Finite Group Databasebeta

← C5×#19002 #11941722

Subgroups — C5×#19002 #11941722

Order 1280.

884 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#563C211yesmaximal, characteristic, complemented
2C5×#3234C211yesmaximal, characteristic, complemented
3C5×#3213C211yesmaximal, characteristic
4C5×#3142C211yesmaximal, characteristic, complemented
5C5×#1664C214yesmaximal, complemented
6C5×#1657C214yesmaximal, complemented
7C5×#1534C211yesmaximal, characteristic, complemented
8C5×#1528C211yesmaximal, characteristic, complemented
9C5×#1527C211yesmaximal, characteristic, complemented
10C5×#563—22no—
11C5×#563—22no—
12C5×#563—22no—
13C5×#563C2214yes—
14C5×#532C2211yescharacteristic
15C2×C5×C4⋊Q8—21no—
16C2×C5×#126—21no—
17C2×C5×#126—21no—
18C2×C5×#125C2211yescharacteristic
19C2×C5×#125C2211yescharacteristic
20C2×C5×#124C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8—21no—
24C5×#501C2212yescomplemented
25C5×#496C2212yes—
26C5×#491C2212yescomplemented
27C5×#490C2212yescomplemented
28C5×#490C2212yescomplemented
29C5×#489C2212yes—
30C5×#488—22no—
31C5×#481—21no—
32C5×#480—21no—
33C5×#478—22no—
34C5×#463—22no—
35C5×#448—21no—
36C5×#447—21no—
37C5×#432C2211yescharacteristic
38C5×#432C2211yescharacteristic
39C5×#417—21no—
40C5×#417—21no—
41C4×C5×M16C2211yescharacteristic
42C5×#330C2214yescomplemented
43C5×#330C2214yescomplemented
44C5×#329C2214yes—
45#19002C511yesmaximal, characteristic, direct product factor, Sylow
46C2×C5×#41—21no—
47C22×C5×Q8—21no—
48C22×C5×Q8D411yescharacteristic
49C22×C5×D4D411yescharacteristic
50C23×C4×C5—21no—
51C2×C5×SD16—22no—
52C2×C5×D8—22no—
53C2×C5×M16—21no—
54C5×C4⋊Q8—24no—
55C5×C4⋊Q8—24no—
56C5×C4⋊Q8C2311yescharacteristic
57C5×#127C2311yescharacteristic
58C5×#126—24no—
59C5×#126—24no—
60C5×#126—24no—
61C5×#126—24no—
62C5×#125—21no—
63C5×#125—21no—
64C5×#125—21no—
65C5×#125—21no—
66C5×#125D412yes—
67C5×#125D412yes—
68C5×#125C2312yes—
69C5×#125C2312yes—
70C5×#124—21no—
71C5×#124—21no—
72C5×#124—21no—
73C5×#124D412yes—
74C5×#124C2312yes—
75C5×#123—24no—
76C5×#123—24no—
77C5×C22⋊Q8—24no—
78C5×C22⋊Q8—24no—
79C5×C22⋊Q8—24no—
80C5×C22⋊Q8—24no—
81C5×#121—21no—
82C5×#121—21no—
83C4×C5×D4—21no—
84C4×C5×D4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4D411yescharacteristic
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4D411yescharacteristic
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C42×C5—21no—
101C2×C42×C5C2311yescharacteristic
102C5×#107—22no—
103C5×#106—22no—
104C5×C4⋊C8—21no—
105C5×C4⋊C8—21no—
106C5×#103—22no—
107C5×#103—22no—
108C5×#103—22no—
109C5×#102—22no—
110C5×#102—22no—
111C5×#102—22no—
112C5×#102—22no—
113C5×#102—22no—
114C5×C22⋊C8—21no—
115C5×C22⋊C8—21no—
116C5×#97C2312yes—
117C5×#97C2312yes—
118C5×#97C2312yes—
119C4×C5×C8—21no—
120C2×#563C2×C511yescharacteristic, complemented
121#3234C2×C511yescharacteristic, complemented
122#3213C2×C511yescharacteristic
123#3142C2×C511yescharacteristic, complemented
124#1664C2×C514yescomplemented
125#1657C2×C514yescomplemented
126#1534C2×C511yescharacteristic, complemented
127#1528C2×C511yescharacteristic, complemented
128#1527C2×C511yescharacteristic, complemented
129C24×C5—21no—
130C5×#41—44no—
131C2×C5×Q8—24no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—81no—
135C2×C5×Q8—82no—
