Finite Group Databasebeta

← C5×#24097 #11946817

Subgroups — C5×#24097 #11946817

Order 1280.

1138 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic
2C2×C5×#483C211yesmaximal, characteristic, complemented
3C22×C5×#106C211yesmaximal, characteristic, complemented
4C5×#2486C211yesmaximal, characteristic
5C5×#2058C212yesmaximal, complemented
6C5×#2035C212yesmaximal, complemented
7C5×#1892C211yesmaximal, characteristic, complemented
8C5×#1869C211yesmaximal, characteristic
9C5×#1865C212yesmaximal, complemented
10C5×#1853C212yesmaximal, complemented
11C5×#1824C211yesmaximal, characteristic, complemented
12C23×C5×C8C2211yescharacteristic
13C5×#554—24no—
14C5×#554—24no—
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C5×#125—21no—
17C2×C5×#123—21no—
18C2×C5×C22⋊Q8—21no—
19C2×C5×C22⋊Q8—21no—
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×D4—21no—
24C2×C4×C5×D4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C5×#483—24no—
29C2×C5×#106—24no—
30C2×C5×#106C2212yes—
31C2×C5×#106C2212yes—
32C2×C5×#106C2212yes—
33C2×C5×#103C2212yes—
34C2×C5×#103C2212yes—
35C2×C5×C22⋊C8C2212yes—
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#398—21no—
38C5×#397—21no—
39C5×#389C2212yes—
40C5×#381—21no—
41C5×#380C2212yes—
42C5×#380C2211yescharacteristic
43C5×#340C2212yes—
44C5×#340C2212yes—
45C5×#340C2212yes—
46C5×#336C2212yes—
47#24097C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C22×C5×Q8C2311yescharacteristic
50C22×C5×D4D411yescharacteristic
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C22×C5×C8—22no—
57C22×C5×C8—24no—
58C22×C5×C8C2312yes—
59C22×C5×C8C2312yes—
60C5×C4⋊Q8—22no—
61C5×C4⋊Q8—22no—
62C5×#125—28no—
63C5×#123—44no—
64C5×C22⋊Q8—28no—
65C5×C22⋊Q8—28no—
66C5×C22⋊Q8—22no—
67C5×C22⋊Q8—22no—
68C5×C22⋊Q8—22no—
69C5×C22⋊Q8D414yes—
70C4×C5×Q8—22no—
71C4×C5×Q8—22no—
72C4×C5×D4—28no—
73C4×C5×D4—22no—
74C4×C5×D4—22no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4D411yescharacteristic
89C2×C5×C4⋊C4D414yes—
90C2×C5×C4⋊C4C2312yes—
91C2×C5×C4⋊C4C2312yes—
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4D411yescharacteristic
100C2×C5×C22⋊C4D411yescharacteristic
101C2×C42×C5—21no—
102C2×C42×C5C2311yescharacteristic
103C5×#106—24no—
104C5×#106—24no—
105C5×#106—24no—
106C5×#103—24no—
107C5×#103—24no—
108C5×C22⋊C8—22no—
109C5×C22⋊C8—24no—
110C5×#95—22no—
111C5×#95—21no—
112C5×#95—22no—
113C2×#554C2×C511yescharacteristic
114C2×#483C2×C511yescharacteristic, complemented
115C22×#106C2×C511yescharacteristic, complemented
116#2486C2×C511yescharacteristic
117#2058C2×C512yescomplemented
118#2035C2×C512yescomplemented
119#1892C2×C511yescharacteristic, complemented
120#1869C2×C511yescharacteristic
121#1865C2×C512yescomplemented
122#1853C2×C512yescomplemented
123#1824C2×C511yescharacteristic, complemented
124C24×C5C2×D411yescharacteristic
125C24×C5C2×D411yescharacteristic
126C2×C5×Q8—24no—
127C2×C5×Q8—21no—
128C2×C5×Q8—22no—
129C2×C5×Q8—22no—
130C2×C5×Q8—82no—
131C2×C5×Q8C2×D412yes—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4SD1614yes—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—24no—
142C22×C4×C5—24no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—42no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5—82no—
153C22×C4×C5—82no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D412yes—
158C22×C4×C5C2×D412yes—
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2411yescharacteristic
161C2×C5×C8—28no—
