Finite Group Databasebeta

← C5×#29707 #11952427

Subgroups — C5×#29707 #11952427

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3460C211yesmaximal, characteristic
2C5×#3080C212yesmaximal, complemented
3C5×#2566C211yesmaximal, characteristic, complemented
4C5×#2061C211yesmaximal, characteristic, complemented
5C5×#2060C211yesmaximal, characteristic, complemented
6C5×#2040C211yesmaximal, characteristic, complemented
7C5×#2039C211yesmaximal, characteristic, complemented
8C5×#2037C212yesmaximal, complemented
9C5×#2037C212yesmaximal, complemented
10C5×#1806C212yesmaximal, complemented
11C5×#1800C211yesmaximal, characteristic, complemented
12C5×#544C2211yescharacteristic
13C5×#542—22no—
14C5×#540—22no—
15C5×#538—22no—
16C5×#537C2211yescharacteristic
17C5×#535C2212yes—
18C5×#532—22no—
19C5×#529—22no—
20C2×C5×#125C2211yescharacteristic
21C5×#525—22no—
22C4×C5×#41C2212yes—
23C2×C4×C5×D4C2211yescharacteristic
24C5×#479—22no—
25C5×#479—22no—
26C5×#478—22no—
27C5×#478—22no—
28C5×#428C2212yes—
29C5×#428C2212yes—
30C5×#423C2212yes—
31C2×C5×#104C2212yes—
32C2×C5×#104C2212yes—
33C5×#417C2212yes—
34C5×#417C2212yes—
35C2×C5×#100C2212yes—
36C5×#396—22no—
37C5×#390C2211yescharacteristic
38C5×#390C2211yescharacteristic
39C5×#385—22no—
40C5×#384C2211yescharacteristic
41C5×#382C2211yescharacteristic
42C4×C5×C4⋊C4C2211yescharacteristic
43C5×#343C2211yescharacteristic
44C5×#343C2211yescharacteristic
45C5×#339C2212yes—
46C5×#339C2212yes—
47#29707C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—22no—
49C2×C5×#41C2312yes—
50C22×C5×D4C2311yescharacteristic
51C23×C4×C5D412yes—
52C2×C5×M16C2312yes—
53C2×C5×M16C2312yes—
54C5×C4⋊Q8—22no—
55C5×#127—22no—
56C5×#126—24no—
57C5×#125—22no—
58C5×#125—22no—
59C5×#125—22no—
60C5×#124—24no—
61C5×#124—22no—
62C5×#123—24no—
63C5×#123—24no—
64C5×C22⋊Q8—22no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8—22no—
67C5×#121—22no—
68C5×#121—24no—
69C5×#121—22no—
70C5×#121—22no—
71C5×#121—22no—
72C5×#121—22no—
73C5×#120—24no—
74C4×C5×Q8D412yes—
75C4×C5×Q8D412yes—
76C4×C5×D4—24no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C4×C5×D4D412yes—
82C4×C5×D4D412yes—
83C5×#117—22no—
84C5×#117—22no—
85C5×#117C2312yes—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C22⋊C4—22no—
94C2×C5×C22⋊C4—22no—
95C2×C5×C22⋊C4D412yes—
96C2×C42×C5—22no—
97C2×C42×C5C2311yescharacteristic
98C2×C42×C5C2311yescharacteristic
99C2×C42×C5C2311yescharacteristic
100C5×#107—22no—
101C5×#107—22no—
102C5×#106—22no—
103C5×#106—22no—
104C5×C4⋊C8—22no—
105C5×C4⋊C8—22no—
106C5×#104—42no—
107C5×#104—42no—
108C5×#103—22no—
109C5×#103—22no—
110C5×#102—22no—
111C5×#102—22no—
112C5×#100—42no—
113C5×#95—21no—
114C5×#95—22no—
115#3460C2×C511yescharacteristic
116#3080C2×C512yescomplemented
117#2566C2×C511yescharacteristic, complemented
118#2061C2×C511yescharacteristic, complemented
119#2060C2×C511yescharacteristic, complemented
120#2040C2×C511yescharacteristic, complemented
121#2039C2×C511yescharacteristic, complemented
122#2037C2×C512yescomplemented
123#2037C2×C512yescomplemented
124#1806C2×C512yescomplemented
125#1800C2×C511yescharacteristic, complemented
126C24×C5C2×D412yes—
127C5×#41—22no—
128C5×#41—22no—
129C5×#41—22no—
130C5×#41—22no—
131C5×#41—84no—
132C2×C5×Q8—22no—
133C2×C5×Q8C2×D412yes—
134C2×C5×D4—22no—
135C2×C5×D4—24no—
136C2×C5×D4—24no—
137C2×C5×D4—22no—
138C2×C5×D4—22no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—22no—
