Finite Group Databasebeta

← C5×#18443 #11941163

Subgroups — C5×#18443 #11941163

Order 1280.

832 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3563C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic
3C5×#3230C211yesmaximal, characteristic, complemented
4C5×#2642C211yesmaximal, characteristic, complemented
5C5×#1617C214yesmaximal, complemented
6C5×#1615C214yesmaximal
7C5×#1506C211yesmaximal, characteristic, complemented
8C5×#1500C211yesmaximal, characteristic
9C5×#1470C211yesmaximal, characteristic, complemented
10C5×#564—21no—
11C5×#563—21no—
12C5×#557—21no—
13C5×#554—21no—
14C5×#552—21no—
15C5×#552—21no—
16C5×#552—22no—
17C5×#544—21no—
18C5×#544C2212yes—
19C5×#541—21no—
20C5×#541—22no—
21C5×#539C2212yes—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#125C2211yescharacteristic
26C5×#501—21no—
27C5×#500—21no—
28C5×#489—21no—
29C5×#487—21no—
30C5×#484C2212yes—
31C5×#484C2214yes—
32C5×#481C2212yes—
33C5×#477—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×#328C2214yes—
45C5×#327C2212yes—
46C5×#324C2214yes—
47#18443C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C5×C4⋊Q8—21no—
50C5×C4⋊Q8—22no—
51C5×C4⋊Q8—22no—
52C5×C4⋊Q8—21no—
53C5×C4⋊Q8—21no—
54C5×C4⋊Q8—21no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8D411yescharacteristic
57C5×C4⋊Q8D411yescharacteristic
58C5×#126—22no—
59C5×#126—22no—
60C5×#126—22no—
61C5×#126—22no—
62C5×#126—21no—
63C5×#125—22no—
64C5×#125—22no—
65C5×#125—22no—
66C5×#125—22no—
67C5×#125—21no—
68C5×#125—22no—
69C5×#125—22no—
70C5×#125—22no—
71C5×#125—22no—
72C5×#125—21no—
73C5×#125—21no—
74C5×#125—21no—
75C5×#125—21no—
76C5×#125—21no—
77C5×#125D411yescharacteristic
78C5×#124D411yescharacteristic
79C5×#123—22no—
80C5×#123—21no—
81C5×#123—22no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8C2311yescharacteristic
90C5×C22⋊Q8C2312yes—
91C5×#121C2311yescharacteristic
92C4×C5×Q8—21no—
93C4×C5×Q8—22no—
94C4×C5×Q8—21no—
95C4×C5×Q8—21no—
96C4×C5×Q8D411yescharacteristic
97C4×C5×Q8D412yes—
98C4×C5×D4—21no—
99C4×C5×D4—22no—
100C4×C5×D4D411yescharacteristic
101C5×#117—22no—
102C5×#117—21no—
103C5×#117—21no—
104C5×#117—22no—
105C5×#117—21no—
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×#107—24no—
117C5×#106—22no—
118C5×C4⋊C8—21no—
119C5×C4⋊C8—21no—
120C5×#103—22no—
121C5×#103—24no—
122C5×#102—22no—
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#3563C2×C511yescharacteristic
132#3239C2×C511yescharacteristic
133#3230C2×C511yescharacteristic, complemented
134#2642C2×C511yescharacteristic, complemented
135#1617C2×C514yescomplemented
136#1615C2×C514yes—
137#1506C2×C511yescharacteristic, complemented
138#1500C2×C511yescharacteristic
139#1470C2×C511yescharacteristic, complemented
140C2×C5×Q8—22no—
141C2×C5×Q8—21no—
142C2×C5×Q8—44no—
143C2×C5×Q8—41no—
144C2×C5×Q8—41no—
145C2×C5×Q8C2×D412yes—
146C2×C5×Q8C2×D411yescharacteristic
147C2×C5×D4—21no—
148C2×C5×D4C2×D411yescharacteristic
149C22×C4×C5—22no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2411yescharacteristic
158C2×C5×C8—22no—
159C2×C5×C8—22no—
160C5×C4⋊C4—22no—
161C5×C4⋊C4—22no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—41no—
188C5×C4⋊C4—41no—
189C5×C4⋊C4C2×D411yescharacteristic
190C5×C4⋊C4C2×D411yescharacteristic
191C5×C4⋊C4C2×D412yes—
192C5×C22⋊C4—22no—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4—21no—
201C42×C5—22no—
202C42×C5—22no—
203C42×C5—22no—
204C42×C5—22no—
205C42×C5—21no—
206C42×C5—42no—
207C42×C5C2×D411yescharacteristic
208C42×C5C2×D411yescharacteristic
209C42×C5C2×D411yescharacteristic
210C42×C5C2×D411yescharacteristic
211#564—21no—
212#563—21no—
213#557—21no—
214#554—21no—
215#552—21no—
216#552—21no—
217#552—22no—
218#544—21no—
219#544C22×C512yes—
220#541—21no—
221#541—22no—
222#539C22×C512yes—
223#533C22×C511yescharacteristic
224C2×C4⋊Q8C22×C511yescharacteristic
225#529C22×C511yescharacteristic
226C2×#125C22×C511yescharacteristic
227#501—21no—
228#500—21no—
229#489—21no—
230#487—21no—
231#484C22×C514yes—
232#484C22×C512yes—
233#481C22×C512yes—
234#477—22no—
235#475—21no—
236#474—21no—
237#432C22×C511yescharacteristic
238#431C22×C511yescharacteristic
239#400—22no—
240#400C22×C514yes—
241#391—21no—
242#391—21no—
243#376C22×C511yescharacteristic
244#328C22×C514yes—
245#328C22×C512yes—
246#327C22×C512yes—
247#324C22×C514yes—
248C23×C5—21no—
249C23×C5C22×D411yescharacteristic
250C5×Q8—41no—
251C5×Q8—42no—
252C5×Q8—42no—
253C5×Q8—82no—
254C5×Q8—82no—
255C5×Q8—82no—
256C5×D4—41no—
257C5×D4—42no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—22no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—24no—
