Finite Group Databasebeta

← C5×#24071 #11946791

Subgroups — C5×#24071 #11946791

Order 1280.

1002 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#541C211yesmaximal, characteristic
2C2×C5×#484C211yesmaximal, characteristic
3C2×C5×#483C211yesmaximal, characteristic
4C5×#2317C211yesmaximal, characteristic
5C5×#2059C212yesmaximal, complemented
6C5×#2043C212yesmaximal, complemented
7C5×#1873C211yesmaximal, characteristic
8C5×#1873C211yesmaximal, characteristic
9C5×#1865C212yesmaximal, complemented
10C5×#1863C212yesmaximal, complemented
11C5×#1818C211yesmaximal, characteristic
12C5×#541—24no—
13C5×#541—24no—
14C2×C5×C4⋊Q8C2211yescharacteristic
15C2×C5×#126—21no—
16C2×C5×#126—21no—
17C2×C5×#125—21no—
18C2×C5×#125—21no—
19C2×C5×#125C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×Q8C2211yescharacteristic
24C2×C5×#117C2211yescharacteristic
25C2×C5×#117C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C5×#484—24no—
28C5×#483—24no—
29C2×C5×#107C2212yes—
30C2×C5×#106C2212yes—
31C2×C5×#103C2212yes—
32C2×C5×#103C2212yes—
33C2×C5×#103C2212yes—
34C2×C5×#103C2212yes—
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#24071C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8C2311yescharacteristic
49C22×C5×Q8C2311yescharacteristic
50C23×C4×C5—21no—
51C23×C4×C5C2311yescharacteristic
52C22×C5×C8C2312yes—
53C22×C5×C8C2312yes—
54C5×C4⋊Q8—22no—
55C5×C4⋊Q8—22no—
56C5×#126—28no—
57C5×#126—28no—
58C5×#125—28no—
59C5×#125—28no—
60C5×#125—22no—
61C5×#125—22no—
62C5×C22⋊Q8—22no—
63C5×C22⋊Q8—22no—
64C5×C22⋊Q8D414yes—
65C5×C22⋊Q8D414yes—
66C4×C5×Q8—22no—
67C4×C5×Q8—22no—
68C4×C5×Q8—22no—
69C4×C5×Q8—22no—
70C5×#117—22no—
71C5×#117—22no—
72C5×#117—24no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
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⋊C4D411yescharacteristic
96C2×C5×C22⋊C4D411yescharacteristic
97C2×C42×C5—21no—
98C2×C42×C5—21no—
99C2×C42×C5—21no—
100C2×C42×C5C2311yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C5×#107—24no—
103C5×#106—24no—
104C5×#103—24no—
105C5×#103—24no—
106C5×#103—24no—
107C5×#103—24no—
108C5×C22⋊C8—22no—
109C5×C22⋊C8—22no—
110C5×#95—22no—
111C5×#95—22no—
112C2×#541C2×C511yescharacteristic
113C2×#484C2×C511yescharacteristic
114C2×#483C2×C511yescharacteristic
115#2317C2×C511yescharacteristic
116#2059C2×C512yescomplemented
117#2043C2×C512yescomplemented
118#1873C2×C511yescharacteristic
119#1873C2×C511yescharacteristic
120#1865C2×C512yescomplemented
121#1863C2×C512yescomplemented
122#1818C2×C511yescharacteristic
123C24×C5C2×D411yescharacteristic
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—22no—
127C2×C5×Q8—22no—
128C2×C5×Q8—22no—
129C2×C5×Q8—22no—
130C2×C5×Q8C2×D412yes—
131C2×C5×Q8C2×D412yes—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—42no—
141C22×C4×C5—82no—
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D412yes—
148C22×C4×C5C2×D412yes—
149C22×C4×C5C2411yescharacteristic
150C2×C5×C8—22no—
151C2×C5×C8—22no—
152C2×C5×C8—22no—