136C2×C5×Q8C2×D412yes—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—41no—
142C2×C5×D4—81no—
143C2×C5×D4C2×D412yes—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—24no—
150C22×C4×C5—41no—
151C22×C4×C5—82no—
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C5×SD16—82no—
156C5×D8—82no—
157C5×M16—42no—
158C2×C5×C8—22no—
159C2×C5×C8—22no—
160C2×C5×C8—22no—
161C5×C4⋊C4—24no—
162C5×C4⋊C4—24no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4C2×D412yes—
178C5×C4⋊C4C2×D412yes—
179C5×C4⋊C4C2×D412yes—
180C5×C4⋊C4C2×D412yes—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—24no—
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×C5C2×D411yescharacteristic
192C42×C5C2×D411yescharacteristic
193C42×C5C2×D411yescharacteristic
194C42×C5C2411yescharacteristic
195#563—22no—
196#563—22no—
197#563—22no—
198#563C22×C514yes—
199#532C22×C511yescharacteristic
200C2×C4⋊Q8—21no—
201C2×#126—21no—
202C2×#126—21no—
203C2×#125C22×C511yescharacteristic
204C2×#125C22×C511yescharacteristic
205C2×#124C22×C511yescharacteristic
206C2×#123—21no—
207C2×C22⋊Q8—21no—
208C2×C22⋊Q8—21no—
209#501C22×C512yescomplemented
210#496C22×C512yes—
211#491C22×C512yescomplemented
212#490C22×C512yescomplemented
213#490C22×C512yescomplemented
214#489C22×C512yes—
215#488—22no—
216#481—21no—
217#480—21no—
218#478—22no—
219#463—22no—
220#448—21no—
221#447—21no—
222#432C22×C511yescharacteristic
223#432C22×C511yescharacteristic
224#417—21no—
225#417—21no—
226C4×M16C22×C511yescharacteristic
227#330C22×C514yescomplemented
228#330C22×C514yescomplemented
229#329C22×C514yes—
230C23×C5—22no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—42no—
234C23×C5—41no—
235C23×C5#12011yescharacteristic
236C5×Q8—42no—
237C5×Q8—42no—
238C5×Q8—81no—
239C5×Q8—84no—
240C5×D4—42no—
241C5×D4—42no—
242C5×D4—42no—
243C5×D4—42no—
244C5×D4—81no—
245C5×D4—82no—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—41no—
260C2×C4×C5—82no—
261C2×C4×C5—84no—
262C2×C4×C5#12011yescharacteristic
263C2×C4×C5#12011yescharacteristic
264C2×C4×C5#12011yescharacteristic
265C2×C4×C5C22×D411yescharacteristic
266C2×C4×C5C22×D411yescharacteristic
267C2×C4×C5C22×D411yescharacteristic
268C5×C8—42no—
269C5×C8—42no—
270C5×C8—42no—
271C2×#41—21no—
272C22×Q8—21no—
273C22×Q8C5×D411yescharacteristic
274C22×D4C5×D411yescharacteristic
275C23×C4—21no—
276C2×SD16—22no—
277C2×D8—22no—
278C2×M16—21no—
279C4⋊Q8—24no—
280C4⋊Q8—24no—
281C4⋊Q8C23×C511yescharacteristic
282#127C23×C511yescharacteristic
283#126—24no—
284#126—24no—
285#126—24no—
286#126—24no—
287#125—21no—
288#125—21no—
289#125—21no—
290#125—21no—
291#125C5×D412yes—
292#125C5×D412yes—
293#125C23×C512yes—
294#125C23×C512yes—
295#124—21no—
296#124—21no—
297#124—21no—
298#124C5×D412yes—
299#124C23×C512yes—
300#123—24no—
301#123—24no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—24no—
306#121—21no—
307#121—21no—
308C4×D4—21no—
309C4×D4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4C5×D411yescharacteristic
317C2×C4⋊C4C5×D411yescharacteristic
318C2×C4⋊C4C5×D411yescharacteristic
319C2×C4⋊C4C5×D411yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C42—21no—
326C2×C42C23×C511yescharacteristic
327#107—22no—
328#106—22no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331#103—22no—
332#103—22no—
333#103—22no—
334#102—22no—
