Finite Group Databasebeta

← C5×#24073 #11946793

Subgroups — C5×#24073 #11946793

Order 1280.

1066 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
1C2×C5×#542C211yesmaximal, characteristic
2C2×C5×#484C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic
4C5×#2317C211yesmaximal, characteristic, complemented
5C5×#2057C212yesmaximal, complemented
6C5×#2042C212yesmaximal, complemented
7C5×#1875C211yesmaximal, characteristic
8C5×#1873C211yesmaximal, characteristic, complemented
9C5×#1863C212yesmaximal, complemented
10C5×#1862C212yesmaximal, complemented
11C5×#1818C211yesmaximal, characteristic, complemented
12C5×#542—24no—
13C5×#542—24no—
14C2×C5×C4⋊Q8C2211yescharacteristic
15C2×C5×#126—21no—
16C2×C5×#124—21no—
17C2×C5×#124C2211yescharacteristic
18C2×C5×#123—21no—
19C2×C5×C22⋊Q8—21no—
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×D4C2211yescharacteristic
24C2×C5×#117C2211yescharacteristic
25C2×C5×#117C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C5×#484—24no—
28C5×#480—24no—
29C2×C5×#107C2212yes—
30C2×C5×#107C2212yes—
31C2×C5×#103C2212yes—
32C2×C5×#103C2212yes—
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#24073C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C22×C5×Q8C2311yescharacteristic
50C22×C5×D4—21no—
51C22×C5×D4C2311yescharacteristic
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C23×C4×C5C2311yescharacteristic
55C22×C5×C8C2312yes—
56C22×C5×C8C2312yes—
57C5×C4⋊Q8—22no—
58C5×C4⋊Q8—22no—
59C5×#126—28no—
60C5×#124—28no—
61C5×#124—22no—
62C5×#124—22no—
63C5×#123—28no—
64C5×C22⋊Q8—28no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8D414yes—
67C5×#121—22no—
68C5×#121D414yes—
69C4×C5×Q8—22no—
70C4×C5×Q8—22no—
71C4×C5×D4—22no—
72C4×C5×D4—22no—
73C5×#117—22no—
74C5×#117—22no—
75C5×#117—24no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4D411yescharacteristic
85C2×C5×C4⋊C4D411yescharacteristic
86C2×C5×C4⋊C4C2312yes—
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2312yes—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4D411yescharacteristic
97C2×C5×C22⋊C4D411yescharacteristic
98C2×C42×C5—21no—
99C2×C42×C5—21no—
100C2×C42×C5C2311yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C5×#107—24no—
103C5×#107—24no—
104C5×#103—24no—
105C5×#103—24no—
106C5×#102—24no—
107C5×#102—24no—
108C5×C22⋊C8—22no—
109C5×C22⋊C8—22no—
110C5×#95—22no—
111C5×#95—22no—
112C2×#542C2×C511yescharacteristic
113C2×#484C2×C511yescharacteristic, complemented
114C2×#480C2×C511yescharacteristic
115#2317C2×C511yescharacteristic, complemented
116#2057C2×C512yescomplemented
117#2042C2×C512yescomplemented
118#1875C2×C511yescharacteristic
119#1873C2×C511yescharacteristic, complemented
120#1863C2×C512yescomplemented
121#1862C2×C512yescomplemented
122#1818C2×C511yescharacteristic, complemented
123C24×C5—21no—
124C24×C5C2×D411yescharacteristic
125C2×C5×Q8—24no—
126C2×C5×Q8—21no—
127C2×C5×Q8—22no—
128C2×C5×Q8—22no—
129C2×C5×Q8—82no—
130C2×C5×Q8C2×D412yes—
131C2×C5×D4—24no—
132C2×C5×D4—21no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—82no—
136C2×C5×D4C2×D412yes—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—21no—
143C22×C4×C5—24no—
144C22×C4×C5—22no—
145C22×C4×C5—42no—
146C22×C4×C5—82no—
147C22×C4×C5—82no—
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D412yes—
155C22×C4×C5C2411yescharacteristic
