Finite Group Databasebeta

← C5×#18440 #11941160

Subgroups — C5×#18440 #11941160

Order 1280.

904 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic, complemented
3C5×#3226C211yesmaximal, characteristic, complemented
4C5×#2660C211yesmaximal, characteristic, complemented
5C5×#1610C214yesmaximal, complemented
6C5×#1609C214yesmaximal, complemented
7C5×#1505C211yesmaximal, characteristic, complemented
8C5×#1500C211yesmaximal, characteristic, complemented
9C5×#1470C211yesmaximal, characteristic, complemented
10C5×#563—21no—
11C5×#562—21no—
12C5×#554—21no—
13C5×#553—21no—
14C5×#553—21no—
15C5×#547—22no—
16C5×#547—21no—
17C5×#544—21no—
18C5×#540—21no—
19C5×#539—22no—
20C5×#539C2212yes—
21C5×#537C2212yes—
22C5×#532C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#125C2211yescharacteristic
26C5×#501—21no—
27C5×#500—21no—
28C5×#489—21no—
29C5×#486—21no—
30C5×#483C2212yes—
31C5×#480C2212yes—
32C5×#480C2214yes—
33C5×#477—21no—
34C5×#476—21no—
35C5×#474—22no—
36C5×#432C2211yescharacteristic
37C5×#431C2211yescharacteristic
38C5×#398C2214yes—
39C5×#395—22no—
40C5×#384—21no—
41C5×#382—21no—
42C5×#376C2211yescharacteristic
43C5×#328C2212yes—
44C5×#327C2212yes—
45C5×#327C2214yes—
46C5×#324C2214yes—
47#18440C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—21no—
49C2×C5×#41—22no—
50C22×C5×Q8—21no—
51C5×C4⋊Q8—21no—
52C5×C4⋊Q8—22no—
53C5×C4⋊Q8—21no—
54C5×C4⋊Q8—21no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8D411yescharacteristic
58C5×#127D411yescharacteristic
59C5×#126—22no—
60C5×#126—22no—
61C5×#126—21no—
62C5×#125—21no—
63C5×#125—22no—
64C5×#125—21no—
65C5×#125—21no—
66C5×#125—21no—
67C5×#125—21no—
68C5×#125D411yescharacteristic
69C5×#124—21no—
70C5×#124D411yescharacteristic
71C5×#123—22no—
72C5×#123—22no—
73C5×#123—22no—
74C5×#123—22no—
75C5×#123—22no—
76C5×#123—21no—
77C5×#123—22no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8—22no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8C2311yescharacteristic
85C5×#121—21no—
86C5×#121—22no—
87C5×#121—21no—
88C5×#121—22no—
89C5×#121—22no—
90C5×#121—21no—
91C5×#121—22no—
92C5×#121C2311yescharacteristic
93C5×#121C2312yes—
94C4×C5×Q8D411yescharacteristic
95C4×C5×D4—22no—
96C4×C5×D4—21no—
97C4×C5×D4—21no—
98C4×C5×D4—21no—
99C4×C5×D4—22no—
100C4×C5×D4—21no—
101C4×C5×D4D412yes—
102C4×C5×D4D411yescharacteristic
103C5×#117—21no—
104C5×#117—21no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—24no—
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D412yes—
112C2×C5×C4⋊C4C2312yes—
113C2×C5×C4⋊C4C2312yes—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C5×#107—24no—
117C5×#107—22no—
118C5×#106—22no—
119C5×C4⋊C8—21no—
120C5×C4⋊C8—21no—
121C5×#103—22no—
122C5×#102—24no—
123C5×#102—22no—
124C5×C22⋊C8C2312yes—
125C5×C22⋊C8C2312yes—
126C5×#97—21no—
127C4×C5×C8—21no—
128C5×#95—21no—
129C5×#95—24no—
130C5×#95C2312yes—
131#3559C2×C511yescharacteristic
132#3238C2×C511yescharacteristic, complemented
133#3226C2×C511yescharacteristic, complemented
134#2660C2×C511yescharacteristic, complemented
135#1610C2×C514yescomplemented
136#1609C2×C514yescomplemented
137#1505C2×C511yescharacteristic, complemented
138#1500C2×C511yescharacteristic, complemented
139#1470C2×C511yescharacteristic, complemented
140C5×#41—82no—
141C5×#41—84no—
142C2×C5×Q8—22no—
143C2×C5×Q8—21no—
144C2×C5×Q8—41no—
145C2×C5×Q8—41no—
146C2×C5×Q8—82no—
147C2×C5×Q8C2×D411yescharacteristic
148C2×C5×D4—21no—
149C2×C5×D4—22no—
150C2×C5×D4—22no—
151C2×C5×D4—22no—
