×C42×C5—42no—
71C2×C42×C5—42no—
72C2×C42×C5—42no—
73C2×C42×C5D414yes—
74C5×#95—24no—
75C5×#95—22no—
76C5×#95—22no—
77C5×#95—22no—
78C5×#95—22no—
79C5×#95—24no—
80C5×#95—22no—
81C5×#95—24no—
82C5×#95—42no—
83C5×#95—42no—
84C5×#95—42no—
85C5×#95C2×C418yes—
86C5×#95C2×C414yes—
87C5×#95Q818yes—
88C2×#398C2×C511yescharacteristic
89C2×#387C2×C511yescharacteristic
90C2×C4×C4⋊C4C2×C511yescharacteristic
91#1445C2×C511yescharacteristic
92#1444C2×C511yescharacteristic
93#1441C2×C511yescharacteristic
94#1436C2×C512yes—
95#1436C2×C512yes—
96#1436C2×C512yes—
97C4⋊#95C2×C512yes—
98C4×#95C2×C511yescharacteristic
99C24×C5C2411yescharacteristic
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—21no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—22no—
120C22×C4×C5—21no—
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—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C22×C414yes—
152C22×C4×C5C22×C412yes—
153C22×C4×C5C22×C412yes—
154C22×C4×C5C22×C414yes—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×D412yes—
158C22×C4×C5C2×Q814yes—
159C22×C4×C5C2×Q814yes—
160C22×C4×C5C2×Q814yes—
161C22×C4×C5#4114yes—
162C22×C4×C5#4112yes—
163C22×C4×C5#4114yes—
164C22×C4×C5#4114yes—
165C5×C4⋊C4—28no—
166C5×C4⋊C4—28no—
167C5×C4⋊C4—28no—
168C5×C4⋊C4—48no—
169C5×C4⋊C4—48no—
170C5×C4⋊C4—44no—
171C42×C5—28no—
172C42×C5—48no—
173C42×C5—48no—
174C22×C4⋊C4C22×C511yescharacteristic
175C22×C4⋊C4C22×C511yescharacteristic
176C22×C4⋊C4C22×C512yes—
177C22×C4⋊C4C22×C511yescharacteristic
178C22×C4⋊C4C22×C511yescharacteristic
179C22×C4⋊C4C22×C512yes—
180C22×C42C22×C512yes—
181C22×C42C22×C511yescharacteristic
182C22×C42C22×C512yes—
183#398C4×C518yescomplemented
184#387—24no—
185C4×C4⋊C4—24no—
186C2×#95C22×C511yescharacteristic
187C2×#95C22×C511yescharacteristic
188C2×#95C22×C512yes—
189C2×#95C22×C512yes—
190C2×#95C22×C512yes—
191C2×#95C22×C511yescharacteristic
192C2×#95C22×C511yescharacteristic
193C2×#95C22×C511yescharacteristic
194C2×#95C22×C512yes—
195C2×#95C22×C512yes—
196C2×#95C22×C512yes—
197C2×#95C22×C511yescharacteristic
198C2×#95C22×C512yes—
199C2×#95C22×C512yes—
200C23×C5C23×C411yescharacteristic
201C23×C5C22×D411yescharacteristic
202C23×C5C22×Q812yes—
203C23×C5C2×#4111yescharacteristic
204C23×C5C2×#4112yes—
205C23×C5C2×#4112yes—
206C23×C5C2×#4112yes—
207C23×C5H(5,𝔽2)11yescharacteristic
208C23×C5H(5,𝔽2)11yescharacteristic
209C23×C5H(5,𝔽2)11yescharacteristic
210C23×C52−1+411yescharacteristic
211C2×C4×C5—24no—
212C2×C4×C5—24no—
213C2×C4×C5—24no—
214C2×C4×C5—22no—
215C2×C4×C5—22no—
216C2×C4×C5—22no—
217C2×C4×C5—24no—
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—24no—
222C2×C4×C5—24no—
223C2×C4×C5—24no—
224C2×C4×C5—24no—
225C2×C4×C5—24no—
226C2×C4×C5—24no—
227C2×C4×C5—24no—
228C2×C4×C5—24no—
229C2×C4×C5—24no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—24no—
233C2×C4×C5—22no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—22no—
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—41no—
244C2×C4×C5—41no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—41no—
251C2×C4×C5—42no—
252C2×C4×C5—41no—
253C2×C4×C5—42no—
254C2×C4×C5—41no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—41no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5C4×D414yes—
273C2×C4×C5C4×Q818yes—
274C2×C4×C5#12314yes—
275C2×C4×C5C4⋊Q814yes—
276C23×C4C23×C511yescharacteristic
277C23×C4C23×C511yescharacteristic
278C23×C4C23×C511yescharacteristic
279C23×C4C23×C511yescharacteristic
280C23×C4C23×C512yes—
281C23×C4C23×C512yes—
282C23×C4C23×C512yes—
283C23×C4C23×C511yescharacteristic
284C23×C4C23×C512yes—
285C23×C4C23×C511yescharacteristic
286C23×C4C23×C511yescharacteristic
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4C2×C4×C514yes—
301C2×C4⋊C4C2×C4×C514yes—
302C2×C4⋊C4C2×C4×C518yes—
303C2×C42—24no—
304C2×C42—24no—
305C2×C42—24no—
306C2×C42—24no—
307C2×C42—42no—