142C2×C5×D4C2×D412yes—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—82no—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
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—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—24no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—42no—
172C5×C4⋊C4—41no—
173C5×C4⋊C4—42no—
174C5×C4⋊C4—41no—
175C5×C4⋊C4—82no—
176C5×C4⋊C4C2×D412yes—
177C5×C4⋊C4C2×D412yes—
178C5×C22⋊C4—24no—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—24no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—44no—
186C5×C22⋊C4—82no—
187C42×C5—22no—
188C42×C5—22no—
189C42×C5—22no—
190C42×C5—21no—
191C42×C5—21no—
192C42×C5—21no—
193C42×C5—21no—
194C42×C5C2×D412yes—
195C42×C5C2×D412yes—
196#544C22×C511yescharacteristic
197#542—22no—
198#540—22no—
199#538—22no—
200#537C22×C511yescharacteristic
201#535C22×C512yes—
202#532—22no—
203#529—22no—
204C2×#125C22×C511yescharacteristic
205#525—22no—
206C4×#41C22×C512yes—
207C2×C4×D4C22×C511yescharacteristic
208#479—22no—
209#479—22no—
210#478—22no—
211#478—22no—
212#428C22×C512yes—
213#428C22×C512yes—
214#423C22×C512yes—
215C2×#104C22×C512yes—
216C2×#104C22×C512yes—
217#417C22×C512yes—
218#417C22×C512yes—
219C2×#100C22×C512yes—
220#396—22no—
221#390C22×C511yescharacteristic
222#390C22×C511yescharacteristic
223#385—22no—
224#384C22×C511yescharacteristic
225#382C22×C511yescharacteristic
226C4×C4⋊C4C22×C511yescharacteristic
227#343C22×C511yescharacteristic
228#343C22×C511yescharacteristic
229#339C22×C512yes—
230#339C22×C512yes—
231C23×C5—22no—
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5C22×D411yescharacteristic
238C5×Q8—22no—
239C5×Q8—22no—
240C5×Q8—82no—
241C5×D4—22no—
242C5×D4—22no—
243C5×D4—42no—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—42no—
247C5×D4—84no—
248C5×D4—82no—
249C5×D4—84no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—44no—
258C2×C4×C5—44no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—41no—
266C2×C4×C5—42no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—82no—
272C2×C4×C5—82no—
273C2×C4×C5#12011yescharacteristic
274C2×C4×C5#12012yes—
275C2×C4×C5#12011yescharacteristic
276C2×C4×C5C22×D412yes—
277C2×C4×C5H(5,𝔽2)11yescharacteristic
278C2×C4×C52−1+411yescharacteristic
279C2×C4×C52−1+412yes—
280C5×C8—42no—
281C5×C8—42no—
282C2×#41—22no—
283C2×#41C23×C512yes—
284C22×D4C23×C511yescharacteristic
285C23×C4C5×D412yes—
286C2×M16C23×C512yes—
287C2×M16C23×C512yes—
288C4⋊Q8—22no—
289#127—22no—
290#126—24no—
291#125—22no—
292#125—22no—
293#125—22no—
294#124—24no—
295#124—22no—
296#123—24no—
297#123—24no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301#121—22no—
302#121—24no—
303#121—22no—
304#121—22no—
305#121—22no—
306#121—22no—
307#120—24no—
308C4×Q8C5×D412yes—
309C4×Q8C5×D412yes—
310C4×D4—24no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4C5×D412yes—
316C4×D4C5×D412yes—
317#117—22no—
318#117—22no—
319#117C23×C512yes—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4C23×C511yescharacteristic
325C2×C4⋊C4C23×C511yescharacteristic
326C2×C4⋊C4C23×C511yescharacteristic
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4C5×D412yes—
330C2×C42—22no—
331C2×C42C23×C511yescharacteristic
332C2×C42C23×C511yescharacteristic
333C2×C42C23×C511yescharacteristic
334#107—22no—
335#107—22no—
336#106—22no—
337#106—22no—
338C4⋊C8—22no—
339C4⋊C8—22no—
340#104—42no—
341#104—42no—
342#103—22no—
343#103—22no—
