Finite Group Databasebeta

← C5×#24078 #11946798

Subgroups — C5×#24078 #11946798

Order 1280.

1038 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3493C211yesmaximal, characteristic
2C5×#3093C212yesmaximal, complemented
3C5×#2285C211yesmaximal, characteristic, complemented
4C5×#2061C211yesmaximal, characteristic, complemented
5C5×#2060C211yesmaximal, characteristic, complemented
6C5×#2040C211yesmaximal, characteristic, complemented
7C5×#2039C211yesmaximal, characteristic, complemented
8C5×#1896C212yesmaximal, complemented
9C5×#1860C212yesmaximal, complemented
10C5×#1859C212yesmaximal, complemented
11C5×#1822C211yesmaximal, characteristic, complemented
12C5×#556—22no—
13C5×#555—22no—
14C5×#553—22no—
15C5×#552—22no—
16C5×#544C2211yescharacteristic
17C5×#538—22no—
18C5×#537C2211yescharacteristic
19C5×#529—22no—
20C5×#525C2212yes—
21C5×#520C2212yes—
22C2×C5×#117C2211yescharacteristic
23C2×C5×#117C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
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×#384C2211yescharacteristic
37C5×#384C2211yescharacteristic
38C5×#382C2211yescharacteristic
39C5×#382C2211yescharacteristic
40C5×#380—22no—
41C4×C5×C4⋊C4—22no—
42C5×#343C2211yescharacteristic
43C5×#343C2211yescharacteristic
44C5×#343C2212yes—
45C5×#339C2212yes—
46C5×#339C2212yes—
47#24078C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41C2312yes—
49C23×C4×C5—21no—
50C23×C4×C5C2311yescharacteristic
51C2×C5×M16C2312yes—
52C2×C5×M16C2312yes—
53C5×C4⋊Q8—22no—
54C5×#126—24no—
55C5×#126—24no—
56C5×#125—22no—
57C5×#125—22no—
58C5×#124—22no—
59C5×#124—24no—
60C5×#123—24no—
61C5×#123—22no—
62C5×C22⋊Q8—22no—
63C5×C22⋊Q8—22no—
64C5×C22⋊Q8D412yes—
65C5×C22⋊Q8D412yes—
66C5×#121—24no—
67C5×#121—22no—
68C5×#121—22no—
69C5×#121D412yes—
70C5×#121D412yes—
71C5×#120—22no—
72C4×C5×Q8—22no—
73C4×C5×Q8—22no—
74C4×C5×D4—22no—
75C4×C5×D4—22no—
76C4×C5×D4—24no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C5×#117—24no—
80C5×#117—22no—
81C5×#117—22no—
82C5×#117—22no—
83C5×#117—22no—
84C5×#117—22no—
85C5×#117C2312yes—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4D412yes—
95C2×C42×C5—21no—
96C2×C42×C5—22no—
97C2×C42×C5—22no—
98C2×C42×C5—21no—
99C2×C42×C5D412yes—
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#3493C2×C511yescharacteristic
117#3093C2×C512yescomplemented
118#2285C2×C511yescharacteristic, complemented
119#2061C2×C511yescharacteristic, complemented
120#2060C2×C511yescharacteristic, complemented
121#2040C2×C511yescharacteristic, complemented
122#2039C2×C511yescharacteristic, complemented
123#1896C2×C512yescomplemented
124#1860C2×C512yescomplemented
125#1859C2×C512yescomplemented
126#1822C2×C511yescharacteristic, complemented
127C24×C5C2×D411yescharacteristic
128C5×#41—22no—
129C5×#41—22no—
130C5×#41—22no—
131C5×#41—22no—
132C2×C5×Q8—22no—
133C2×C5×Q8C2×D412yes—
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—22no—
137C2×C5×D4—22no—
138C2×C5×D4C2×D412yes—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—24no—
144C22×C4×C5—21no—
145C22×C4×C5—24no—
146C22×C4×C5—22no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—42no—
150C22×C4×C5—42no—
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D412yes—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D412yes—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2411yescharacteristic
