Finite Group Databasebeta

← C5×#24098 #11946818

Subgroups — C5×#24098 #11946818

Order 1280.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic
2C2×C5×#484C211yesmaximal, characteristic, complemented
3C22×C5×#107C211yesmaximal, characteristic, complemented
4C5×#2487C211yesmaximal, characteristic
5C5×#2057C212yesmaximal, complemented
6C5×#2036C212yesmaximal, complemented
7C5×#1892C211yesmaximal, characteristic, complemented
8C5×#1869C211yesmaximal, characteristic
9C5×#1863C212yesmaximal, complemented
10C5×#1852C212yesmaximal, complemented
11C5×#1824C211yesmaximal, characteristic, complemented
12C23×C5×C8C2211yescharacteristic
13C5×#554—24no—
14C5×#554—24no—
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C5×#125—21no—
17C2×C5×C22⋊Q8—21no—
18C2×C5×C22⋊Q8—21no—
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C4×C5×Q8C2211yescharacteristic
22C2×C4×C5×D4—21no—
23C2×C4×C5×D4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C5×#484—24no—
28C2×C5×#107—24no—
29C2×C5×#107C2212yes—
30C2×C5×#107C2212yes—
31C2×C5×#107C2212yes—
32C2×C5×#103C2212yes—
33C2×C5×#103C2212yes—
34C2×C5×C22⋊C8C2212yes—
35C2×C5×C22⋊C8C2211yescharacteristic
36C5×#400—21no—
37C5×#399—21no—
38C5×#389C2212yes—
39C5×#386—21no—
40C5×#385—21no—
41C5×#380C2212yes—
42C5×#380C2211yescharacteristic
43C5×#340C2212yes—
44C5×#340C2212yes—
45C5×#340C2212yes—
46C5×#336C2212yes—
47#24098C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C22×C5×Q8C2311yescharacteristic
50C22×C5×D4D411yescharacteristic
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C22×C5×C8—22no—
57C22×C5×C8—24no—
58C22×C5×C8C2312yes—
59C22×C5×C8C2312yes—
60C5×C4⋊Q8—22no—
61C5×C4⋊Q8—22no—
62C5×#125—28no—
63C5×C22⋊Q8—28no—
64C5×C22⋊Q8—28no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8—22no—
67C5×C22⋊Q8—22no—
68C5×C22⋊Q8D414yes—
69C4×C5×Q8—22no—
70C4×C5×Q8—22no—
71C4×C5×D4—28no—
72C4×C5×D4—22no—
73C4×C5×D4—22no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—22no—
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—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4D411yescharacteristic
88C2×C5×C4⋊C4D414yes—
89C2×C5×C4⋊C4C2312yes—
90C2×C5×C4⋊C4C2312yes—
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4D411yescharacteristic
99C2×C5×C22⋊C4D411yescharacteristic
100C2×C42×C5—21no—
101C2×C42×C5C2311yescharacteristic
102C5×#107—24no—
103C5×#107—24no—
104C5×#107—24no—
105C5×#103—24no—
106C5×#103—24no—
107C5×C22⋊C8—22no—
108C5×C22⋊C8—24no—
109C5×#95—22no—
110C5×#95—21no—
111C5×#95—22no—
112C2×#554C2×C511yescharacteristic
113C2×#484C2×C511yescharacteristic, complemented
114C22×#107C2×C511yescharacteristic, complemented
115#2487C2×C511yescharacteristic
116#2057C2×C512yescomplemented
117#2036C2×C512yescomplemented
118#1892C2×C511yescharacteristic, complemented
119#1869C2×C511yescharacteristic
120#1863C2×C512yescomplemented
121#1852C2×C512yescomplemented
122#1824C2×C511yescharacteristic, complemented
123C24×C5C2×D411yescharacteristic
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—22no—
132C2×C5×D4—22no—
133C2×C5×D4Q1614yes—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—24no—
141C22×C4×C5—24no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—42no—
149C22×C4×C5—82no—
150C22×C4×C5—82no—
151C22×C4×C5—82no—
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2411yescharacteristic
159C2×C5×C8—28no—
160C2×C5×C8—22no—
161C2×C5×C8—22no—
