Finite Group Databasebeta

← C5×#24069 #11946789

Subgroups — C5×#24069 #11946789

Order 1280.

1130 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
1C2×C5×#540C211yesmaximal, characteristic
2C2×C5×#481C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic, complemented
4C5×#2317C211yesmaximal, characteristic, complemented
5C5×#2059C212yesmaximal, complemented
6C5×#2041C212yesmaximal, complemented
7C5×#1875C211yesmaximal, characteristic, complemented
8C5×#1875C211yesmaximal, characteristic, complemented
9C5×#1864C212yesmaximal, complemented
10C5×#1862C212yesmaximal, complemented
11C5×#1818C211yesmaximal, characteristic, complemented
12C5×#540—24no—
13C5×#540—24no—
14C2×C5×#127C2211yescharacteristic
15C2×C5×#125C2211yescharacteristic
16C2×C5×#123—21no—
17C2×C5×#123—21no—
18C2×C5×#121—21no—
19C2×C5×#121—21no—
20C2×C5×#121C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C2×C4×C5×D4C2211yescharacteristic
24C2×C5×#117C2211yescharacteristic
25C2×C5×#117C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C5×#481—24no—
28C5×#480—24no—
29C2×C5×#107C2212yes—
30C2×C5×#106C2212yes—
31C2×C5×#102C2212yes—
32C2×C5×#102C2212yes—
33C2×C5×#102C2212yes—
34C2×C5×#102C2212yes—
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#389C2212yes—
38C5×#389C2212yes—
39C5×#385—21no—
40C5×#385—21no—
41C5×#384—21no—
42C5×#382—21no—
43C5×#340C2212yes—
44C5×#340C2212yes—
45C5×#336C2212yes—
46C5×#336C2212yes—
47#24069C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×D4—21no—
49C22×C5×D4—21no—
50C22×C5×D4—21no—
51C22×C5×D4—21no—
52C22×C5×D4C2311yescharacteristic
53C22×C5×D4C2311yescharacteristic
54C23×C4×C5—21no—
55C23×C4×C5—21no—
56C23×C4×C5—21no—
57C23×C4×C5C2311yescharacteristic
58C22×C5×C8C2312yes—
59C22×C5×C8C2312yes—
60C5×#127—22no—
61C5×#127—22no—
62C5×#125—22no—
63C5×#125—22no—
64C5×#123—28no—
65C5×#123—28no—
66C5×#121—28no—
67C5×#121—28no—
68C5×#121—22no—
69C5×#121—22no—
70C5×#121D414yes—
71C5×#121D414yes—
72C4×C5×D4—22no—
73C4×C5×D4—22no—
74C4×C5×D4—22no—
75C4×C5×D4—22no—
76C5×#117—22no—
77C5×#117—22no—
78C5×#117—24no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4D411yescharacteristic
87C2×C5×C4⋊C4D411yescharacteristic
88C2×C5×C4⋊C4C2312yes—
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2312yes—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4D411yescharacteristic
98C2×C5×C22⋊C4D411yescharacteristic
99C2×C42×C5—21no—
100C2×C42×C5C2311yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C5×#107—24no—
103C5×#106—24no—
104C5×#102—24no—
105C5×#102—24no—
106C5×#102—24no—
107C5×#102—24no—
108C5×C22⋊C8—22no—
109C5×C22⋊C8—22no—
110C5×#95—22no—
111C5×#95—22no—
112C2×#540C2×C511yescharacteristic
113C2×#481C2×C511yescharacteristic, complemented
114C2×#480C2×C511yescharacteristic, complemented
115#2317C2×C511yescharacteristic, complemented
116#2059C2×C512yescomplemented
117#2041C2×C512yescomplemented
118#1875C2×C511yescharacteristic, complemented
119#1875C2×C511yescharacteristic, complemented
120#1864C2×C512yescomplemented
121#1862C2×C512yescomplemented
122#1818C2×C511yescharacteristic, complemented
123C24×C5—21no—
124C24×C5—21no—
125C24×C5C2×D411yescharacteristic
126C2×C5×D4—24no—
127C2×C5×D4—24no—
128C2×C5×D4—24no—
129C2×C5×D4—24no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—82no—
137C2×C5×D4—82no—
138C2×C5×D4—82no—
139C2×C5×D4—82no—
140C2×C5×D4C2×D412yes—
141C2×C5×D4C2×D412yes—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—24no—
