Finite Group Databasebeta

← C5×#19057 #11941777

Subgroups — C5×#19057 #11941777

Order 1280.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3548C211yesmaximal, characteristic
2C5×#3237C211yesmaximal, characteristic, complemented
3C5×#3216C211yesmaximal, characteristic, complemented
4C5×#3135C211yesmaximal, characteristic, complemented
5C5×#1662C214yesmaximal, complemented
6C5×#1661C214yesmaximal, complemented
7C5×#1536C211yesmaximal, characteristic, complemented
8C5×#1531C211yesmaximal, characteristic, complemented
9C5×#1530C211yesmaximal, characteristic, complemented
10C5×#562C2214yes—
11C5×#554—21no—
12C5×#554—21no—
13C5×#550—21no—
14C5×#550—21no—
15C5×#547—21no—
16C5×#547—21no—
17C5×#540—22no—
18C5×#537—22no—
19C5×#537—22no—
20C5×#533C2211yescharacteristic
21C5×#533C2211yescharacteristic
22C5×#532C2211yescharacteristic
23C5×#532C2211yescharacteristic
24C5×#501C2212yes—
25C5×#497C2212yes—
26C5×#491—21no—
27C5×#491C2212yes—
28C5×#490—21no—
29C5×#489C2212yes—
30C5×#489C2212yes—
31C5×#489C2212yes—
32C5×#485—22no—
33C5×#477—21no—
34C5×#475—21no—
35C5×#462—21no—
36C5×#460—21no—
37C5×#452—22no—
38C5×#432C2211yescharacteristic
39C5×#432C2211yescharacteristic
40C5×#416—22no—
41C2×C5×#97C2211yescharacteristic
42C5×#330C2214yes—
43C5×#329C2214yes—
44C5×#329C2214yes—
45#19057C511yesmaximal, characteristic, direct product factor, Sylow
46C2×C5×#41—22no—
47C2×C5×#41—22no—
48C2×C5×#41D412yes—
49C2×C5×#41D412yes—
50C2×C5×Q16—22no—
51C2×C5×SD16—22no—
52C22×C5×C8—21no—
53C5×C4⋊Q8D411yescharacteristic
54C5×C4⋊Q8D411yescharacteristic
55C5×C4⋊Q8D411yescharacteristic
56C5×C4⋊Q8D411yescharacteristic
57C5×C4⋊Q8C2311yescharacteristic
58C5×C4⋊Q8C2311yescharacteristic
59C5×#127—22no—
60C5×#127D411yescharacteristic
61C5×#127D411yescharacteristic
62C5×#125—22no—
63C5×#125—21no—
64C5×#125C2312yes—
65C5×#124C2312yes—
66C5×#124C2312yes—
67C5×#123—24no—
68C5×#123—24no—
69C5×C22⋊Q8—22no—
70C5×C22⋊Q8—22no—
71C5×C22⋊Q8—24no—
72C5×C22⋊Q8—24no—
73C5×C22⋊Q8—21no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8—21no—
77C5×#121—24no—
78C5×#121—24no—
79C5×#121—22no—
80C5×#121—22no—
81C5×#121—24no—
82C5×#121—24no—
83C5×#121—21no—
84C5×#121—21no—
85C5×#121—21no—
86C5×#121—21no—
87C4×C5×Q8—21no—
88C4×C5×Q8—21no—
89C4×C5×Q8—21no—
90C4×C5×Q8—21no—
91C4×C5×D4—22no—
92C4×C5×D4—22no—
93C4×C5×D4—21no—
94C4×C5×D4—21no—
95C4×C5×D4—21no—
96C4×C5×D4—21no—
97C5×#117—21no—
98C5×#117D412yes—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
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×#103—22no—
110C5×#103—22no—
111C5×#102—22no—
112C5×#102—22no—
113C5×#102—22no—
114C5×C22⋊C8—21no—
115C5×C22⋊C8—21no—
116C5×#97—21no—
117C5×#97C2312yes—
118C5×#97C2312yes—
119C5×#97C2312yes—
120#3548C2×C511yescharacteristic
121#3237C2×C511yescharacteristic, complemented
122#3216C2×C511yescharacteristic, complemented
123#3135C2×C511yescharacteristic, complemented
124#1662C2×C514yescomplemented
125#1661C2×C514yescomplemented
126#1536C2×C511yescharacteristic, complemented
127#1531C2×C511yescharacteristic, complemented