156C2×C5×C8—22no—
157C2×C5×C8—22no—
158C2×C5×C8—22no—
159C2×C5×C8—22no—
160C2×C5×C8—22no—
161C2×C5×C8—22no—
162C5×C4⋊C4—24no—
163C5×C4⋊C4—24no—
164C5×C4⋊C4—24no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—42no—
173C5×C4⋊C4—82no—
174C5×C4⋊C4—82no—
175C5×C4⋊C4C2×D412yes—
176C5×C4⋊C4C2×D412yes—
177C5×C4⋊C4#4114yes—
178C5×C22⋊C4—24no—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—24no—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—24no—
186C42×C5—24no—
187C42×C5—24no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5—21no—
191C42×C5—21no—
192#542—24no—
193#542—24no—
194C2×C4⋊Q8C22×C511yescharacteristic
195C2×#126—21no—
196C2×#124—21no—
197C2×#124C22×C511yescharacteristic
198C2×#123—21no—
199C2×C22⋊Q8—21no—
200C2×C22⋊Q8C22×C511yescharacteristic
201C2×#121C22×C511yescharacteristic
202C2×C4×Q8C22×C511yescharacteristic
203C2×C4×D4C22×C511yescharacteristic
204C2×#117C22×C511yescharacteristic
205C2×#117C22×C511yescharacteristic
206C22×C4⋊C4C22×C511yescharacteristic
207#484—24no—
208#480—24no—
209C2×#107C22×C512yes—
210C2×#107C22×C512yes—
211C2×#103C22×C512yes—
212C2×#103C22×C512yes—
213C2×#102C22×C512yes—
214C2×#102C22×C512yes—
215C2×C22⋊C8C22×C511yescharacteristic
216C2×C22⋊C8C22×C511yescharacteristic
217#389C22×C512yes—
218#389C22×C512yes—
219#385—21no—
220#385—21no—
221#384—21no—
222#382—21no—
223#340C22×C512yes—
224#340C22×C512yes—
225#336C22×C512yes—
226#336C22×C512yes—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5—22no—
230C23×C5—22no—
231C23×C5—22no—
232C23×C5—41no—
233C23×C5—41no—
234C23×C5—42no—
235C23×C5—42no—
236C23×C5#12012yes—
237C23×C5C22×D411yescharacteristic
238C5×Q8—24no—
239C5×Q8—42no—
240C5×Q8—84no—
241C5×D4—24no—
242C5×D4—42no—
243C5×D4—84no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—24no—
247C2×C4×C5—24no—
248C2×C4×C5—21no—
249C2×C4×C5—21no—
250C2×C4×C5—22no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—24no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—84no—
270C2×C4×C5—84no—
271C2×C4×C5#12012yes—
272C2×C4×C5C22×D411yescharacteristic
273C2×C4×C5C22×D411yescharacteristic
274C2×C4×C5C2×#4112yes—
275C2×C4×C52−1+412yes—
276C5×C8—42no—
277C5×C8—42no—
278C22×Q8—21no—
279C22×Q8C23×C511yescharacteristic
280C22×D4—21no—
281C22×D4C23×C511yescharacteristic
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C23×C511yescharacteristic
285C22×C8C23×C512yes—
286C22×C8C23×C512yes—
287C4⋊Q8—22no—
288C4⋊Q8—22no—
289#126—28no—
290#124—28no—
291#124—22no—
292#124—22no—
293#123—28no—
294C22⋊Q8—28no—
295C22⋊Q8—22no—
296C22⋊Q8C5×D414yes—
297#121—22no—
298#121C5×D414yes—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×D4—22no—
302C4×D4—22no—
303#117—22no—
304#117—22no—
305#117—24no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4C5×D411yescharacteristic
315C2×C4⋊C4C5×D411yescharacteristic
316C2×C4⋊C4C23×C512yes—
317C2×C4⋊C4C23×C511yescharacteristic
318C2×C4⋊C4C23×C511yescharacteristic
319C2×C4⋊C4C23×C512yes—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4C5×D411yescharacteristic
327C2×C22⋊C4C5×D411yescharacteristic
328C2×C42—21no—
329C2×C42—21no—
330C2×C42C23×C511yescharacteristic
331C2×C42C23×C511yescharacteristic
332#107—24no—
333#107—24no—
334#103—24no—
335#103—24no—
336#102—24no—
337#102—24no—
338C22⋊C8—22no—
339C22⋊C8—22no—
340#95—22no—
341#95—22no—
342C22×C5—22no—
343C22×C5—22no—