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4C2×D411yescharacteristic
155C2×C5×D4C2×D412yes—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5C2×D412yes—
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2411yescharacteristic
168C2×C5×C8—22no—
169C2×C5×C8—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—41no—
190C5×C4⋊C4—41no—
191C5×C4⋊C4—84no—
192C5×C4⋊C4C2×D412yes—
193C5×C4⋊C4C2×D411yescharacteristic
194C5×C4⋊C4C2×D411yescharacteristic
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—22no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—21no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—21no—
203C5×C22⋊C4—21no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—22no—
207C42×C5—24no—
208C42×C5—22no—
209C42×C5—21no—
210C42×C5C2×D411yescharacteristic
211C42×C5C2×D411yescharacteristic
212C42×C5C2×D411yescharacteristic
213C42×C5C2×D411yescharacteristic
214#563—21no—
215#562—21no—
216#554—21no—
217#553—21no—
218#553—21no—
219#547—22no—
220#547—21no—
221#544—21no—
222#540—21no—
223#539—22no—
224#539C22×C512yes—
225#537C22×C512yes—
226#532C22×C511yescharacteristic
227C2×C4⋊Q8C22×C511yescharacteristic
228#529C22×C511yescharacteristic
229C2×#125C22×C511yescharacteristic
230#501—21no—
231#500—21no—
232#489—21no—
233#486—21no—
234#483C22×C512yes—
235#480C22×C514yes—
236#480C22×C512yes—
237#477—21no—
238#476—21no—
239#474—22no—
240#432C22×C511yescharacteristic
241#431C22×C511yescharacteristic
242#398C22×C514yes—
243#395—22no—
244#384—21no—
245#382—21no—
246#376C22×C511yescharacteristic
247#328C22×C512yes—
248#327C22×C514yes—
249#327C22×C512yes—
250#324C22×C514yes—
251C23×C5—21no—
252C23×C5—22no—
253C23×C5C22×D411yescharacteristic
254C5×Q8—41no—
255C5×Q8—81no—
256C5×Q8—82no—
257C5×Q8—82no—
258C5×Q8—82no—
259C5×D4—42no—
260C5×D4—41no—
261C5×D4—44no—
262C5×D4—42no—
263C5×D4—42no—
264C5×D4—81no—
265C5×D4—82no—
266C5×D4—82no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—24no—
277C2×C4×C5—41no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—44no—
284C2×C4×C5—82no—
285C2×C4×C5—82no—
286C2×C4×C5—82no—
287C2×C4×C5—82no—
288C2×C4×C5#12011yescharacteristic
289C2×C4×C5#12011yescharacteristic
290C2×C4×C5#12011yescharacteristic
291C2×C4×C5#12011yescharacteristic
292C2×C4×C5C22×D411yescharacteristic
293C2×C4×C5C22×D411yescharacteristic
294C5×C8—42no—
295C5×C8—42no—
296C2×#41—21no—
297C2×#41—22no—
298C22×Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—22no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C5×D411yescharacteristic
306#127C5×D411yescharacteristic
307#126—22no—
308#126—22no—
309#126—21no—
310#125—21no—
311#125—22no—
312#125—21no—
313#125—21no—
314#125—21no—
315#125—21no—
316#125C5×D411yescharacteristic
317#124—21no—
318#124C5×D411yescharacteristic
319#123—22no—
320#123—22no—
321#123—22no—
322#123—22no—
323#123—22no—
324#123—21no—
325#123—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8C23×C511yescharacteristic
333#121—21no—
334#121—22no—
335#121—21no—
336#121—22no—
337#121—22no—
338#121—21no—
339#121—22no—
340#121C23×C511yescharacteristic
341#121C23×C512yes—
342C4×Q8C5×D411yescharacteristic
343C4×D4—22no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—22no—
348C4×D4—21no—
349C4×D4C5×D411yescharacteristic
350C4×D4C5×D412yes—
351#117—21no—
352#117—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4C5×D411yescharacteristic
358C2×C4⋊C4C5×D412yes—
359C2×C4⋊C4C5×D411yescharacteristic
360C2×C4⋊C4C23×C512yes—