157C5×M16—22no—
158C5×M16—22no—
159C5×M16—22no—
160C5×M16—22no—
161C2×C5×C8—22no—
162C2×C5×C8—22no—
163C5×C4⋊C4—24no—
164C5×C4⋊C4—24no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—44no—
174C5×C4⋊C4—44no—
175C5×C4⋊C4C2×D412yes—
176C5×C4⋊C4C2×D412yes—
177C5×C22⋊C4—24no—
178C5×C22⋊C4—24no—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—42no—
186C42×C5—24no—
187C42×C5—24no—
188C42×C5—22no—
189C42×C5—22no—
190C42×C5—22no—
191C42×C5—21no—
192C42×C5—21no—
193C42×C5—41no—
194C42×C5—41no—
195C42×C5#4112yes—
196C42×C5#4112yes—
197#556—22no—
198#555—22no—
199#553—22no—
200#552—22no—
201#544C22×C511yescharacteristic
202#538—22no—
203#537C22×C511yescharacteristic
204#529—22no—
205#525C22×C512yes—
206#520C22×C512yes—
207C2×#117C22×C511yescharacteristic
208C2×#117C22×C511yescharacteristic
209C22×C42C22×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#384C22×C511yescharacteristic
222#384C22×C511yescharacteristic
223#382C22×C511yescharacteristic
224#382C22×C511yescharacteristic
225#380—22no—
226C4×C4⋊C4—22no—
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#12012yes—
238C23×C5C22×D411yescharacteristic
239C5×Q8—22no—
240C5×Q8—22no—
241C5×Q8—82no—
242C5×D4—22no—
243C5×D4—22no—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—82no—
247C5×D4—82no—
248C5×D4—82no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—21no—
252C2×C4×C5—22no—
253C2×C4×C5—21no—
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—22no—
264C2×C4×C5—48no—
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—41no—
274C2×C4×C5—41no—
275C2×C4×C5—84no—
276C2×C4×C5#12011yescharacteristic
277C2×C4×C5#12011yescharacteristic
278C2×C4×C5C22×D412yes—
279C2×C4×C5C2×#4111yescharacteristic
280C2×C4×C5C2×#4111yescharacteristic
281C2×C4×C52−1+412yes—
282C5×C8—42no—
283C5×C8—42no—
284C2×#41C23×C512yes—
285C23×C4—21no—
286C23×C4C23×C511yescharacteristic
287C2×M16C23×C512yes—
288C2×M16C23×C512yes—
289C4⋊Q8—22no—
290#126—24no—
291#126—24no—
292#125—22no—
293#125—22no—
294#124—22no—
295#124—24no—
296#123—24no—
297#123—22no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8C5×D412yes—
301C22⋊Q8C5×D412yes—
302#121—24no—
303#121—22no—
304#121—22no—
305#121C5×D412yes—
306#121C5×D412yes—
307#120—22no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—22no—
315#117—24no—
316#117—22no—
317#117—22no—
318#117—22no—
319#117—22no—
320#117—22no—
321#117C23×C512yes—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4C23×C511yescharacteristic
326C2×C4⋊C4C23×C511yescharacteristic
327C2×C4⋊C4C23×C511yescharacteristic
328C2×C4⋊C4C23×C511yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4C5×D412yes—
331C2×C42—21no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—21no—
335C2×C42C5×D412yes—
336C2×C42C23×C511yescharacteristic
337C2×C42C23×C511yescharacteristic
338#107—22no—
339#107—22no—
340#106—22no—
341#106—22no—
342#104—24no—
343#104—24no—
344#103—22no—
345#103—22no—
346#102—22no—
347#102—22no—
348C22⋊C8—22no—
349C22⋊C8—22no—
350#95—22no—
351#95—22no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—22no—
355C22×C5—22no—
356C22×C5—22no—
357C22×C5—42no—
358C22×C5—42no—
