Finite Group Databasebeta

← C5×#18441 #11941161

Subgroups — C5×#18441 #11941161

Order 1280.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3227C211yesmaximal, characteristic, complemented
4C5×#2642C211yesmaximal, characteristic, complemented
5C5×#1616C214yesmaximal, complemented
6C5×#1615C214yesmaximal, 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×#498—21no—
28C5×#489—21no—
29C5×#486—21no—
30C5×#484C2212yes—
31C5×#481C2212yes—
32C5×#481C2214yes—
33C5×#476—22no—
34C5×#475—21no—
35C5×#474—21no—
36C5×#432C2211yescharacteristic
37C5×#431C2211yescharacteristic
38C5×#400—22no—
39C5×#400C2214yes—
40C5×#391—21no—
41C5×#391—21no—
42C5×#376C2211yescharacteristic
43C5×#328C2212yes—
44C5×#327C2212yes—
45C5×#327C2214yes—
46C5×#324C2214yes—
47#18441C511yesmaximal, 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×D4D411yescharacteristic
102C4×C5×D4D412yes—
103C5×#117—21no—
104C5×#117—21no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4D412yes—
111C2×C5×C4⋊C4C2312yes—
112C2×C5×C4⋊C4C2312yes—
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C5×#107—22no—
116C5×#106—22no—
117C5×#106—24no—
118C5×C4⋊C8—21no—
119C5×C4⋊C8—21no—
120C5×#103—22no—
121C5×#102—22no—
122C5×#102—24no—
123C5×C22⋊C8C2312yes—
124C5×C22⋊C8C2312yes—
125C5×#97—21no—
126C4×C5×C8—21no—
127C5×#95—21no—
128C5×#95—24no—
129C5×#95—24no—
130C5×#95C2312yes—
131#3559C2×C511yescharacteristic
132#3239C2×C511yescharacteristic, complemented
133#3227C2×C511yescharacteristic, complemented
134#2642C2×C511yescharacteristic, complemented
135#1616C2×C514yescomplemented
136#1615C2×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—44no—
145C2×C5×Q8—41no—
146C2×C5×Q8—41no—
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—21no—
160C22×C4×C5—22no—
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⋊C4C2×D412yes—
192C5×C4⋊C4C2×D411yescharacteristic
193C5×C4⋊C4C2×D411yescharacteristic
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—22no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4—21no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—21no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—21no—
205C5×C22⋊C4—22no—
206C42×C5—22no—
207C42×C5—21no—
208C42×C5—42no—
209C42×C5C2×D411yescharacteristic
210C42×C5C2×D411yescharacteristic
211C42×C5C2×D411yescharacteristic
212C42×C5C2×D411yescharacteristic
213#563—21no—
214#562—21no—
215#554—21no—
216#553—21no—
217#553—21no—
218#547—22no—
219#547—21no—
220#544—21no—
221#540—21no—
222#539—22no—
223#539C22×C512yes—
224#537C22×C512yes—
225#532C22×C511yescharacteristic
226C2×C4⋊Q8C22×C511yescharacteristic
227#529C22×C511yescharacteristic
228C2×#125C22×C511yescharacteristic
229#501—21no—
230#498—21no—
231#489—21no—
232#486—21no—
233#484C22×C512yes—
234#481C22×C514yes—
235#481C22×C512yes—
236#476—22no—
237#475—21no—
238#474—21no—
239#432C22×C511yescharacteristic
240#431C22×C511yescharacteristic
241#400—22no—
242#400C22×C514yes—
243#391—21no—
244#391—21no—
245#376C22×C511yescharacteristic
246#328C22×C512yes—
247#327C22×C514yes—
248#327C22×C512yes—
249#324C22×C514yes—
250C23×C5—21no—
251C23×C5—22no—
252C23×C5C22×D411yescharacteristic
253C5×Q8—41no—
254C5×Q8—81no—
255C5×Q8—82no—
256C5×Q8—82no—
257C5×Q8—82no—
258C5×D4—42no—
259C5×D4—41no—
260C5×D4—44no—
261C5×D4—42no—
262C5×D4—42no—
263C5×D4—81no—
264C5×D4—82no—
265C5×D4—82no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—21no—
273C2×C4×C5—22no—
274C2×C4×C5—24no—
275C2×C4×C5—41no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—44no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—82no—
284C2×C4×C5—82no—
285C2×C4×C5—82no—
286C2×C4×C5—82no—
287C2×C4×C5#12011yescharacteristic
288C2×C4×C5#12011yescharacteristic
289C2×C4×C5#12011yescharacteristic
290C2×C4×C5#12011yescharacteristic
291C2×C4×C5C22×D411yescharacteristic
292C2×C4×C5C22×D411yescharacteristic
293C5×C8—42no—
294C5×C8—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—22no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C5×D411yescharacteristic
305#127C5×D411yescharacteristic
306#126—22no—
307#126—22no—
308#126—21no—
309#125—21no—
310#125—22no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125—21no—
315#125C5×D411yescharacteristic