162C2×C5×C8—22no—
163C2×C5×C8—22no—
164C2×C5×C8—22no—
165C2×C5×C8#4114yes—
166C5×C4⋊C4—24no—
167C5×C4⋊C4—24no—
168C5×C4⋊C4—24no—
169C5×C4⋊C4—24no—
170C5×C4⋊C4—24no—
171C5×C4⋊C4—24no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—42no—
181C5×C4⋊C4—82no—
182C5×C4⋊C4C2×D412yes—
183C5×C4⋊C4C2×D412yes—
184C5×C4⋊C4C2×D412yes—
185C5×C22⋊C4—24no—
186C5×C22⋊C4—24no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—42no—
190C5×C22⋊C4—82no—
191C42×C5—24no—
192C42×C5—21no—
193C42×C5—21no—
194C23×C8C22×C511yescharacteristic
195#554—24no—
196#554—24no—
197C2×C4⋊Q8C22×C511yescharacteristic
198C2×#125—21no—
199C2×C22⋊Q8—21no—
200C2×C22⋊Q8—21no—
201C2×C22⋊Q8C22×C511yescharacteristic
202C2×C22⋊Q8C22×C511yescharacteristic
203C2×C4×Q8C22×C511yescharacteristic
204C2×C4×D4—21no—
205C2×C4×D4C22×C511yescharacteristic
206C22×C4⋊C4C22×C511yescharacteristic
207C22×C4⋊C4C22×C511yescharacteristic
208C22×C4⋊C4C22×C511yescharacteristic
209#484—24no—
210C2×#107—24no—
211C2×#107C22×C512yes—
212C2×#107C22×C512yes—
213C2×#107C22×C512yes—
214C2×#103C22×C512yes—
215C2×#103C22×C512yes—
216C2×C22⋊C8C22×C511yescharacteristic
217C2×C22⋊C8C22×C512yes—
218#400—21no—
219#399—21no—
220#389C22×C512yes—
221#386—21no—
222#385—21no—
223#380C22×C511yescharacteristic
224#380C22×C512yes—
225#340C22×C512yes—
226#340C22×C512yes—
227#340C22×C512yes—
228#336C22×C512yes—
229C23×C5—22no—
230C23×C5—22no—
231C23×C5—21no—
232C23×C5—22no—
233C23×C5—21no—
234C23×C5—22no—
235C23×C5#12012yes—
236C23×C5C2×Q1612yes—
237C23×C5C2×Q1612yes—
238C23×C5#13712yes—
239C23×C5C22×D411yescharacteristic
240C5×Q8—24no—
241C5×Q8—41no—
242C5×Q8—41no—
243C5×Q8—84no—
244C5×D4—28no—
245C2×C4×C5—21no—
246C2×C4×C5—22no—
247C2×C4×C5—21no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—24no—
251C2×C4×C5—22no—
252C2×C4×C5—21no—
253C2×C4×C5—22no—
254C2×C4×C5—21no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—84no—
273C2×C4×C5—84no—
274C2×C4×C5—84no—
275C2×C4×C5#12012yes—
276C2×C4×C5C2×Q1612yes—
277C2×C4×C5C22×D411yescharacteristic
278C2×C4×C5C22×D411yescharacteristic
279C2×C4×C5C2×#4112yes—
280C2×C4×C52−1+412yes—
281C5×C8—24no—
282C5×C8—42no—
283C22×Q8—21no—
284C22×Q8C23×C511yescharacteristic
285C22×D4C5×D411yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4C23×C511yescharacteristic
290C23×C4C23×C511yescharacteristic
291C22×C8—22no—
292C22×C8—24no—
293C22×C8C23×C512yes—
294C22×C8C23×C512yes—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297#125—28no—
298C22⋊Q8—28no—
299C22⋊Q8—28no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C22⋊Q8C5×D414yes—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×D4—28no—
307C4×D4—22no—
308C4×D4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4C5×D411yescharacteristic
323C2×C4⋊C4C5×D414yes—
324C2×C4⋊C4C23×C512yes—
325C2×C4⋊C4C23×C512yes—
326C2×C4⋊C4C23×C511yescharacteristic
327C2×C4⋊C4C23×C511yescharacteristic
328C2×C4⋊C4C23×C511yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4C5×D411yescharacteristic
334C2×C22⋊C4C5×D411yescharacteristic
335C2×C42—21no—
336C2×C42C23×C511yescharacteristic
337#107—24no—
338#107—24no—
339#107—24no—
340#103—24no—
341#103—24no—
342C22⋊C8—22no—
343C22⋊C8—24no—
344#95—22no—
345#95—21no—
346#95—22no—
347C22×C5—24no—
348C22×C5—24no—
349C22×C5—22no—
350C22×C5—22no—
351C22×C5—24no—
352C22×C5—22no—
353C22×C5—42no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5#45114yes—