359C22×C5—42no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5C2×#12011yescharacteristic
363C22×C5#52511yescharacteristic
364C22×C5#53611yescharacteristic
365C4×C5—24no—
366C4×C5—21no—
367C4×C5—21no—
368C4×C5—42no—
369C4×C5—42no—
370C4×C5—42no—
371C4×C5—42no—
372C4×C5—42no—
373C4×C5—42no—
374C4×C5—81no—
375C4×C5—81no—
376C4×C5#54712yes—
377C4×C5#54712yes—
378C24C2×C5×D411yescharacteristic
379#41—22no—
380#41—22no—
381#41—22no—
382#41—22no—
383C2×Q8—22no—
384C2×Q8C2×C5×D412yes—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4C2×C5×D412yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4C2×C5×D411yescharacteristic
403C22×C4C2×C5×D412yes—
404C22×C4C2×C5×D412yes—
405C22×C4C2×C5×D412yes—
406C22×C4C2×C5×D412yes—
407C22×C4C24×C511yescharacteristic
408M16—22no—
409M16—22no—
410M16—22no—
411M16—22no—
412C2×C8—22no—
413C2×C8—22no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—44no—
425C4⋊C4—44no—
426C4⋊C4C2×C5×D412yes—
427C4⋊C4C2×C5×D412yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—42no—
437C42—24no—
438C42—24no—
439C42—22no—
440C42—22no—
441C42—22no—
442C42—21no—
443C42—21no—
444C42—41no—
445C42—41no—
446C42C5×#4112yes—
447C42C5×#4112yes—
448C2×C5—21no—
449C2×C5—21no—
450C2×C5—42no—
451C2×C5—82no—
452C2×C5#240611yescharacteristic
453C2×C5#301811yescharacteristic
454C2×C5#301811yescharacteristic
455C23—21no—
456C23—21no—
457C23—22no—
458C23—41no—
459C23—41no—
460C23C5×#12012yes—
461C23C22×C5×D411yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—82no—
465D4—22no—
466D4—22no—
467D4—42no—
468D4—42no—
469D4—82no—
470D4—82no—
471D4—82no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
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—48no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—84no—
499C2×C4C5×#12011yescharacteristic
500C2×C4C5×#12011yescharacteristic
501C2×C4C22×C5×D412yes—
502C2×C4C2×C5×#4111yescharacteristic
503C2×C4C2×C5×#4111yescharacteristic
504C2×C4C5×2−1+412yes—
505C8—42no—
506C8—42no—
507C5#2407811yescharacteristic, direct product factor, Sylow
508C22—21no—
509C22—21no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22C2×C5×#12011yescharacteristic
519C22C5×#52511yescharacteristic
520C22C5×#53611yescharacteristic
521C4—24no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—81no—
531C4—81no—
532C4C5×#54712yes—
533C4C5×#54712yes—
534C2—21no—
535C2—21no—
536C2—42no—
537C2—82no—
538C2C5×#240611yescharacteristic
539C2C5×#301811yescharacteristic
540C2C5×#301811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3493C2
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×#2285C2semidirect
4. C5×#2061C2semidirect
5. C5×#2060C2semidirect
6. C5×#2040C2semidirect
7. C5×#2039C2semidirect
8. C5×#1896C2semidirect
9. C5×#1860C2semidirect
10. C5×#1859C2semidirect
11. C5×#1822C2semidirect
47. #24078C5direct (N × H)
117. #3093C2×C5semidirect
118. #2285C2×C5semidirect
119. #2061C2×C5semidirect
120. #2060C2×C5semidirect
121. #2040C2×C5semidirect
122. #2039C2×C5semidirect
123. #1896C2×C5semidirect
124. #1860C2×C5semidirect
125. #1859C2×C5semidirect
126. #1822C2×C5semidirect
507. C5#24078direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34932
C5×#30932
C5×#22852
C5×#20612
C5×#20602
C5×#20402
C5×#20392
C5×#18962
C5×#18602
C5×#18592
C5×#18222
#240785