316#124—21no—
317#124C5×D411yescharacteristic
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322#123—22no—
323#123—21no—
324#123—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8C23×C511yescharacteristic
332#121—21no—
333#121—22no—
334#121—21no—
335#121—22no—
336#121—22no—
337#121—21no—
338#121—22no—
339#121C23×C511yescharacteristic
340#121C23×C512yes—
341C4×Q8C5×D411yescharacteristic
342C4×D4—22no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4C5×D411yescharacteristic
349C4×D4C5×D412yes—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4C5×D411yescharacteristic
356C2×C4⋊C4C5×D412yes—
357C2×C4⋊C4C5×D411yescharacteristic
358C2×C4⋊C4C23×C512yes—
359C2×C4⋊C4C23×C512yes—
360C2×C42—21no—
361C2×C42C23×C511yescharacteristic
362#107—22no—
363#106—22no—
364#106—24no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367#103—22no—
368#102—22no—
369#102—24no—
370C22⋊C8C23×C512yes—
371C22⋊C8C23×C512yes—
372#97—21no—
373C4×C8—21no—
374#95—21no—
375#95—24no—
376#95—24no—
377#95C23×C512yes—
378C22×C5—21no—
379C22×C5—21no—
380C22×C5—42no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—42no—
384C22×C5—42no—
385C22×C5—41no—
386C22×C5C2×#12011yescharacteristic
387C22×C5#57712yes—
388C4×C5—21no—
389C4×C5—21no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—42no—
394C4×C5—42no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—42no—
398C4×C5—41no—
399C4×C5—82no—
400C4×C5—82no—
401C4×C5#45412yes—
402#41—82no—
403#41—84no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—44no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8C2×C5×D411yescharacteristic
410C2×D4—21no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4C2×C5×D411yescharacteristic
417C2×D4C2×C5×D412yes—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4C2×C5×D412yes—
426C22×C4C2×C5×D411yescharacteristic
427C22×C4C2×C5×D411yescharacteristic
428C22×C4C2×C5×D412yes—
429C22×C4C24×C511yescharacteristic
430C2×C8—22no—
431C2×C8—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4C2×C5×D412yes—
454C4⋊C4C2×C5×D411yescharacteristic
455C4⋊C4C2×C5×D411yescharacteristic
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—22no—
466C22⋊C4—21no—
467C22⋊C4—22no—
468C42—22no—
469C42—21no—
470C42—42no—
471C42C2×C5×D411yescharacteristic
472C42C2×C5×D411yescharacteristic
473C42C2×C5×D411yescharacteristic
474C42C2×C5×D411yescharacteristic
475C2×C5—22no—
476C2×C5—81no—
477C2×C5—82no—
478C2×C5#300911yescharacteristic
479C2×C5C2×#45411yescharacteristic
480C2×C5#302811yescharacteristic
481C23—21no—
482C23—22no—
483C23C22×C5×D411yescharacteristic
484Q8—41no—
485Q8—81no—
486Q8—82no—
487Q8—82no—
488Q8—82no—
489D4—42no—
490D4—41no—
491D4—44no—
492D4—42no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—82no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4C5×#12011yescharacteristic
519C2×C4C5×#12011yescharacteristic
520C2×C4C5×#12011yescharacteristic
521C2×C4C5×#12011yescharacteristic
522C2×C4C22×C5×D411yescharacteristic
523C2×C4C22×C5×D411yescharacteristic
524C8—42no—
525C8—42no—
526C5#1844111yescharacteristic, direct product factor, Sylow
527C22—21no—
528C22—21no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—42no—
533C22—42no—
534C22—41no—
535C22C2×C5×#12011yescharacteristic
536C22C5×#57712yes—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—42no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—41no—
548C4—82no—
549C4—82no—
550C4C5×#45412yes—
551C2—22no—
552C2—81no—
553C2—82no—
554C2C5×#300911yescharacteristic
555C2C2×C5×#45411yescharacteristic
556C2C5×#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×#3239C2semidirect
3. C5×#3227C2semidirect
4. C5×#2642C2semidirect
5. C5×#1616C2semidirect
6. C5×#1615C2semidirect
7. C5×#1505C2semidirect
8. C5×#1500C2semidirect
9. C5×#1470C2semidirect
47. #18441C5direct (N × H)
132. #3239C2×C5semidirect
133. #3227C2×C5semidirect
134. #2642C2×C5semidirect
135. #1616C2×C5semidirect
136. #1615C2×C5semidirect
137. #1505C2×C5semidirect
138. #1500C2×C5semidirect
139. #1470C2×C5semidirect
526. C5#18441direct (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×#32392
C5×#32272
C5×#26422
C5×#16162
C5×#16152
C5×#15052
C5×#15002
C5×#14702
#184415