Finite Group Databasebeta

← C5×#24079 #11946799

Subgroups — C5×#24079 #11946799

Order 1280.

1030 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3492C211yesmaximal, characteristic
2C5×#3093C212yesmaximal, complemented
3C5×#2317C211yesmaximal, characteristic, complemented
4C5×#2061C211yesmaximal, characteristic, complemented
5C5×#2060C211yesmaximal, characteristic, complemented
6C5×#2040C211yesmaximal, characteristic, complemented
7C5×#2039C211yesmaximal, characteristic, complemented
8C5×#1897C212yesmaximal, complemented
9C5×#1860C212yesmaximal, complemented
10C5×#1859C212yesmaximal, complemented
11C5×#1821C211yesmaximal, characteristic, complemented
12C5×#554—22no—
13C5×#553—22no—
14C5×#552—22no—
15C5×#547—22no—
16C5×#544C2211yescharacteristic
17C5×#539—22no—
18C5×#537C2211yescharacteristic
19C5×#525—22no—
20C5×#525C2212yes—
21C5×#520C2212yes—
22C2×C5×#117C2211yescharacteristic
23C2×C5×#117C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C5×#485—22no—
26C5×#485—22no—
27C5×#482—22no—
28C5×#482—22no—
29C5×#428C2212yes—
30C5×#428C2212yes—
31C2×C5×#104C2212yes—
32C2×C5×#104C2212yes—
33C5×#417C2212yes—
34C5×#417C2212yes—
35C5×#407C2212yes—
36C5×#389—22no—
37C5×#385—22no—
38C5×#384C2211yescharacteristic
39C5×#384C2211yescharacteristic
40C5×#382C2211yescharacteristic
41C5×#382C2211yescharacteristic
42C5×#343C2211yescharacteristic
43C5×#343C2211yescharacteristic
44C5×#343C2212yes—
45C5×#339C2212yes—
46C5×#339C2212yes—
47#24079C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—22no—
49C2×C5×#41C2312yes—
50C23×C4×C5D412yes—
51C23×C4×C5C2311yescharacteristic
52C2×C5×M16C2312yes—
53C2×C5×M16C2312yes—
54C5×C4⋊Q8—22no—
55C5×#126—24no—
56C5×#125—24no—
57C5×#125—22no—
58C5×#123—24no—
59C5×#123—24no—
60C5×#123—22no—
61C5×C22⋊Q8—22no—
62C5×C22⋊Q8—24no—
63C5×C22⋊Q8—22no—
64C5×C22⋊Q8—22no—
65C5×C22⋊Q8D412yes—
66C5×C22⋊Q8D412yes—
67C5×#121—22no—
68C5×#121—22no—
69C5×#121—22no—
70C5×#121D412yes—
71C5×#121D412yes—
72C5×#120—22no—
73C4×C5×Q8—22no—
74C4×C5×D4—24no—
75C4×C5×D4—22no—
76C4×C5×D4—24no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C5×#117—22no—
80C5×#117—22no—
81C5×#117—22no—
82C5×#117—22no—
83C5×#117—22no—
84C5×#117—22no—
85C5×#117C2312yes—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4D412yes—
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C42×C5—21no—
100C2×C42×C5C2311yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C5×#107—22no—
103C5×#107—22no—
104C5×#106—22no—
105C5×#106—22no—
106C5×#104—24no—
107C5×#104—24no—
108C5×#103—22no—
109C5×#103—22no—
110C5×#102—22no—
111C5×#102—22no—
112C5×C22⋊C8—22no—
113C5×C22⋊C8—22no—
114C5×#95—22no—
115C5×#95—22no—
116#3492C2×C511yescharacteristic
117#3093C2×C512yescomplemented
118#2317C2×C511yescharacteristic, complemented
119#2061C2×C511yescharacteristic, complemented
120#2060C2×C511yescharacteristic, complemented
121#2040C2×C511yescharacteristic, complemented
122#2039C2×C511yescharacteristic, complemented
123#1897C2×C512yescomplemented
124#1860C2×C512yescomplemented
125#1859C2×C512yescomplemented
126#1821C2×C511yescharacteristic, complemented
127C24×C5C2×D411yescharacteristic
128C5×#41—22no—
129C5×#41—22no—
130C5×#41—22no—
131C5×#41—22no—
132C5×#41—84no—
133C2×C5×Q8—22no—
134C2×C5×Q8C2×D412yes—
135C2×C5×D4—22no—
136C2×C5×D4—22no—
137C2×C5×D4—22no—
138C2×C5×D4—22no—
139C2×C5×D4C2×D412yes—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—24no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—82no—