344#102—22no—
345#102—22no—
346#100—42no—
347#95—21no—
348#95—22no—
349C22×C5—21no—
350C22×C5—21no—
351C22×C5—44no—
352C22×C5—42no—
353C22×C5—42no—
354C22×C5—42no—
355C22×C5—42no—
356C22×C5—42no—
357C22×C5—42no—
358C22×C5—82no—
359C22×C5C2×#12011yescharacteristic
360C22×C5#53611yescharacteristic
361C22×C5#53711yescharacteristic
362C4×C5—22no—
363C4×C5—21no—
364C4×C5—21no—
365C4×C5—42no—
366C4×C5—42no—
367C4×C5—42no—
368C4×C5—42no—
369C4×C5—42no—
370C4×C5—81no—
371C4×C5—81no—
372C4×C5—81no—
373C4×C5#53612yes—
374C4×C5#53712yes—
375C24C2×C5×D412yes—
376#41—22no—
377#41—22no—
378#41—22no—
379#41—22no—
380#41—84no—
381C2×Q8—22no—
382C2×Q8C2×C5×D412yes—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4C2×C5×D412yes—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—82no—
402C22×C4C2×C5×D412yes—
403C22×C4C2×C5×D411yescharacteristic
404C22×C4C2×C5×D411yescharacteristic
405C22×C4C24×C511yescharacteristic
406M16—22no—
407M16—22no—
408M16—22no—
409M16—22no—
410C2×C8—22no—
411C2×C8—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—42no—
421C4⋊C4—41no—
422C4⋊C4—42no—
423C4⋊C4—41no—
424C4⋊C4—82no—
425C4⋊C4C2×C5×D412yes—
426C4⋊C4C2×C5×D412yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—44no—
435C22⋊C4—82no—
436C42—22no—
437C42—22no—
438C42—22no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42—21no—
443C42C2×C5×D412yes—
444C42C2×C5×D412yes—
445C2×C5—21no—
446C2×C5—21no—
447C2×C5—82no—
448C2×C5—82no—
449C2×C5#261611yescharacteristic
450C2×C5#301811yescharacteristic
451C2×C5#301911yescharacteristic
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23C22×C5×D411yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—82no—
462D4—22no—
463D4—22no—
464D4—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—82no—
469D4—84no—
470D4—84no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4C5×#12011yescharacteristic
495C2×C4C5×#12012yes—
496C2×C4C5×#12011yescharacteristic
497C2×C4C22×C5×D412yes—
498C2×C4C5×H(5,𝔽2)11yescharacteristic
499C2×C4C5×2−1+411yescharacteristic
500C2×C4C5×2−1+412yes—
501C8—42no—
502C8—42no—
503C5#2970711yescharacteristic, direct product factor, Sylow
504C22—21no—
505C22—21no—
506C22—44no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—82no—
514C22C2×C5×#12011yescharacteristic
515C22C5×#53611yescharacteristic
516C22C5×#53711yescharacteristic
517C4—22no—
518C4—21no—
519C4—21no—
520C4—42no—
521C4—42no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—81no—
526C4—81no—
527C4—81no—
528C4C5×#53612yes—
529C4C5×#53712yes—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—82no—
534C2C5×#261611yescharacteristic
535C2C5×#301811yescharacteristic
536C2C5×#301911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3080C2semidirect
3. C5×#2566C2semidirect
4. C5×#2061C2semidirect
5. C5×#2060C2semidirect
6. C5×#2040C2semidirect
7. C5×#2039C2semidirect
8. C5×#2037C2semidirect
9. C5×#2037C2semidirect
10. C5×#1806C2semidirect
11. C5×#1800C2semidirect
47. #29707C5direct (N × H)
116. #3080C2×C5semidirect
117. #2566C2×C5semidirect
118. #2061C2×C5semidirect
119. #2060C2×C5semidirect
120. #2040C2×C5semidirect
121. #2039C2×C5semidirect
122. #2037C2×C5semidirect
123. #2037C2×C5semidirect
124. #1806C2×C5semidirect
125. #1800C2×C5semidirect
503. C5#29707direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34602
C5×#30802
C5×#25662
C5×#20612
C5×#20602
C5×#20402
C5×#20392
C5×#20372
C5×#18062
C5×#18002
#297075