153C2×C5×C8—22no—
154C2×C5×C8—22no—
155C2×C5×C8—22no—
156C5×C4⋊C4—24no—
157C5×C4⋊C4—24no—
158C5×C4⋊C4—24no—
159C5×C4⋊C4—24no—
160C5×C4⋊C4—24no—
161C5×C4⋊C4—24no—
162C5×C4⋊C4—24no—
163C5×C4⋊C4—24no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—42no—
172C5×C4⋊C4—82no—
173C5×C4⋊C4—82no—
174C5×C4⋊C4C2×D412yes—
175C5×C4⋊C4C2×D412yes—
176C5×C4⋊C4#4114yes—
177C5×C22⋊C4—24no—
178C5×C22⋊C4—24no—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C42×C5—24no—
183C42×C5—24no—
184C42×C5—24no—
185C42×C5—21no—
186C42×C5—21no—
187C42×C5—21no—
188C42×C5—21no—
189#541—24no—
190#541—24no—
191C2×C4⋊Q8C22×C511yescharacteristic
192C2×#126—21no—
193C2×#126—21no—
194C2×#125—21no—
195C2×#125—21no—
196C2×#125C22×C511yescharacteristic
197C2×C22⋊Q8C22×C511yescharacteristic
198C2×C22⋊Q8C22×C511yescharacteristic
199C2×C4×Q8C22×C511yescharacteristic
200C2×C4×Q8C22×C511yescharacteristic
201C2×#117C22×C511yescharacteristic
202C2×#117C22×C511yescharacteristic
203C22×C4⋊C4C22×C511yescharacteristic
204#484—24no—
205#483—24no—
206C2×#107C22×C512yes—
207C2×#106C22×C512yes—
208C2×#103C22×C512yes—
209C2×#103C22×C512yes—
210C2×#103C22×C512yes—
211C2×#103C22×C512yes—
212C2×C22⋊C8C22×C511yescharacteristic
213C2×C22⋊C8C22×C511yescharacteristic
214#389C22×C512yes—
215#389C22×C512yes—
216#385—21no—
217#385—21no—
218#384—21no—
219#382—21no—
220#340C22×C512yes—
221#340C22×C512yes—
222#336C22×C512yes—
223#336C22×C512yes—
224C23×C5—21no—
225C23×C5—21no—
226C23×C5—22no—
227C23×C5—22no—
228C23×C5#12012yes—
229C23×C5C22×D411yescharacteristic
230C5×Q8—24no—
231C5×Q8—24no—
232C5×Q8—42no—
233C5×Q8—42no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—24no—
237C2×C4×C5—24no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5—24no—
247C2×C4×C5—22no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—84no—
263C2×C4×C5#12012yes—
264C2×C4×C5C22×D411yescharacteristic
265C2×C4×C5C22×D411yescharacteristic
266C2×C4×C5C2×#4112yes—
267C2×C4×C52−1+412yes—
268C5×C8—42no—
269C5×C8—42no—
270C22×Q8C23×C511yescharacteristic
271C22×Q8C23×C511yescharacteristic
272C23×C4—21no—
273C23×C4C23×C511yescharacteristic
274C22×C8C23×C512yes—
275C22×C8C23×C512yes—
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278#126—28no—
279#126—28no—
280#125—28no—
281#125—28no—
282#125—22no—
283#125—22no—
284C22⋊Q8—22no—
285C22⋊Q8—22no—
286C22⋊Q8C5×D414yes—
287C22⋊Q8C5×D414yes—
288C4×Q8—22no—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×Q8—22no—
292#117—22no—
293#117—22no—
294#117—24no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4C5×D411yescharacteristic
309C2×C4⋊C4C5×D411yescharacteristic
310C2×C4⋊C4C23×C512yes—
311C2×C4⋊C4C23×C511yescharacteristic
312C2×C4⋊C4C23×C511yescharacteristic
313C2×C4⋊C4C23×C512yes—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4C5×D411yescharacteristic
318C2×C22⋊C4C5×D411yescharacteristic
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42C23×C511yescharacteristic
323C2×C42C23×C511yescharacteristic
324#107—24no—