148C22×C4×C5—24no—
149C22×C4×C5—22no—
150C22×C4×C5—42no—
151C22×C4×C5—82no—
152C22×C4×C5—82no—
153C22×C4×C5—82no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2411yescharacteristic
162C2×C5×C8—22no—
163C2×C5×C8—22no—
164C2×C5×C8—22no—
165C2×C5×C8—22no—
166C2×C5×C8—22no—
167C2×C5×C8—22no—
168C5×C4⋊C4—24no—
169C5×C4⋊C4—24no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—42no—
178C5×C4⋊C4—82no—
179C5×C4⋊C4—82no—
180C5×C4⋊C4C2×D412yes—
181C5×C4⋊C4C2×D412yes—
182C5×C4⋊C4#4114yes—
183C5×C22⋊C4—24no—
184C5×C22⋊C4—24no—
185C5×C22⋊C4—24no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—24no—
189C5×C22⋊C4—24no—
190C42×C5—24no—
191C42×C5—21no—
192C42×C5—21no—
193C42×C5—21no—
194C42×C5—21no—
195#540—24no—
196#540—24no—
197C2×#127C22×C511yescharacteristic
198C2×#125C22×C511yescharacteristic
199C2×#123—21no—
200C2×#123—21no—
201C2×#121—21no—
202C2×#121—21no—
203C2×#121C22×C511yescharacteristic
204C2×#121C22×C511yescharacteristic
205C2×C4×D4C22×C511yescharacteristic
206C2×C4×D4C22×C511yescharacteristic
207C2×#117C22×C511yescharacteristic
208C2×#117C22×C511yescharacteristic
209C22×C4⋊C4C22×C511yescharacteristic
210#481—24no—
211#480—24no—
212C2×#107C22×C512yes—
213C2×#106C22×C512yes—
214C2×#102C22×C512yes—
215C2×#102C22×C512yes—
216C2×#102C22×C512yes—
217C2×#102C22×C512yes—
218C2×C22⋊C8C22×C511yescharacteristic
219C2×C22⋊C8C22×C511yescharacteristic
220#389C22×C512yes—
221#389C22×C512yes—
222#385—21no—
223#385—21no—
224#384—21no—
225#382—21no—
226#340C22×C512yes—
227#340C22×C512yes—
228#336C22×C512yes—
229#336C22×C512yes—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—22no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5—42no—
244C23×C5#12012yes—
245C23×C5C22×D411yescharacteristic
246C5×D4—24no—
247C5×D4—24no—
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—84no—
251C5×D4—84no—
252C5×D4—84no—
253C5×D4—84no—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—24no—
257C2×C4×C5—24no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—24no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—84no—
277C2×C4×C5—84no—
278C2×C4×C5—84no—
279C2×C4×C5#12012yes—
280C2×C4×C5C22×D411yescharacteristic
281C2×C4×C5C22×D411yescharacteristic
282C2×C4×C5C2×#4112yes—
283C2×C4×C52−1+412yes—
284C5×C8—42no—
285C5×C8—42no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C23×C511yescharacteristic
291C22×D4C23×C511yescharacteristic
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4C23×C511yescharacteristic
296C22×C8C23×C512yes—
297C22×C8C23×C512yes—
298#127—22no—
299#127—22no—
300#125—22no—
301#125—22no—
302#123—28no—
303#123—28no—
304#121—28no—
305#121—28no—
306#121—22no—
307#121—22no—
308#121C5×D414yes—
309#121C5×D414yes—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314#117—22no—
315#117—22no—
316#117—24no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4C5×D411yescharacteristic
325C2×C4⋊C4C5×D411yescharacteristic
326C2×C4⋊C4C23×C512yes—
327C2×C4⋊C4C23×C511yescharacteristic
328C2×C4⋊C4C23×C511yescharacteristic
329C2×C4⋊C4C23×C512yes—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4C5×D411yescharacteristic
336C2×C22⋊C4C5×D411yescharacteristic
337C2×C42—21no—
338C2×C42C23×C511yescharacteristic
339C2×C42C23×C511yescharacteristic
340#107—24no—
341#106—24no—
342#102—24no—
343#102—24no—
344#102—24no—
345#102—24no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348#95—22no—
