Finite Group Databasebeta

← C5×#14649 #11937369

Subgroups — C5×#14649 #11937369

Order 1280.

1290 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#393C211yesmaximal, characteristic
2C5×#1446C212yesmaximal, complemented
3C5×#1443C212yesmaximal, complemented
4C5×#1442C212yesmaximal, complemented
5C5×#1440C212yesmaximal
6C5×#1440C211yesmaximal, characteristic
7C5×#1439C212yesmaximal
8C5×#1437C211yesmaximal, characteristic
9C5×#1436C212yesmaximal, complemented
10C23×C5×Q8C2211yescharacteristic
11C22×C5×C4⋊C4C2212yes—
12C22×C5×C22⋊C4C2212yes—
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2212yes—
17C22×C42×C5C2211yescharacteristic
18C5×#393C418yescomplemented
19C2×C5×#95C2212yes—
20C2×C5×#95C2212yes—
21C2×C5×#95C2212yes—
22C2×C5×#95C2212yes—
23C2×C5×#95C2212yes—
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2212yes—
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2211yescharacteristic
32#14649C511yesmaximal, characteristic, direct product factor, Sylow
33C25×C5C2311yescharacteristic
34C22×C5×Q8—42no—
35C22×C5×Q8—41no—
36C22×C5×Q8—42no—
37C22×C5×Q8—41no—
38C22×C5×Q8C2×C414yes—
39C23×C4×C5C2312yes—
40C23×C4×C5C2312yes—
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2312yes—
47C2×C5×C4⋊C4—24no—
48C2×C5×C4⋊C4—42no—
49C2×C5×C4⋊C4—42no—
50C2×C5×C22⋊C4—24no—
51C2×C5×C22⋊C4—41no—
52C2×C5×C22⋊C4—42no—
53C2×C5×C22⋊C4—41no—
54C2×C5×C22⋊C4—42no—
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⋊C4C2×C414yes—
62C2×C5×C22⋊C4C2×C418yes—
63C2×C42×C5—42no—
64C2×C42×C5—41no—
65C5×#95—24no—
66C5×#95—42no—
67C5×#95—42no—
68C5×#95—42no—
69C5×#95—41no—
70C5×#95—42no—
71C5×#95—42no—
72C5×#95—42no—
73C5×#95—42no—
74C5×#95—42no—
75C5×#95—42no—
76C5×#95C2×C418yes—
77C5×#95C2×C414yes—
78C2×#393C2×C511yescharacteristic
79#1446C2×C512yescomplemented
80#1443C2×C512yescomplemented
81#1442C2×C512yescomplemented
82#1440C2×C512yes—
83#1440C2×C511yescharacteristic
84#1439C2×C512yes—
85#1437C2×C511yescharacteristic
86#1436C2×C512yescomplemented
87C24×C5—22no—
88C24×C5—22no—
89C24×C5—22no—
90C24×C5—21no—
91C24×C5—21no—
92C24×C5—22no—
93C24×C5—22no—
94C24×C5—22no—
95C24×C5C22×C412yes—
96C24×C5C2411yescharacteristic
97C2×C5×Q8—44no—
98C2×C5×Q8—48no—
99C2×C5×Q8—48no—
100C2×C5×Q8—44no—
101C2×C5×Q8—44no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—21no—
105C22×C4×C5—22no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—21no—
112C22×C4×C5—22no—
113C22×C4×C5—21no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
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×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5C22×C412yes—
150C22×C4×C5C22×C414yes—
151C22×C4×C5C22×C414yes—
152C22×C4×C5C22×C412yes—
153C22×C4×C5#4114yes—
154C5×C4⋊C4—48no—
155C5×C22⋊C4—48no—
156C5×C22⋊C4—44no—
157C5×C22⋊C4—48no—
158C5×C22⋊C4—44no—
159C5×C22⋊C4—44no—
160C42×C5—44no—
161C23×Q8C22×C511yescharacteristic
162C22×C4⋊C4C22×C512yes—
163C22×C22⋊C4C22×C512yes—
164C22×C22⋊C4C22×C511yescharacteristic
165C22×C22⋊C4C22×C511yescharacteristic
