Finite Group Databasebeta

← C5×#14646 #11937366

Subgroups — C5×#14646 #11937366

Order 1280.

1226 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2C5×#1443C212yesmaximal, complemented
3C5×#1441C212yesmaximal, complemented
4C5×#1441C212yesmaximal, complemented
5C5×#1440C212yesmaximal
6C5×#1440C211yesmaximal, characteristic
7C5×#1439C212yesmaximal
8C5×#1437C211yesmaximal, characteristic
9C5×#1436C212yesmaximal, complemented
10C22×C5×C4⋊C4C2212yes—
11C22×C5×C4⋊C4C2212yes—
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C22⋊C4C2212yes—
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2211yescharacteristic
17C22×C5×C22⋊C4C2212yes—
18C22×C42×C5C2211yescharacteristic
19C5×#399C418yescomplemented
20C2×C5×#95C2212yes—
21C2×C5×#95C2212yes—
22C2×C5×#95C2212yes—
23C2×C5×#95C2212yes—
24C2×C5×#95C2212yes—
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2211yescharacteristic
32#14646C511yesmaximal, characteristic, direct product factor, Sylow
33C25×C5C2311yescharacteristic
34C23×C4×C5C2312yes—
35C23×C4×C5C2312yes—
36C23×C4×C5C2312yes—
37C23×C4×C5C2312yes—
38C23×C4×C5C2311yescharacteristic
39C23×C4×C5C2311yescharacteristic
40C23×C4×C5C2312yes—
41C23×C4×C5C2312yes—
42C2×C5×C4⋊C4—42no—
43C2×C5×C4⋊C4—41no—
44C2×C5×C4⋊C4—42no—
45C2×C5×C4⋊C4—41no—
46C2×C5×C4⋊C4—42no—
47C2×C5×C4⋊C4—42no—
48C2×C5×C4⋊C4—42no—
49C2×C5×C4⋊C4C2×C418yes—
50C2×C5×C4⋊C4C2×C414yes—
51C2×C5×C22⋊C4—24no—
52C2×C5×C22⋊C4—41no—
53C2×C5×C22⋊C4—42no—
54C2×C5×C22⋊C4—41no—
55C2×C5×C22⋊C4—42no—
56C2×C5×C22⋊C4—42no—
57C2×C5×C22⋊C4—42no—
58C2×C5×C22⋊C4—41no—
59C2×C5×C22⋊C4—42no—
60C2×C5×C22⋊C4—41no—
61C2×C5×C22⋊C4—42no—
62C2×C5×C22⋊C4C2×C414yes—
63C2×C5×C22⋊C4C2×C418yes—
64C2×C42×C5—42no—
65C2×C42×C5—41no—
66C5×#95—24no—
67C5×#95—24no—
68C5×#95—42no—
69C5×#95—42no—
70C5×#95—42no—
71C5×#95—41no—
72C5×#95—42no—
73C5×#95—42no—
74C5×#95—42no—
75C5×#95—42no—
76C5×#95—42no—
77C5×#95C2×C414yes—
78C2×#399C2×C511yescharacteristic
79#1443C2×C512yescomplemented
80#1441C2×C512yescomplemented
81#1441C2×C512yescomplemented
82#1440C2×C512yes—
83#1440C2×C511yescharacteristic
84#1439C2×C512yes—
85#1437C2×C511yescharacteristic
86#1436C2×C512yescomplemented
87C24×C5—22no—
88C24×C5—22no—
89C24×C5—21no—
90C24×C5—22no—
91C24×C5—21no—
92C24×C5—22no—
93C24×C5—22no—
94C24×C5—22no—
95C24×C5C22×C412yes—
96C24×C5C2411yescharacteristic
97C22×C4×C5—22no—
98C22×C4×C5—22no—
99C22×C4×C5—21no—
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—22no—
109C22×C4×C5—22no—
110C22×C4×C5—21no—
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—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—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C22×C414yes—
146C22×C4×C5C22×C414yes—
147C22×C4×C5C22×C412yes—
148C22×C4×C5#4114yes—
149C5×C4⋊C4—48no—
150C5×C4⋊C4—44no—
151C5×C4⋊C4—48no—
152C5×C22⋊C4—48no—
153C5×C22⋊C4—44no—
154C5×C22⋊C4—48no—
155C5×C22⋊C4—44no—
156C5×C22⋊C4—44no—
157C42×C5—44no—
158C22×C4⋊C4C22×C512yes—