268C2×C4×C5—41no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—44no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—82no—
277C2×C4×C5#12011yescharacteristic
278C2×C4×C5#12011yescharacteristic
279C2×C4×C5#12011yescharacteristic
280C2×C4×C5#12011yescharacteristic
281C2×C4×C5C22×D411yescharacteristic
282C2×C4×C5C22×D411yescharacteristic
283C5×C8—42no—
284C5×C8—42no—
285C22×Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—22no—
288C4⋊Q8—22no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C5×D411yescharacteristic
294C4⋊Q8C5×D411yescharacteristic
295#126—22no—
296#126—22no—
297#126—22no—
298#126—22no—
299#126—21no—
300#125—22no—
301#125—22no—
302#125—22no—
303#125—22no—
304#125—21no—
305#125—22no—
306#125—22no—
307#125—22no—
308#125—22no—
309#125—21no—
310#125—21no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125C5×D411yescharacteristic
315#124C5×D411yescharacteristic
316#123—22no—
317#123—21no—
318#123—22no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8C23×C511yescharacteristic
327C22⋊Q8C23×C512yes—
328#121C23×C511yescharacteristic
329C4×Q8—21no—
330C4×Q8—22no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8C5×D411yescharacteristic
334C4×Q8C5×D412yes—
335C4×D4—21no—
336C4×D4—22no—
337C4×D4C5×D411yescharacteristic
338#117—22no—
339#117—21no—
340#117—21no—
341#117—22no—
342#117—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C5×D411yescharacteristic
346C2×C4⋊C4C5×D412yes—
347C2×C4⋊C4C5×D411yescharacteristic
348C2×C4⋊C4C23×C512yes—
349C2×C4⋊C4C23×C512yes—
350C2×C42—21no—
351C2×C42C23×C511yescharacteristic
352#107—22no—
353#107—24no—
354#106—22no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357#103—22no—
358#103—24no—
359#102—22no—
360C22⋊C8C23×C512yes—
361C22⋊C8C23×C512yes—
362#97—21no—
363C4×C8—21no—
364#95—21no—
365#95—24no—
366#95—24no—
367#95C23×C512yes—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5—41no—
371C22×C5—41no—
372C22×C5—41no—
373C22×C5C2×#12011yescharacteristic
374C22×C5#57812yes—
375C4×C5—21no—
376C4×C5—21no—
377C4×C5—21no—
378C4×C5—21no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5—42no—
384C4×C5—42no—
385C4×C5—42no—
386C4×C5—41no—
387C4×C5—82no—
388C4×C5—82no—
389C4×C5#45412yes—
390C2×Q8—22no—
391C2×Q8—21no—
392C2×Q8—44no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8C2×C5×D412yes—
396C2×Q8C2×C5×D411yescharacteristic
397C2×D4—21no—
398C2×D4C2×C5×D411yescharacteristic
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4C2×C5×D412yes—
404C22×C4C2×C5×D411yescharacteristic
405C22×C4C2×C5×D411yescharacteristic
406C22×C4C2×C5×D412yes—
407C22×C4C24×C511yescharacteristic
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4C2×C5×D411yescharacteristic
440C4⋊C4C2×C5×D411yescharacteristic
441C4⋊C4C2×C5×D412yes—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—22no—
455C42—21no—
456C42—42no—
457C42C2×C5×D411yescharacteristic
458C42C2×C5×D411yescharacteristic
459C42C2×C5×D411yescharacteristic
460C42C2×C5×D411yescharacteristic
461C2×C5—22no—
462C2×C5—81no—
463C2×C5#301111yescharacteristic
464C2×C5C2×#45411yescharacteristic
465C2×C5#302811yescharacteristic
466C23—21no—
467C23C22×C5×D411yescharacteristic
468Q8—41no—
469Q8—42no—
470Q8—42no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—41no—
475D4—42no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—82no—
495C2×C4C5×#12011yescharacteristic
496C2×C4C5×#12011yescharacteristic
497C2×C4C5×#12011yescharacteristic
498C2×C4C5×#12011yescharacteristic
499C2×C4C22×C5×D411yescharacteristic
500C2×C4C22×C5×D411yescharacteristic
501C8—42no—
502C8—42no—
503C5#1844311yescharacteristic, direct product factor, Sylow
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C2×C5×#12011yescharacteristic
510C22C5×#57812yes—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—41no—
523C4—82no—
524C4—82no—
525C4C5×#45412yes—
526C2—22no—
527C2—81no—
528C2C5×#301111yescharacteristic
529C2C2×C5×#45411yescharacteristic
530C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#121C23
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
3. C5×#3230C2semidirect
4. C5×#2642C2semidirect
5. C5×#1617C2semidirect
7. C5×#1506C2semidirect
9. C5×#1470C2semidirect
47. #18443C5direct (N × H)
133. #3230C2×C5semidirect
134. #2642C2×C5semidirect
135. #1617C2×C5semidirect
137. #1506C2×C5semidirect
139. #1470C2×C5semidirect
503. C5#18443direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35632
C5×#32392
C5×#32302
C5×#26422
C5×#16172
C5×#16152
C5×#15062
C5×#15002
C5×#14702
#184435