344C22×C5—22no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5—42no—
349C22×C5—42no—
350C22×C5—82no—
351C22×C5—82no—
352C22×C5C2×#12011yescharacteristic
353C22×C5#52511yescharacteristic
354C22×C5#53611yescharacteristic
355C22×C5#57612yes—
356C22×C5#57812yes—
357C4×C5—22no—
358C4×C5—44no—
359C4×C5—42no—
360C4×C5—41no—
361C4×C5—41no—
362C4×C5—42no—
363C4×C5—42no—
364C4×C5—41no—
365C4×C5—41no—
366C4×C5—82no—
367C4×C5#54712yes—
368C4×C5#54712yes—
369C24—21no—
370C24C2×C5×D411yescharacteristic
371C2×Q8—24no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—82no—
376C2×Q8C2×C5×D412yes—
377C2×D4—24no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—82no—
382C2×D4C2×C5×D412yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—82no—
393C22×C4—82no—
394C22×C4C2×C5×D411yescharacteristic
395C22×C4C2×C5×D411yescharacteristic
396C22×C4C2×C5×D411yescharacteristic
397C22×C4C2×C5×D411yescharacteristic
398C22×C4C2×C5×D411yescharacteristic
399C22×C4C2×C5×D412yes—
400C22×C4C2×C5×D412yes—
401C22×C4C24×C511yescharacteristic
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—42no—
419C4⋊C4—82no—
420C4⋊C4—82no—
421C4⋊C4C2×C5×D412yes—
422C4⋊C4C2×C5×D412yes—
423C4⋊C4C5×#4114yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—24no—
432C42—24no—
433C42—24no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42—21no—
438C2×C5—42no—
439C2×C5—82no—
440C2×C5#240611yescharacteristic
441C2×C5#300811yescharacteristic
442C2×C5#301111yescharacteristic
443C2×C5#312412yes—
444C2×C5#324312yes—
445C23—21no—
446C23—21no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—41no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23C5×#12012yes—
455C23C22×C5×D411yescharacteristic
456Q8—24no—
457Q8—42no—
458Q8—84no—
459D4—24no—
460D4—42no—
461D4—84no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—84no—
488C2×C4—84no—
489C2×C4C5×#12012yes—
490C2×C4C22×C5×D411yescharacteristic
491C2×C4C22×C5×D411yescharacteristic
492C2×C4C2×C5×#4112yes—
493C2×C4C5×2−1+412yes—
494C8—42no—
495C8—42no—
496C5#2407311yescharacteristic, direct product factor, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—82no—
506C22—82no—
507C22C2×C5×#12011yescharacteristic
508C22C5×#52511yescharacteristic
509C22C5×#53611yescharacteristic
510C22C5×#57612yes—
511C22C5×#57812yes—
512C4—22no—
513C4—41no—
514C4—41no—
515C4—42no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—44no—
520C4—42no—
521C4—82no—
522C4C5×#54712yes—
523C4C5×#54712yes—
524C2—42no—
525C2—82no—
526C2C5×#240611yescharacteristic
527C2C5×#300811yescharacteristic
528C2C5×#301111yescharacteristic
529C2C5×#312412yes—
530C2C5×#324312yes—
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
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×#484C2semidirect
4. C5×#2317C2semidirect
5. C5×#2057C2semidirect
6. C5×#2042C2semidirect
8. C5×#1873C2semidirect
9. C5×#1863C2semidirect
10. C5×#1862C2semidirect
11. C5×#1818C2semidirect
47. #24073C5direct (N × H)
113. C2×#484C2×C5semidirect
115. #2317C2×C5semidirect
116. #2057C2×C5semidirect
117. #2042C2×C5semidirect
119. #1873C2×C5semidirect
120. #1863C2×C5semidirect
121. #1862C2×C5semidirect
122. #1818C2×C5semidirect
496. C5#24073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×C5×#4842
C2×C5×#4802
C5×#23172
C5×#20572
C5×#20422
C5×#18752
C5×#18732
C5×#18632
C5×#18622
C5×#18182
#240735