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D412yes—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2411yescharacteristic
158C5×M16—22no—
159C5×M16—22no—
160C5×M16—22no—
161C5×M16—22no—
162C2×C5×C8—22no—
163C2×C5×C8—22no—
164C5×C4⋊C4—24no—
165C5×C4⋊C4—24no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—24no—
169C5×C4⋊C4—24no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—82no—
177C5×C4⋊C4—82no—
178C5×C4⋊C4C2×D412yes—
179C5×C4⋊C4C2×D412yes—
180C5×C22⋊C4—24no—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—41no—
189C5×C22⋊C4—41no—
190C42×C5—24no—
191C42×C5—22no—
192C42×C5—21no—
193C42×C5—21no—
194C42×C5—42no—
195C42×C5#4112yescomplemented
196C42×C5#4112yescomplemented
197#554—22no—
198#553—22no—
199#552—22no—
200#547—22no—
201#544C22×C511yescharacteristic
202#539—22no—
203#537C22×C511yescharacteristic
204#525—22no—
205#525C22×C512yes—
206#520C22×C512yes—
207C2×#117C22×C511yescharacteristic
208C2×#117C22×C511yescharacteristic
209C22×C4⋊C4C22×C511yescharacteristic
210#485—22no—
211#485—22no—
212#482—22no—
213#482—22no—
214#428C22×C512yes—
215#428C22×C512yes—
216C2×#104C22×C512yes—
217C2×#104C22×C512yes—
218#417C22×C512yes—
219#417C22×C512yes—
220#407C22×C512yes—
221#389—22no—
222#385—22no—
223#384C22×C511yescharacteristic
224#384C22×C511yescharacteristic
225#382C22×C511yescharacteristic
226#382C22×C511yescharacteristic
227#343C22×C511yescharacteristic
228#343C22×C511yescharacteristic
229#343C22×C512yes—
230#339C22×C512yes—
231#339C22×C512yes—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5—22no—
235C23×C5—41no—
236C23×C5—41no—
237C23×C5#12011yescharacteristic
238C23×C5#12011yescharacteristic
239C23×C5C22×D411yescharacteristic
240C5×Q8—22no—
241C5×Q8—22no—
242C5×Q8—82no—
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—44no—
246C5×D4—44no—
247C5×D4—42no—
248C5×D4—42no—
249C5×D4—82no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—44no—
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—41no—
275C2×C4×C5—41no—
276C2×C4×C5—82no—
277C2×C4×C5—84no—
278C2×C4×C5#12012yes—
279C2×C4×C5C22×D412yes—
280C2×C4×C5C2×#4111yescharacteristic
281C2×C4×C5C2×#4111yescharacteristic
282C2×C4×C52−1+412yes—
283C5×C8—42no—
284C5×C8—42no—
285C2×#41—22no—
286C2×#41C23×C512yes—
287C23×C4C5×D412yes—
288C23×C4C23×C511yescharacteristic
289C2×M16C23×C512yes—
290C2×M16C23×C512yes—
291C4⋊Q8—22no—
292#126—24no—
293#125—24no—
294#125—22no—
295#123—24no—
296#123—24no—
297#123—22no—
298C22⋊Q8—22no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302C22⋊Q8C5×D412yes—
303C22⋊Q8C5×D412yes—
304#121—22no—
305#121—22no—
306#121—22no—
307#121C5×D412yes—
308#121C5×D412yes—
309#120—22no—
310C4×Q8—22no—
311C4×D4—24no—
312C4×D4—22no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4—22no—
316#117—22no—
317#117—22no—
318#117—22no—
319#117—22no—
320#117—22no—
321#117—22no—
322#117C23×C512yes—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4C5×D412yes—
330C2×C4⋊C4C23×C511yescharacteristic
331C2×C4⋊C4C23×C511yescharacteristic
332C2×C4⋊C4C23×C511yescharacteristic
333C2×C4⋊C4C23×C511yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42—21no—
337C2×C42C23×C511yescharacteristic
338C2×C42C23×C511yescharacteristic
339#107—22no—
340#107—22no—
341#106—22no—
342#106—22no—
343#104—24no—
344#104—24no—
345#103—22no—
346#103—22no—
347#102—22no—
348#102—22no—
349C22⋊C8—22no—
350C22⋊C8—22no—
351#95—22no—
352#95—22no—
353C22×C5—21no—