325#106—24no—
326#103—24no—
327#103—24no—
328#103—24no—
329#103—24no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332#95—22no—
333#95—22no—
334C22×C5—22no—
335C22×C5—22no—
336C22×C5—22no—
337C22×C5—42no—
338C22×C5—42no—
339C22×C5C2×#12011yescharacteristic
340C22×C5#52511yescharacteristic
341C22×C5#53611yescharacteristic
342C22×C5#57712yes—
343C22×C5#57812yes—
344C4×C5—22no—
345C4×C5—44no—
346C4×C5—42no—
347C4×C5—42no—
348C4×C5—41no—
349C4×C5—41no—
350C4×C5—42no—
351C4×C5—41no—
352C4×C5—41no—
353C4×C5—42no—
354C4×C5—82no—
355C4×C5#54712yes—
356C4×C5#54712yes—
357C24C2×C5×D411yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8C2×C5×D412yes—
365C2×Q8C2×C5×D412yes—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—82no—
376C22×C4C2×C5×D411yescharacteristic
377C22×C4C2×C5×D411yescharacteristic
378C22×C4C2×C5×D411yescharacteristic
379C22×C4C2×C5×D411yescharacteristic
380C22×C4C2×C5×D411yescharacteristic
381C22×C4C2×C5×D412yes—
382C22×C4C2×C5×D412yes—
383C22×C4C24×C511yescharacteristic
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—42no—
406C4⋊C4—82no—
407C4⋊C4—82no—
408C4⋊C4C2×C5×D412yes—
409C4⋊C4C2×C5×D412yes—
410C4⋊C4C5×#4114yes—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C42—24no—
417C42—24no—
418C42—24no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—21no—
423C2×C5—42no—
424C2×C5#240611yescharacteristic
425C2×C5#301011yescharacteristic
426C2×C5#301111yescharacteristic
427C2×C5#312012yes—
428C2×C5#324212yes—
429C23—21no—
430C23—21no—
431C23—22no—
432C23—22no—
433C23C5×#12012yes—
434C23C22×C5×D411yescharacteristic
435Q8—24no—
436Q8—24no—
437Q8—42no—
438Q8—42no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—84no—
468C2×C4C5×#12012yes—
469C2×C4C22×C5×D411yescharacteristic
470C2×C4C22×C5×D411yescharacteristic
471C2×C4C2×C5×#4112yes—
472C2×C4C5×2−1+412yes—
473C8—42no—
474C8—42no—
475C5#2407111yescharacteristic, direct product factor, Sylow
476C22—22no—
477C22—22no—
478C22—22no—
479C22—42no—
480C22—42no—
481C22C2×C5×#12011yescharacteristic
482C22C5×#52511yescharacteristic
483C22C5×#53611yescharacteristic
484C22C5×#57712yes—
485C22C5×#57812yes—
486C4—22no—
487C4—41no—
488C4—41no—
489C4—42no—
490C4—41no—
491C4—41no—
492C4—42no—
493C4—44no—
494C4—42no—
495C4—42no—
496C4—82no—
497C4C5×#54712yes—
498C4C5×#54712yes—
499C2—42no—
500C2C5×#240611yescharacteristic
501C2C5×#301011yescharacteristic
502C2C5×#301111yescharacteristic
503C2C5×#312012yes—
504C2C5×#324212yes—
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
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
5. C5×#2059C2semidirect
6. C5×#2043C2semidirect
9. C5×#1865C2semidirect
10. C5×#1863C2semidirect
47. #24071C5direct (N × H)
116. #2059C2×C5semidirect
117. #2043C2×C5semidirect
120. #1865C2×C5semidirect
121. #1863C2×C5semidirect
475. C5#24071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5412
C2×C5×#4842
C2×C5×#4832
C5×#23172
C5×#20592
C5×#20432
C5×#18732
C5×#18652
C5×#18632
C5×#18182
#240715