357C22×C5C2×#12011yescharacteristic
358C22×C5#54712yes—
359C22×C5C22×Q1611yescharacteristic
360C22×C5C2×#13711yescharacteristic
361C22×C5#57612yes—
362C4×C5—22no—
363C4×C5—22no—
364C4×C5—41no—
365C4×C5—42no—
366C4×C5—41no—
367C4×C5—42no—
368C4×C5—42no—
369C4×C5—42no—
370C4×C5—82no—
371C4×C5—82no—
372C4×C5#52511yescharacteristic
373C4×C5#53611yescharacteristic
374C4×C5#54712yes—
375C24C2×C5×D411yescharacteristic
376C24C2×C5×D411yescharacteristic
377C2×Q8—24no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—82no—
382C2×Q8C2×C5×D412yes—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4C5×Q1614yes—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—82no—
402C22×C4—82no—
403C22×C4—82no—
404C22×C4C2×C5×D411yescharacteristic
405C22×C4C2×C5×D411yescharacteristic
406C22×C4C2×C5×D411yescharacteristic
407C22×C4C2×C5×D412yes—
408C22×C4C2×C5×D412yes—
409C22×C4C2×C5×D411yescharacteristic
410C22×C4C24×C511yescharacteristic
411C2×C8—28no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8C5×#4114yes—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—42no—
433C4⋊C4—82no—
434C4⋊C4C2×C5×D412yes—
435C4⋊C4C2×C5×D412yes—
436C4⋊C4C2×C5×D412yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—42no—
442C22⋊C4—82no—
443C42—24no—
444C42—21no—
445C42—21no—
446C2×C5—24no—
447C2×C5—42no—
448C2×C5#240611yescharacteristic
449C2×C5C2×#45111yescharacteristic
450C2×C5#300811yescharacteristic
451C2×C5#333812yes—
452C2×C5#334612yes—
453C23—22no—
454C23—22no—
455C23—21no—
456C23—22no—
457C23—21no—
458C23—22no—
459C23C5×#12012yes—
460C23C2×C5×Q1612yes—
461C23C2×C5×Q1612yes—
462C23C5×#13712yes—
463C23C22×C5×D411yescharacteristic
464Q8—24no—
465Q8—41no—
466Q8—41no—
467Q8—84no—
468D4—28no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—84no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4C5×#12012yes—
500C2×C4C2×C5×Q1612yes—
501C2×C4C22×C5×D411yescharacteristic
502C2×C4C22×C5×D411yescharacteristic
503C2×C4C2×C5×#4112yes—
504C2×C4C5×2−1+412yes—
505C8—24no—
506C8—42no—
507C5#2409811yescharacteristic, direct product factor, Sylow
508C22—22no—
509C22—24no—
510C22—24no—
511C22—22no—
512C22—22no—
513C22—24no—
514C22—41no—
515C22—42no—
516C22—41no—
517C22C5×#45114yes—
518C22C2×C5×#12011yescharacteristic
519C22C5×#54712yes—
520C22C22×C5×Q1611yescharacteristic
521C22C2×C5×#13711yescharacteristic
522C22C5×#57612yes—
523C4—22no—
524C4—22no—
525C4—41no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—41no—
530C4—42no—
531C4—82no—
532C4—82no—
533C4C5×#52511yescharacteristic
534C4C5×#53611yescharacteristic
535C4C5×#54712yes—
536C2—24no—
537C2—42no—
538C2C5×#240611yescharacteristic
539C2C2×C5×#45111yescharacteristic
540C2C5×#300811yescharacteristic
541C2C5×#333812yes—
542C2C5×#334612yes—
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#484C2semidirect
3. C22×C5×#107C2semidirect
5. C5×#2057C2semidirect
6. C5×#2036C2semidirect
7. C5×#1892C2semidirect
9. C5×#1863C2semidirect
10. C5×#1852C2semidirect
11. C5×#1824C2semidirect
47. #24098C5direct (N × H)
113. C2×#484C2×C5semidirect
114. C22×#107C2×C5semidirect
116. #2057C2×C5semidirect
117. #2036C2×C5semidirect
118. #1892C2×C5semidirect
120. #1863C2×C5semidirect
121. #1852C2×C5semidirect
122. #1824C2×C5semidirect
507. C5#24098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×C5×#4842
C22×C5×#1072
C5×#24872
C5×#20572
C5×#20362
C5×#18922
C5×#18692
C5×#18632
C5×#18522
C5×#18242
#240985