354C22×C5—21no—
355C22×C5—21no—
356C22×C5—21no—
357C22×C5—21no—
358C22×C5—21no—
359C22×C5—21no—
360C22×C5—21no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5C2×#12011yescharacteristic
367C22×C5#52511yescharacteristic
368C22×C5#53611yescharacteristic
369C4×C5—22no—
370C4×C5—42no—
371C4×C5—42no—
372C4×C5—42no—
373C4×C5—42no—
374C4×C5—42no—
375C4×C5—42no—
376C4×C5—42no—
377C4×C5—81no—
378C4×C5—81no—
379C4×C5#54712yes—
380C4×C5#54712yes—
381C24C2×C5×D411yescharacteristic
382#41—22no—
383#41—22no—
384#41—22no—
385#41—22no—
386#41—84no—
387C2×Q8—22no—
388C2×Q8C2×C5×D412yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4C2×C5×D412yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—82no—
406C22×C4C2×C5×D411yescharacteristic
407C22×C4C2×C5×D412yes—
408C22×C4C2×C5×D412yes—
409C22×C4C2×C5×D412yes—
410C22×C4C2×C5×D412yes—
411C22×C4C24×C511yescharacteristic
412M16—22no—
413M16—22no—
414M16—22no—
415M16—22no—
416C2×C8—22no—
417C2×C8—22no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—82no—
431C4⋊C4—82no—
432C4⋊C4C2×C5×D412yes—
433C4⋊C4C2×C5×D412yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C42—24no—
445C42—22no—
446C42—21no—
447C42—21no—
448C42—42no—
449C42C5×#4112yescomplemented
450C42C5×#4112yescomplemented
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—41no—
454C2×C5—41no—
455C2×C5—82no—
456C2×C5#240611yescharacteristic
457C2×C5#301911yescharacteristic
458C2×C5#302011yescharacteristic
459C23—21no—
460C23—21no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23C5×#12011yescharacteristic
465C23C5×#12011yescharacteristic
466C23C22×C5×D411yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—82no—
470D4—22no—
471D4—22no—
472D4—44no—
473D4—44no—
474D4—42no—
475D4—42no—
476D4—82no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—44no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—82no—
504C2×C4—84no—
505C2×C4C5×#12012yes—
506C2×C4C22×C5×D412yes—
507C2×C4C2×C5×#4111yescharacteristic
508C2×C4C2×C5×#4111yescharacteristic
509C2×C4C5×2−1+412yes—
510C8—42no—
511C8—42no—
512C5#2407911yescharacteristic, direct product factor, Sylow
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22C2×C5×#12011yescharacteristic
527C22C5×#52511yescharacteristic
528C22C5×#53611yescharacteristic
529C4—22no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—81no—
538C4—81no—
539C4C5×#54712yes—
540C4C5×#54712yes—
541C2—21no—
542C2—21no—
543C2—41no—
544C2—41no—
545C2—82no—
546C2C5×#240611yescharacteristic
547C2C5×#301911yescharacteristic
548C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3492C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3093C2semidirect
3. C5×#2317C2semidirect
4. C5×#2061C2semidirect
5. C5×#2060C2semidirect
6. C5×#2040C2semidirect
7. C5×#2039C2semidirect
8. C5×#1897C2semidirect
9. C5×#1860C2semidirect
10. C5×#1859C2semidirect
11. C5×#1821C2semidirect
47. #24079C5direct (N × H)
117. #3093C2×C5semidirect
118. #2317C2×C5semidirect
119. #2061C2×C5semidirect
120. #2060C2×C5semidirect
121. #2040C2×C5semidirect
122. #2039C2×C5semidirect
123. #1897C2×C5semidirect
124. #1860C2×C5semidirect
125. #1859C2×C5semidirect
126. #1821C2×C5semidirect
195. C42×C5#41semidirect
196. C42×C5#41semidirect
449. C42C5×#41semidirect
450. C42C5×#41semidirect
512. C5#24079direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34922
C5×#30932
C5×#23172
C5×#20612
C5×#20602
C5×#20402
C5×#20392
C5×#18972
C5×#18602
C5×#18592
C5×#18212
#240795