128#1530C2×C511yescharacteristic, complemented
129C5×#41—44no—
130C5×#41—82no—
131C5×#41—84no—
132C5×#41—84no—
133C2×C5×Q8—21no—
134C2×C5×Q8—21no—
135C2×C5×Q8—21no—
136C2×C5×Q8—21no—
137C2×C5×Q8C2×D412yes—
138C2×C5×Q8C2×D412yes—
139C2×C5×D4—24no—
140C2×C5×D4—24no—
141C2×C5×D4—22no—
142C2×C5×D4—22no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4C2×D412yes—
148C2×C5×D4C2×D412yes—
149C22×C4×C5—24no—
150C22×C4×C5—24no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C5×Q16—82no—
157C5×SD16—82no—
158C2×C5×C8—22no—
159C2×C5×C8—22no—
160C2×C5×C8—22no—
161C2×C5×C8—42no—
162C5×C4⋊C4—24no—
163C5×C4⋊C4—24no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—41no—
177C5×C4⋊C4—41no—
178C5×C4⋊C4C2×D412yes—
179C5×C4⋊C4C2×D412yes—
180C5×C22⋊C4—24no—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—41no—
188C42×C5—22no—
189C42×C5—41no—
190C42×C5C2×D411yescharacteristic
191C42×C5C2×D411yescharacteristic
192C42×C5C2×D411yescharacteristic
193C42×C5C2411yescharacteristic
194#562C22×C514yes—
195#554—21no—
196#554—21no—
197#550—21no—
198#550—21no—
199#547—21no—
200#547—21no—
201#540—22no—
202#537—22no—
203#537—22no—
204#533C22×C511yescharacteristic
205#533C22×C511yescharacteristic
206#532C22×C511yescharacteristic
207#532C22×C511yescharacteristic
208#501C22×C512yes—
209#497C22×C512yes—
210#491—21no—
211#491C22×C512yes—
212#490—21no—
213#489C22×C512yes—
214#489C22×C512yes—
215#489C22×C512yes—
216#485—22no—
217#477—21no—
218#475—21no—
219#462—21no—
220#460—21no—
221#452—22no—
222#432C22×C511yescharacteristic
223#432C22×C511yescharacteristic
224#416—22no—
225C2×#97C22×C511yescharacteristic
226#330C22×C514yes—
227#329C22×C514yes—
228#329C22×C514yes—
229C23×C5—22no—
230C23×C5—22no—
231C23×C5#12011yescharacteristic
232C5×Q8—42no—
233C5×Q8—42no—
234C5×Q8—42no—
235C5×Q8—41no—
236C5×Q8—41no—
237C5×Q8—42no—
238C5×Q8—42no—
239C5×D4—42no—
240C5×D4—42no—
241C5×D4—42no—
242C5×D4—42no—
243C5×D4—42no—
244C5×D4—42no—
245C5×D4—82no—
246C5×D4—82no—
247C5×D4—84no—
248C5×D4—84no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5—44no—
257C2×C4×C5—44no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—84no—
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—22no—
272C2×#41—22no—
273C2×#41C5×D412yes—
274C2×#41C5×D412yes—
275C2×Q16—22no—
276C2×SD16—22no—
277C22×C8—21no—
278C4⋊Q8C5×D411yescharacteristic
279C4⋊Q8C5×D411yescharacteristic
280C4⋊Q8C5×D411yescharacteristic
281C4⋊Q8C5×D411yescharacteristic
282C4⋊Q8C23×C511yescharacteristic
283C4⋊Q8C23×C511yescharacteristic
284#127—22no—
285#127C5×D411yescharacteristic
286#127C5×D411yescharacteristic
287#125—22no—
288#125—21no—
289#125C23×C512yes—
290#124C23×C512yes—
291#124C23×C512yes—
292#123—24no—
293#123—24no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302#121—24no—
303#121—24no—
304#121—22no—
305#121—22no—
306#121—24no—
307#121—24no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322#117—21no—
323#117C5×D412yes—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
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#103—22no—