349#95—22no—
350C22×C5—22no—
351C22×C5—22no—
352C22×C5—22no—
353C22×C5—42no—
354C22×C5—42no—
355C22×C5—42no—
356C22×C5—42no—
357C22×C5—42no—
358C22×C5—42no—
359C22×C5—42no—
360C22×C5—42no—
361C22×C5—82no—
362C22×C5—82no—
363C22×C5—82no—
364C22×C5—82no—
365C22×C5C2×#12011yescharacteristic
366C22×C5#52511yescharacteristic
367C22×C5#53611yescharacteristic
368C22×C5#57612yes—
369C22×C5#57712yes—
370C4×C5—22no—
371C4×C5—44no—
372C4×C5—41no—
373C4×C5—41no—
374C4×C5—42no—
375C4×C5—41no—
376C4×C5—41no—
377C4×C5—42no—
378C4×C5—82no—
379C4×C5#54712yes—
380C4×C5#54712yes—
381C24—21no—
382C24—21no—
383C24C2×C5×D411yescharacteristic
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—82no—
395C2×D4—82no—
396C2×D4—82no—
397C2×D4—82no—
398C2×D4C2×C5×D412yes—
399C2×D4C2×C5×D412yes—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—42no—
409C22×C4—82no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4C2×C5×D411yescharacteristic
413C22×C4C2×C5×D411yescharacteristic
414C22×C4C2×C5×D411yescharacteristic
415C22×C4C2×C5×D411yescharacteristic
416C22×C4C2×C5×D411yescharacteristic
417C22×C4C2×C5×D412yes—
418C22×C4C2×C5×D412yes—
419C22×C4C24×C511yescharacteristic
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—82no—
437C4⋊C4—82no—
438C4⋊C4C2×C5×D412yes—
439C4⋊C4C2×C5×D412yes—
440C4⋊C4C5×#4114yes—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C42—24no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—21no—
453C2×C5—42no—
454C2×C5—82no—
455C2×C5—82no—
456C2×C5#240611yescharacteristic
457C2×C5#300811yescharacteristic
458C2×C5#300911yescharacteristic
459C2×C5#311912yes—
460C2×C5#324112yes—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23C5×#12012yes—
476C23C22×C5×D411yescharacteristic
477D4—24no—
478D4—24no—
479D4—42no—
480D4—42no—
481D4—84no—
482D4—84no—
483D4—84no—
484D4—84no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—84no—
508C2×C4—84no—
509C2×C4—84no—
510C2×C4C5×#12012yes—
511C2×C4C22×C5×D411yescharacteristic
512C2×C4C22×C5×D411yescharacteristic
513C2×C4C2×C5×#4112yes—
514C2×C4C5×2−1+412yes—
515C8—42no—
516C8—42no—
517C5#2406911yescharacteristic, direct product factor, Sylow
518C22—22no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22C2×C5×#12011yescharacteristic
534C22C5×#52511yescharacteristic
535C22C5×#53611yescharacteristic
536C22C5×#57612yes—
537C22C5×#57712yes—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—42no—
545C4—44no—
546C4—82no—
547C4C5×#54712yes—
548C4C5×#54712yes—
549C2—42no—
550C2—82no—
551C2—82no—
552C2C5×#240611yescharacteristic
553C2C5×#300811yescharacteristic
554C2C5×#300911yescharacteristic
555C2C5×#311912yes—
556C2C5×#324112yes—
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#481C2semidirect
3. C2×C5×#480C2semidirect
4. C5×#2317C2semidirect
5. C5×#2059C2semidirect
6. C5×#2041C2semidirect
7. C5×#1875C2semidirect
8. C5×#1875C2semidirect
9. C5×#1864C2semidirect
10. C5×#1862C2semidirect
11. C5×#1818C2semidirect
47. #24069C5direct (N × H)
113. C2×#481C2×C5semidirect
114. C2×#480C2×C5semidirect
115. #2317C2×C5semidirect
116. #2059C2×C5semidirect
117. #2041C2×C5semidirect
118. #1875C2×C5semidirect
119. #1875C2×C5semidirect
120. #1864C2×C5semidirect
121. #1862C2×C5semidirect
122. #1818C2×C5semidirect
517. C5#24069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5402
C2×C5×#4812
C2×C5×#4802
C5×#23172
C5×#20592
C5×#20412
C5×#18752
C5×#18642
C5×#18622
C5×#18182
#240695