335#102—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341#97C23×C512yes—
342#97C23×C512yes—
343#97C23×C512yes—
344C4×C8—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—42no—
348C22×C5—42no—
349C22×C5—42no—
350C22×C5—84no—
351C22×C5—81no—
352C22×C5—81no—
353C22×C5—81no—
354C22×C5#45412yes—
355C22×C5C2×#12011yescharacteristic
356C4×C5—21no—
357C4×C5—21no—
358C4×C5—21no—
359C4×C5—21no—
360C4×C5—21no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—42no—
364C4×C5—42no—
365C4×C5—42no—
366C4×C5—42no—
367C4×C5—81no—
368C24—21no—
369#41—44no—
370C2×Q8—24no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—81no—
374C2×Q8—82no—
375C2×Q8C2×C5×D412yes—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—41no—
381C2×D4—81no—
382C2×D4C2×C5×D412yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—24no—
389C22×C4—41no—
390C22×C4—82no—
391C22×C4C2×C5×D411yescharacteristic
392C22×C4C2×C5×D411yescharacteristic
393C22×C4C2×C5×D411yescharacteristic
394SD16—82no—
395D8—82no—
396M16—42no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4C2×C5×D412yes—
417C4⋊C4C2×C5×D412yes—
418C4⋊C4C2×C5×D412yes—
419C4⋊C4C2×C5×D412yes—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C42—24no—
430C42C2×C5×D411yescharacteristic
431C42C2×C5×D411yescharacteristic
432C42C2×C5×D411yescharacteristic
433C42C24×C511yescharacteristic
434C2×C5—22no—
435C2×C5—82no—
436C2×C5—161no—
437C2×C5C2×#45411yescharacteristic
438C2×C5#301911yescharacteristic
439C2×C5#302011yescharacteristic
440C23—22no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23C5×#12011yescharacteristic
446Q8—42no—
447Q8—42no—
448Q8—81no—
449Q8—84no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—81no—
455D4—82no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—84no—
472C2×C4C5×#12011yescharacteristic
473C2×C4C5×#12011yescharacteristic
474C2×C4C5×#12011yescharacteristic
475C2×C4C22×C5×D411yescharacteristic
476C2×C4C22×C5×D411yescharacteristic
477C2×C4C22×C5×D411yescharacteristic
478C8—42no—
479C8—42no—
480C8—42no—
481C5#1900211yescharacteristic, direct product factor, Sylow
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C5×#45412yes—
492C22C2×C5×#12011yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C2—22no—
506C2—82no—
507C2—161no—
508C2C2×C5×#45411yescharacteristic
509C2C5×#301911yescharacteristic
510C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3213C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#563C2semidirect
2. C5×#3234C2semidirect
4. C5×#3142C2semidirect
5. C5×#1664C2semidirect
6. C5×#1657C2semidirect
7. C5×#1534C2semidirect
8. C5×#1528C2semidirect
9. C5×#1527C2semidirect
24. C5×#501C22semidirect
26. C5×#491C22semidirect
27. C5×#490C22semidirect
28. C5×#490C22semidirect
42. C5×#330C22semidirect
43. C5×#330C22semidirect
45. #19002C5direct (N × H)
120. C2×#563C2×C5semidirect
121. #3234C2×C5semidirect
123. #3142C2×C5semidirect
124. #1664C2×C5semidirect
125. #1657C2×C5semidirect
126. #1534C2×C5semidirect
127. #1528C2×C5semidirect
128. #1527C2×C5semidirect
209. #501C22×C5semidirect
211. #491C22×C5semidirect
212. #490C22×C5semidirect
213. #490C22×C5semidirect
227. #330C22×C5semidirect
228. #330C22×C5semidirect
481. C5#19002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5632
C5×#32342
C5×#32132
C5×#31422
C5×#16642
C5×#16572
C5×#15342
C5×#15282
C5×#15272
#190025