159C22×C4⋊C4C22×C512yes—
160C22×C4⋊C4C22×C511yescharacteristic
161C22×C22⋊C4C22×C512yes—
162C22×C22⋊C4C22×C511yescharacteristic
163C22×C22⋊C4C22×C511yescharacteristic
164C22×C22⋊C4C22×C511yescharacteristic
165C22×C22⋊C4C22×C512yes—
166C22×C42C22×C511yescharacteristic
167#399C4×C518yescomplemented
168C2×#95C22×C512yes—
169C2×#95C22×C512yes—
170C2×#95C22×C512yes—
171C2×#95C22×C512yes—
172C2×#95C22×C512yes—
173C2×#95C22×C511yescharacteristic
174C2×#95C22×C512yes—
175C2×#95C22×C512yes—
176C2×#95C22×C512yes—
177C2×#95C22×C512yes—
178C2×#95C22×C512yes—
179C2×#95C22×C511yescharacteristic
180C23×C5—22no—
181C23×C5—22no—
182C23×C5—24no—
183C23×C5—22no—
184C23×C5—24no—
185C23×C5—42no—
186C23×C5—42no—
187C23×C5—42no—
188C23×C5—42no—
189C23×C5—42no—
190C23×C5—42no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5—41no—
194C23×C5—42no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5—42no—
198C23×C5—41no—
199C23×C5—42no—
200C23×C5—42no—
201C23×C5C23×C411yescharacteristic
202C23×C5C2×#4112yes—
203C23×C5H(5,𝔽2)12yes—
204C23×C5H(5,𝔽2)11yescharacteristic
205C23×C5H(5,𝔽2)12yes—
206C23×C5H(5,𝔽2)11yescharacteristic
207C23×C5H(5,𝔽2)12yes—
208C23×C52−1+412yes—
209C23×C52−1+412yes—
210C2×C4×C5—24no—
211C2×C4×C5—24no—
212C2×C4×C5—22no—
213C2×C4×C5—22no—
214C2×C4×C5—24no—
215C2×C4×C5—24no—
216C2×C4×C5—24no—
217C2×C4×C5—24no—
218C2×C4×C5—24no—
219C2×C4×C5—24no—
220C2×C4×C5—24no—
221C2×C4×C5—24no—
222C2×C4×C5—24no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—42no—
228C2×C4×C5—41no—
229C2×C4×C5—42no—
230C2×C4×C5—41no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—41no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C25C23×C511yescharacteristic
263C23×C4C23×C512yes—
264C23×C4C23×C512yes—
265C23×C4C23×C512yes—
266C23×C4C23×C512yes—
267C23×C4C23×C511yescharacteristic
268C23×C4C23×C512yes—
269C23×C4C23×C511yescharacteristic
270C23×C4C23×C512yes—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4C2×C4×C518yes—
279C2×C4⋊C4C2×C4×C514yes—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—41no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—41no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—41no—
291C2×C22⋊C4C2×C4×C514yes—
292C2×C22⋊C4C2×C4×C518yes—
293C2×C42—41no—
294C2×C42—42no—
295#95—24no—
296#95—24no—
297#95—42no—
298#95—42no—
299#95—42no—
300#95—42no—
301#95—42no—
302#95—42no—
303#95—41no—
304#95—42no—
305#95—42no—
306#95C2×C4×C514yes—
307C22×C5—42no—
308C22×C5—44no—
309C22×C5—42no—
310C22×C5—44no—
311C22×C5—42no—
312C22×C5—82no—
313C22×C5—82no—
314C22×C5—82no—
315C22×C5—82no—
316C22×C5C4×#4111yescharacteristic
317C22×C5#51811yescharacteristic
318C22×C5#51812yes—
319C22×C5#51911yescharacteristic
320C22×C5#52012yes—
321C22×C5#53812yes—
322C22×C5#53912yes—
323C22×C5#53912yes—
324C22×C5#54012yes—
325C22×C5#54212yes—
326C22×C5#54212yes—
327C22×C5#56011yescharacteristic
328C22×C5#56011yescharacteristic
329C22×C5#56012yes—
330C22×C5#56011yescharacteristic