335#103—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341#97—21no—
342#97C23×C512yes—
343#97C23×C512yes—
344#97C23×C512yes—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—21no—
348C22×C5—42no—
349C22×C5—42no—
350C22×C5—42no—
351C22×C5—42no—
352C22×C5—42no—
353C22×C5—42no—
354C22×C5C2×#12011yescharacteristic
355C4×C5—21no—
356C4×C5—21no—
357C4×C5—21no—
358C4×C5—21no—
359C4×C5—21no—
360C4×C5—42no—
361C4×C5—42no—
362C4×C5—42no—
363C4×C5—42no—
364C4×C5—81no—
365C4×C5—81no—
366C4×C5#45512yes—
367#41—44no—
368#41—82no—
369#41—84no—
370#41—84no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8C2×C5×D412yes—
376C2×Q8C2×C5×D412yes—
377C2×D4—24no—
378C2×D4—24no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4C2×C5×D412yes—
386C2×D4C2×C5×D412yes—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4C2×C5×D411yescharacteristic
392C22×C4C2×C5×D411yescharacteristic
393C22×C4C2×C5×D411yescharacteristic
394Q16—82no—
395SD16—82no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—42no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4C2×C5×D412yes—
417C4⋊C4C2×C5×D412yes—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—41no—
426C42—22no—
427C42—41no—
428C42C2×C5×D411yescharacteristic
429C42C2×C5×D411yescharacteristic
430C42C2×C5×D411yescharacteristic
431C42C24×C511yescharacteristic
432C2×C5—41no—
433C2×C5—82no—
434C2×C5—82no—
435C2×C5C2×#45511yescharacteristic
436C2×C5#301911yescharacteristic
437C2×C5#302011yescharacteristic
438C23—22no—
439C23—22no—
440C23C5×#12011yescharacteristic
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—41no—
445Q8—41no—
446Q8—42no—
447Q8—42no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—82no—
455D4—82no—
456D4—84no—
457D4—84no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—84no—
470C2×C4—84no—
471C2×C4C5×#12011yescharacteristic
472C2×C4C5×#12011yescharacteristic
473C2×C4C5×#12011yescharacteristic
474C2×C4C22×C5×D411yescharacteristic
475C2×C4C22×C5×D411yescharacteristic
476C2×C4C22×C5×D411yescharacteristic
477C8—42no—
478C8—42no—
479C8—42no—
480C5#1905711yescharacteristic, direct product factor, Sylow
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22C2×C5×#12011yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4C5×#45512yes—
503C2—41no—
504C2—82no—
505C2—82no—
506C2C2×C5×#45511yescharacteristic
507C2C5×#301911yescharacteristic
508C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3548C2
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
2. C5×#3237C2semidirect
3. C5×#3216C2semidirect
4. C5×#3135C2semidirect
5. C5×#1662C2semidirect
6. C5×#1661C2semidirect
7. C5×#1536C2semidirect
8. C5×#1531C2semidirect
9. C5×#1530C2semidirect
45. #19057C5direct (N × H)
121. #3237C2×C5semidirect
122. #3216C2×C5semidirect
123. #3135C2×C5semidirect
124. #1662C2×C5semidirect
125. #1661C2×C5semidirect
126. #1536C2×C5semidirect
127. #1531C2×C5semidirect
128. #1530C2×C5semidirect
480. C5#19057direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35482
C5×#32372
C5×#32162
C5×#31352
C5×#16622
C5×#16612
C5×#15362
C5×#15312
C5×#15302
#190575