308C2×C42—42no—
309C2×C42—42no—
310C2×C42C5×D414yes—
311#95—24no—
312#95—22no—
313#95—22no—
314#95—22no—
315#95—22no—
316#95—24no—
317#95—22no—
318#95—24no—
319#95—42no—
320#95—42no—
321#95—42no—
322#95C2×C4×C518yes—
323#95C2×C4×C514yes—
324#95C5×Q818yes—
325C22×C5C2×C4×D411yescharacteristic
326C22×C5C2×C4×Q812yes—
327C22×C5C4×#4112yes—
328C22×C5#51811yescharacteristic
329C22×C5#52011yescharacteristic
330C22×C5C2×#12311yescharacteristic
331C22×C5#52511yescharacteristic
332C22×C5#52912yes—
333C22×C5C2×C4⋊Q811yescharacteristic
334C22×C5#53211yescharacteristic
335C22×C5#53312yes—
336C22×C5#53511yescharacteristic
337C22×C5#53711yescharacteristic
338C22×C5#54011yescharacteristic
339C22×C5#54211yescharacteristic
340C22×C5#55112yes—
341C22×C5#55112yes—
342C22×C5#55212yes—
343C22×C5#55312yes—
344C22×C5#55412yes—
345C22×C5#55412yes—
346C22×C5#55412yes—
347C22×C5#55712yes—
348C4×C5—28no—
349C4×C5—24no—
350C4×C5—24no—
351C4×C5—24no—
352C4×C5—42no—
353C4×C5—44no—
354C4×C5—44no—
355C4×C5—44no—
356C4×C5—42no—
357C4×C5—81no—
358C4×C5—81no—
359C24C24×C511yescharacteristic
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4C22×C4×C512yes—
411C22×C4C22×C4×C514yes—
412C22×C4C22×C4×C512yes—
413C22×C4C22×C4×C512yes—
414C22×C4C22×C4×C514yes—
415C22×C4C2×C5×D412yes—
416C22×C4C2×C5×D412yes—
417C22×C4C2×C5×D412yes—
418C22×C4C2×C5×Q814yes—
419C22×C4C2×C5×Q814yes—
420C22×C4C2×C5×Q814yes—
421C22×C4C5×#4114yes—
422C22×C4C5×#4112yes—
423C22×C4C5×#4114yes—
424C22×C4C5×#4114yes—
425C4⋊C4—28no—
426C4⋊C4—28no—
427C4⋊C4—28no—
428C4⋊C4—48no—
429C4⋊C4—48no—
430C4⋊C4—44no—
431C42—28no—
432C42—48no—
433C42—48no—
434C2×C5C4×#12311yescharacteristic
435C2×C5C4×C4⋊Q811yescharacteristic
436C2×C5#232411yescharacteristic
437C2×C5#236812yes—
438C2×C5#237012yes—
439C2×C5#249811yescharacteristic
440C2×C5#250211yescharacteristic
441C2×C5#252012yes—
442C2×C5#252212yes—
443C2×C5#258411yescharacteristic
444C2×C5#260311yescharacteristic
445C23C23×C4×C511yescharacteristic
446C23C22×C5×D411yescharacteristic
447C23C22×C5×Q812yes—
448C23C2×C5×#4111yescharacteristic
449C23C2×C5×#4112yes—
450C23C2×C5×#4112yes—
451C23C2×C5×#4112yes—
452C23C5×H(5,𝔽2)11yescharacteristic
453C23C5×H(5,𝔽2)11yescharacteristic
454C23C5×H(5,𝔽2)11yescharacteristic
455C23C5×2−1+411yescharacteristic
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4C4×C5×D414yes—
518C2×C4C4×C5×Q818yes—
519C2×C4C5×#12314yes—
520C2×C4C5×C4⋊Q814yes—
521C5#1424411yescharacteristic, direct product factor, Sylow
522C22C2×C4×C5×D411yescharacteristic
523C22C2×C4×C5×Q812yes—
524C22C4×C5×#4112yes—
525C22C5×#51811yescharacteristic
526C22C5×#52011yescharacteristic
527C22C2×C5×#12311yescharacteristic
528C22C5×#52511yescharacteristic
529C22C5×#52912yes—
530C22C2×C5×C4⋊Q811yescharacteristic
531C22C5×#53211yescharacteristic
532C22C5×#53312yes—
533C22C5×#53511yescharacteristic
534C22C5×#53711yescharacteristic
535C22C5×#54011yescharacteristic
536C22C5×#54211yescharacteristic
537C22C5×#55112yes—
538C22C5×#55112yes—
539C22C5×#55212yes—
540C22C5×#55312yes—
541C22C5×#55412yes—
542C22C5×#55412yes—
543C22C5×#55412yes—
544C22C5×#55712yes—
545C4—24no—
546C4—24no—
547C4—24no—
548C4—28no—
549C4—44no—
550C4—42no—
551C4—42no—
552C4—44no—
553C4—44no—
554C4—81no—
555C4—81no—
556C2C4×C5×#12311yescharacteristic
557C2C4×C5×C4⋊Q811yescharacteristic
558C2C5×#232411yescharacteristic
559C2C5×#236812yes—
560C2C5×#237012yes—
561C2C5×#249811yescharacteristic
562C2C5×#250211yescharacteristic
563C2C5×#252012yes—
564C2C5×#252212yes—
565C2C5×#258411yescharacteristic
566C2C5×#260311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
21. C5×#398C4semidirect
38. #14244C5direct (N × H)
183. #398C4×C5semidirect
521. C5#14244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C2×C5×#3872
C2×C4×C5×C4⋊C42
C5×#14452
C5×#14442
C5×#14412
C5×#14362
C5×C4⋊#952
C4×C5×#952
#142445