331C22×C5#56212yes—
332C22×C5#56212yes—
333C22×C5#56212yes—
334C22×C5#56312yes—
335C22×C5#56312yes—
336C22×C5#56311yescharacteristic
337C4×C5—44no—
338C4×C5—44no—
339C4×C5—42no—
340C4×C5—42no—
341C4×C5—44no—
342C4×C5—82no—
343C4×C5—82no—
344C4×C5—82no—
345C24—22no—
346C24—22no—
347C24—21no—
348C24—22no—
349C24—21no—
350C24—22no—
351C24—22no—
352C24—22no—
353C24C22×C4×C512yes—
354C24C24×C511yescharacteristic
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
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×C4C22×C4×C514yes—
403C22×C4C22×C4×C512yes—
404C22×C4C22×C4×C514yes—
405C22×C4C22×C4×C512yes—
406C22×C4C5×#4114yes—
407C4⋊C4—48no—
408C4⋊C4—44no—
409C4⋊C4—48no—
410C22⋊C4—48no—
411C22⋊C4—44no—
412C22⋊C4—48no—
413C22⋊C4—44no—
414C22⋊C4—44no—
415C42—44no—
416C2×C5—82no—
417C2×C5#233211yescharacteristic
418C2×C5#233512yes—
419C2×C5#237611yescharacteristic
420C2×C5#237812yes—
421C2×C5#238011yescharacteristic
422C2×C5#282712yes—
423C2×C5#282912yes—
424C2×C5#283712yes—
425C2×C5#283812yes—
426C23—22no—
427C23—22no—
428C23—24no—
429C23—22no—
430C23—24no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23—42no—
446C23—42no—
447C23C23×C4×C511yescharacteristic
448C23C2×C5×#4112yes—
449C23C5×H(5,𝔽2)12yes—
450C23C5×H(5,𝔽2)11yescharacteristic
451C23C5×H(5,𝔽2)12yes—
452C23C5×H(5,𝔽2)11yescharacteristic
453C23C5×H(5,𝔽2)12yes—
454C23C5×2−1+412yes—
455C23C5×2−1+412yes—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C5#1464611yescharacteristic, direct product factor, Sylow
509C22—42no—
510C22—44no—
511C22—42no—
512C22—44no—
513C22—42no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C4×C5×#4111yescharacteristic
519C22C5×#51811yescharacteristic
520C22C5×#51812yes—
521C22C5×#51911yescharacteristic
522C22C5×#52012yes—
523C22C5×#53812yes—
524C22C5×#53912yes—
525C22C5×#53912yes—
526C22C5×#54012yes—
527C22C5×#54212yes—
528C22C5×#54212yes—
529C22C5×#56011yescharacteristic
530C22C5×#56011yescharacteristic
531C22C5×#56012yes—
532C22C5×#56011yescharacteristic
533C22C5×#56212yes—
534C22C5×#56212yes—
535C22C5×#56212yes—
536C22C5×#56312yes—
537C22C5×#56312yes—
538C22C5×#56311yescharacteristic
539C4—44no—
540C4—44no—
541C4—42no—
542C4—42no—
543C4—44no—
544C4—82no—
545C4—82no—
546C4—82no—
547C2—82no—
548C2C5×#233211yescharacteristic
549C2C5×#233512yes—
550C2C5×#237611yescharacteristic
551C2C5×#237812yes—
552C2C5×#238011yescharacteristic
553C2C5×#282712yes—
554C2C5×#282912yes—
555C2C5×#283712yes—
556C2C5×#283812yes—
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. C5×#1443C2semidirect
3. C5×#1441C2semidirect
4. C5×#1441C2semidirect
9. C5×#1436C2semidirect
19. C5×#399C4semidirect
32. #14646C5direct (N × H)
79. #1443C2×C5semidirect
80. #1441C2×C5semidirect
81. #1441C2×C5semidirect
86. #1436C2×C5semidirect
167. #399C4×C5semidirect
508. C5#14646direct (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
C5×#14432
C5×#14412
C5×#14402
C5×#14392
C5×#14372
C5×#14362
#146465