162C2×C5×C8—22no—
163C2×C5×C8—22no—
164C2×C5×C8—22no—
165C2×C5×C8—22no—
166C2×C5×C8—22no—
167C2×C5×C8#4114yes—
168C5×C4⋊C4—24no—
169C5×C4⋊C4—24no—
170C5×C4⋊C4—24no—
171C5×C4⋊C4—24no—
172C5×C4⋊C4—24no—
173C5×C4⋊C4—24no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—42no—
183C5×C4⋊C4—44no—
184C5×C4⋊C4C2×D412yes—
185C5×C4⋊C4C2×D412yes—
186C5×C4⋊C4C2×D412yes—
187C5×C22⋊C4—24no—
188C5×C22⋊C4—24no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—42no—
192C5×C22⋊C4—44no—
193C42×C5—24no—
194C42×C5—21no—
195C42×C5—21no—
196C23×C8C22×C511yescharacteristic
197#554—24no—
198#554—24no—
199C2×C4⋊Q8C22×C511yescharacteristic
200C2×#125—21no—
201C2×#123—21no—
202C2×C22⋊Q8—21no—
203C2×C22⋊Q8—21no—
204C2×C22⋊Q8C22×C511yescharacteristic
205C2×C22⋊Q8C22×C511yescharacteristic
206C2×C4×Q8C22×C511yescharacteristic
207C2×C4×D4—21no—
208C2×C4×D4C22×C511yescharacteristic
209C22×C4⋊C4C22×C511yescharacteristic
210C22×C4⋊C4C22×C511yescharacteristic
211C22×C4⋊C4C22×C511yescharacteristic
212#483—24no—
213C2×#106—24no—
214C2×#106C22×C512yes—
215C2×#106C22×C512yes—
216C2×#106C22×C512yes—
217C2×#103C22×C512yes—
218C2×#103C22×C512yes—
219C2×C22⋊C8C22×C511yescharacteristic
220C2×C22⋊C8C22×C512yes—
221#398—21no—
222#397—21no—
223#389C22×C512yes—
224#381—21no—
225#380C22×C511yescharacteristic
226#380C22×C512yes—
227#340C22×C512yes—
228#340C22×C512yes—
229#340C22×C512yes—
230#336C22×C512yes—
231C23×C5—22no—
232C23×C5—22no—
233C23×C5—21no—
234C23×C5—22no—
235C23×C5—21no—
236C23×C5—22no—
237C23×C5#12012yes—
238C23×C5C2×SD1612yes—
239C23×C5C2×SD1612yes—
240C23×C5#13712yes—
241C23×C5C22×D411yescharacteristic
242C5×Q8—24no—
243C5×Q8—41no—
244C5×Q8—41no—
245C5×Q8—84no—
246C5×D4—28no—
247C2×C4×C5—21no—
248C2×C4×C5—22no—
249C2×C4×C5—21no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—24no—
253C2×C4×C5—22no—
254C2×C4×C5—21no—
255C2×C4×C5—22no—
256C2×C4×C5—21no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—84no—
275C2×C4×C5—84no—
276C2×C4×C5—84no—
277C2×C4×C5#12012yes—
278C2×C4×C5C2×SD1612yes—
279C2×C4×C5C22×D411yescharacteristic
280C2×C4×C5C22×D411yescharacteristic
281C2×C4×C5C2×#4112yes—
282C2×C4×C52−1+412yes—
283C5×C8—24no—
284C5×C8—42no—
285C22×Q8—21no—
286C22×Q8C23×C511yescharacteristic
287C22×D4C5×D411yescharacteristic
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4C23×C511yescharacteristic
292C23×C4C23×C511yescharacteristic
293C22×C8—22no—
294C22×C8—24no—
295C22×C8C23×C512yes—
296C22×C8C23×C512yes—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299#125—28no—
300#123—44no—
301C22⋊Q8—28no—
302C22⋊Q8—28no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—22no—
306C22⋊Q8C5×D414yes—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×D4—28no—
310C4×D4—22no—
311C4×D4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4C5×D411yescharacteristic
326C2×C4⋊C4C5×D414yes—
327C2×C4⋊C4C23×C512yes—
328C2×C4⋊C4C23×C512yes—
329C2×C4⋊C4C23×C511yescharacteristic
330C2×C4⋊C4C23×C511yescharacteristic
331C2×C4⋊C4C23×C511yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4C5×D411yescharacteristic
337C2×C22⋊C4C5×D411yescharacteristic
338C2×C42—21no—
339C2×C42C23×C511yescharacteristic
340#106—24no—
341#106—24no—
342#106—24no—
343#103—24no—
344#103—24no—
345C22⋊C8—22no—
346C22⋊C8—24no—
347#95—22no—
348#95—21no—
349#95—22no—
350C22×C5—24no—
351C22×C5—24no—
352C22×C5—22no—
353C22×C5—22no—
354C22×C5—24no—
355C22×C5—22no—