361C2×C4⋊C4C23×C512yes—
362C2×C42—21no—
363C2×C42C23×C511yescharacteristic
364#107—24no—
365#107—22no—
366#106—22no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369#103—22no—
370#102—24no—
371#102—22no—
372C22⋊C8C23×C512yes—
373C22⋊C8C23×C512yes—
374#97—21no—
375C4×C8—21no—
376#95—21no—
377#95—24no—
378#95C23×C512yes—
379C22×C5—21no—
380C22×C5—21no—
381C22×C5—42no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—42no—
385C22×C5—42no—
386C22×C5—41no—
387C22×C5C2×#12011yescharacteristic
388C22×C5#57612yes—
389C4×C5—21no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—21no—
394C4×C5—44no—
395C4×C5—42no—
396C4×C5—42no—
397C4×C5—41no—
398C4×C5—41no—
399C4×C5—42no—
400C4×C5—41no—
401C4×C5—82no—
402C4×C5#45612yes—
403#41—82no—
404#41—84no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—82no—
410C2×Q8C2×C5×D411yescharacteristic
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×C5×D411yescharacteristic
418C2×D4C2×C5×D412yes—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4C2×C5×D412yes—
427C22×C4C2×C5×D411yescharacteristic
428C22×C4C2×C5×D411yescharacteristic
429C22×C4C2×C5×D412yes—
430C22×C4C24×C511yescharacteristic
431C2×C8—22no—
432C2×C8—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—84no—
455C4⋊C4C2×C5×D411yescharacteristic
456C4⋊C4C2×C5×D412yes—
457C4⋊C4C2×C5×D411yescharacteristic
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—22no—
468C22⋊C4—21no—
469C22⋊C4—22no—
470C42—24no—
471C42—22no—
472C42—21no—
473C42C2×C5×D411yescharacteristic
474C42C2×C5×D411yescharacteristic
475C42C2×C5×D411yescharacteristic
476C42C2×C5×D411yescharacteristic
477C2×C5—22no—
478C2×C5—81no—
479C2×C5—82no—
480C2×C5#300811yescharacteristic
481C2×C5C2×#45611yescharacteristic
482C2×C5#302811yescharacteristic
483C23—21no—
484C23—22no—
485C23C22×C5×D411yescharacteristic
486Q8—41no—
487Q8—81no—
488Q8—82no—
489Q8—82no—
490Q8—82no—
491D4—42no—
492D4—41no—
493D4—44no—
494D4—42no—
495D4—42no—
496D4—81no—
497D4—82no—
498D4—82no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4C5×#12011yescharacteristic
521C2×C4C5×#12011yescharacteristic
522C2×C4C5×#12011yescharacteristic
523C2×C4C5×#12011yescharacteristic
524C2×C4C22×C5×D411yescharacteristic
525C2×C4C22×C5×D411yescharacteristic
526C8—42no—
527C8—42no—
528C5#1844011yescharacteristic, direct product factor, Sylow
529C22—21no—
530C22—21no—
531C22—42no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22C2×C5×#12011yescharacteristic
538C22C5×#57612yes—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—44no—
545C4—42no—
546C4—42no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—82no—
552C4C5×#45612yes—
553C2—22no—
554C2—81no—
555C2—82no—
556C2C5×#300811yescharacteristic
557C2C2×C5×#45611yescharacteristic
558C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3559C2
LCSG ▷ C22×C4 ▷ 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×#3238C2semidirect
3. C5×#3226C2semidirect
4. C5×#2660C2semidirect
5. C5×#1610C2semidirect
6. C5×#1609C2semidirect
7. C5×#1505C2semidirect
8. C5×#1500C2semidirect
9. C5×#1470C2semidirect
47. #18440C5direct (N × H)
132. #3238C2×C5semidirect
133. #3226C2×C5semidirect
134. #2660C2×C5semidirect
135. #1610C2×C5semidirect
136. #1609C2×C5semidirect
137. #1505C2×C5semidirect
138. #1500C2×C5semidirect
139. #1470C2×C5semidirect
528. C5#18440direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35592
C5×#32382
C5×#32262
C5×#26602
C5×#16102
C5×#16092
C5×#15052
C5×#15002
C5×#14702
#184405