166C22×C22⋊C4C22×C511yescharacteristic
167C22×C22⋊C4C22×C512yes—
168C22×C42C22×C511yescharacteristic
169#393C4×C518yescomplemented
170C2×#95C22×C512yes—
171C2×#95C22×C512yes—
172C2×#95C22×C512yes—
173C2×#95C22×C512yes—
174C2×#95C22×C512yes—
175C2×#95C22×C511yescharacteristic
176C2×#95C22×C512yes—
177C2×#95C22×C512yes—
178C2×#95C22×C512yes—
179C2×#95C22×C512yes—
180C2×#95C22×C512yes—
181C2×#95C22×C512yes—
182C2×#95C22×C511yescharacteristic
183C23×C5—22no—
184C23×C5—22no—
185C23×C5—24no—
186C23×C5—22no—
187C23×C5—24no—
188C23×C5—42no—
189C23×C5—42no—
190C23×C5—42no—
191C23×C5—42no—
192C23×C5—42no—
193C23×C5—42no—
194C23×C5—42no—
195C23×C5—41no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5—42no—
199C23×C5—42no—
200C23×C5—42no—
201C23×C5—42no—
202C23×C5—42no—
203C23×C5—41no—
204C23×C5C23×C411yescharacteristic
205C23×C5C2×#4112yes—
206C23×C5H(5,𝔽2)12yes—
207C23×C5H(5,𝔽2)12yes—
208C23×C5H(5,𝔽2)11yescharacteristic
209C23×C5H(5,𝔽2)11yescharacteristic
210C23×C5H(5,𝔽2)12yes—
211C23×C52−1+412yes—
212C23×C52−1+412yes—
213C5×Q8—416no—
214C2×C4×C5—24no—
215C2×C4×C5—24no—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—24no—
219C2×C4×C5—24no—
220C2×C4×C5—24no—
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—42no—
228C2×C4×C5—42no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—41no—
237C2×C4×C5—42no—
238C2×C4×C5—41no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
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—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—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C25C23×C511yescharacteristic
267C22×Q8—42no—
268C22×Q8—41no—
269C22×Q8—42no—
270C22×Q8—41no—
271C22×Q8C2×C4×C514yes—
272C23×C4C23×C512yes—
273C23×C4C23×C512yes—
274C23×C4C23×C512yes—
275C23×C4C23×C512yes—
276C23×C4C23×C511yescharacteristic
277C23×C4C23×C512yes—
278C23×C4C23×C511yescharacteristic
279C23×C4C23×C512yes—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—41no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—41no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—41no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4C2×C4×C514yes—
295C2×C22⋊C4C2×C4×C518yes—
296C2×C42—41no—
297C2×C42—42no—
298#95—24no—
299#95—42no—
300#95—42no—
301#95—42no—
302#95—41no—
303#95—42no—
304#95—42no—
305#95—42no—
306#95—42no—
307#95—42no—
308#95—42no—
309#95C2×C4×C518yes—
310#95C2×C4×C514yes—
311C22×C5—42no—
312C22×C5—44no—
313C22×C5—42no—
314C22×C5—44no—
315C22×C5—42no—
316C22×C5—82no—
317C22×C5—82no—
318C22×C5—82no—
319C22×C5—82no—
320C22×C5C4×#4111yescharacteristic
321C22×C5#51811yescharacteristic
322C22×C5#51812yes—
323C22×C5#51911yescharacteristic
324C22×C5#52012yes—
325C22×C5#53812yes—
326C22×C5#53812yes—
327C22×C5#53912yes—
328C22×C5#54212yes—
329C22×C5#54212yes—
330C22×C5#54212yes—
331C22×C5#56012yes—
332C22×C5#56011yescharacteristic
333C22×C5H(3,𝔽4)11yescharacteristic
334C22×C5H(3,𝔽4)11yescharacteristic
335C22×C5#56212yes—
336C22×C5#56212yes—
337C22×C5#56212yes—
338C22×C5#56312yes—