356C22×C5—42no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5#44814yes—
360C22×C5C2×#12011yescharacteristic
361C22×C5#54712yes—
362C22×C5C22×SD1611yescharacteristic
363C22×C5C2×#13711yescharacteristic
364C22×C5#57712yes—
365C4×C5—22no—
366C4×C5—22no—
367C4×C5—41no—
368C4×C5—42no—
369C4×C5—41no—
370C4×C5—42no—
371C4×C5—42no—
372C4×C5—42no—
373C4×C5—82no—
374C4×C5—82no—
375C4×C5#52511yescharacteristic
376C4×C5#53611yescharacteristic
377C4×C5#54712yes—
378C24C2×C5×D411yescharacteristic
379C24C2×C5×D411yescharacteristic
380C2×Q8—24no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—82no—
385C2×Q8C2×C5×D412yes—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4C5×SD1614yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4—82no—
408C22×C4C2×C5×D411yescharacteristic
409C22×C4C2×C5×D411yescharacteristic
410C22×C4C2×C5×D411yescharacteristic
411C22×C4C2×C5×D412yes—
412C22×C4C2×C5×D412yes—
413C22×C4C2×C5×D411yescharacteristic
414C22×C4C24×C511yescharacteristic
415C2×C8—28no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8C5×#4114yes—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—42no—
437C4⋊C4—44no—
438C4⋊C4C2×C5×D412yes—
439C4⋊C4C2×C5×D412yes—
440C4⋊C4C2×C5×D412yes—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—42no—
446C22⋊C4—44no—
447C42—24no—
448C42—21no—
449C42—21no—
450C2×C5—24no—
451C2×C5—42no—
452C2×C5#240611yescharacteristic
453C2×C5C2×#44811yescharacteristic
454C2×C5#300911yescharacteristic
455C2×C5#333512yes—
456C2×C5#334412yes—
457C23—22no—
458C23—22no—
459C23—21no—
460C23—22no—
461C23—21no—
462C23—22no—
463C23C5×#12012yes—
464C23C2×C5×SD1612yes—
465C23C2×C5×SD1612yes—
466C23C5×#13712yes—
467C23C22×C5×D411yescharacteristic
468Q8—24no—
469Q8—41no—
470Q8—41no—
471Q8—84no—
472D4—28no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—84no—
501C2×C4—84no—
502C2×C4—84no—
503C2×C4C5×#12012yes—
504C2×C4C2×C5×SD1612yes—
505C2×C4C22×C5×D411yescharacteristic
506C2×C4C22×C5×D411yescharacteristic
507C2×C4C2×C5×#4112yes—
508C2×C4C5×2−1+412yes—
509C8—24no—
510C8—42no—
511C5#2409711yescharacteristic, direct product factor, Sylow
512C22—22no—
513C22—24no—
514C22—24no—
515C22—22no—
516C22—22no—
517C22—24no—
518C22—41no—
519C22—42no—
520C22—41no—
521C22C5×#44814yes—
522C22C2×C5×#12011yescharacteristic
523C22C5×#54712yes—
524C22C22×C5×SD1611yescharacteristic
525C22C2×C5×#13711yescharacteristic
526C22C5×#57712yes—
527C4—22no—
528C4—22no—
529C4—41no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—41no—
534C4—42no—
535C4—82no—
536C4—82no—
537C4C5×#52511yescharacteristic
538C4C5×#53611yescharacteristic
539C4C5×#54712yes—
540C2—24no—
541C2—42no—
542C2C5×#240611yescharacteristic
543C2C2×C5×#44811yescharacteristic
544C2C5×#300911yescharacteristic
545C2C5×#333512yes—
546C2C5×#334412yes—
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#483C2semidirect
3. C22×C5×#106C2semidirect
5. C5×#2058C2semidirect
6. C5×#2035C2semidirect
7. C5×#1892C2semidirect
9. C5×#1865C2semidirect
10. C5×#1853C2semidirect
11. C5×#1824C2semidirect
47. #24097C5direct (N × H)
114. C2×#483C2×C5semidirect
115. C22×#106C2×C5semidirect
117. #2058C2×C5semidirect
118. #2035C2×C5semidirect
119. #1892C2×C5semidirect
121. #1865C2×C5semidirect
122. #1853C2×C5semidirect
123. #1824C2×C5semidirect
511. C5#24097direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×C5×#4832
C22×C5×#1062
C5×#24862
C5×#20582
C5×#20352
C5×#18922
C5×#18692
C5×#18652
C5×#18532
C5×#18242
#240975