339C22×C5#56312yes—
340C22×C5#56311yescharacteristic
341C4×C5—44no—
342C4×C5—44no—
343C4×C5—42no—
344C4×C5—44no—
345C4×C5—42no—
346C4×C5—82no—
347C4×C5—82no—
348C4×C5—82no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24C22×C4×C512yes—
358C24C24×C511yescharacteristic
359C2×Q8—44no—
360C2×Q8—48no—
361C2×Q8—48no—
362C2×Q8—44no—
363C2×Q8—44no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
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×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×C4C22×C4×C514yes—
412C22×C4C22×C4×C512yes—
413C22×C4C22×C4×C512yes—
414C22×C4C22×C4×C514yes—
415C22×C4C5×#4114yes—
416C4⋊C4—48no—
417C22⋊C4—44no—
418C22⋊C4—48no—
419C22⋊C4—48no—
420C22⋊C4—44no—
421C22⋊C4—44no—
422C42—44no—
423C2×C5—82no—
424C2×C5#233211yescharacteristic
425C2×C5#233712yes—
426C2×C5#237511yescharacteristic
427C2×C5#237812yes—
428C2×C5#237911yescharacteristic
429C2×C5#282412yes—
430C2×C5#283012yes—
431C2×C5#283212yes—
432C2×C5#283812yes—
433C23—22no—
434C23—22no—
435C23—24no—
436C23—22no—
437C23—24no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—41no—
454C23C23×C4×C511yescharacteristic
455C23C2×C5×#4112yes—
456C23C5×H(5,𝔽2)12yes—
457C23C5×H(5,𝔽2)12yes—
458C23C5×H(5,𝔽2)11yescharacteristic
459C23C5×H(5,𝔽2)11yescharacteristic
460C23C5×H(5,𝔽2)12yes—
461C23C5×2−1+412yes—
462C23C5×2−1+412yes—
463Q8—416no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
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—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C5#1464911yescharacteristic, direct product factor, Sylow
517C22—42no—
518C22—44no—
519C22—42no—
520C22—44no—
521C22—42no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22C4×C5×#4111yescharacteristic
527C22C5×#51811yescharacteristic
528C22C5×#51812yes—
529C22C5×#51911yescharacteristic
530C22C5×#52012yes—
531C22C5×#53812yes—
532C22C5×#53812yes—
533C22C5×#53912yes—
534C22C5×#54212yes—
535C22C5×#54212yes—
536C22C5×#54212yes—
537C22C5×#56012yes—
538C22C5×#56011yescharacteristic
539C22C5×H(3,𝔽4)11yescharacteristic
540C22C5×H(3,𝔽4)11yescharacteristic
541C22C5×#56212yes—
542C22C5×#56212yes—
543C22C5×#56212yes—
544C22C5×#56312yes—
545C22C5×#56312yes—
546C22C5×#56311yescharacteristic
547C4—44no—
548C4—44no—
549C4—42no—
550C4—44no—
551C4—42no—
552C4—82no—
553C4—82no—
554C4—82no—
555C2—82no—
556C2C5×#233211yescharacteristic
557C2C5×#233712yes—
558C2C5×#237511yescharacteristic
559C2C5×#237812yes—
560C2C5×#237911yescharacteristic
561C2C5×#282412yes—
562C2C5×#283012yes—
563C2C5×#283212yes—
564C2C5×#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×#1446C2semidirect
3. C5×#1443C2semidirect
4. C5×#1442C2semidirect
9. C5×#1436C2semidirect
18. C5×#393C4semidirect
32. #14649C5direct (N × H)
79. #1446C2×C5semidirect
80. #1443C2×C5semidirect
81. #1442C2×C5semidirect
86. #1436C2×C5semidirect
169. #393C4×C5semidirect
516. C5#14649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3932
C5×#14462
C5×#14432
C5×#14422
C5×#14402
C5×#14392
C5×#14372
C5×#14362
#146495