Finite Group Databasebeta

← C5×#19029 #11941749

Subgroups — C5×#19029 #11941749

Order 1280.

824 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3563C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic
3C2×C5×#501C211yesmaximal, characteristic, complemented
4C5×#3139C211yesmaximal, characteristic, complemented
5C5×#1664C214yesmaximal, complemented
6C5×#1663C214yesmaximal, complemented
7C5×#1531C211yesmaximal, characteristic, complemented
8C5×#1528C211yesmaximal, characteristic, complemented
9C5×#1524C211yesmaximal, characteristic
10C5×#564C2212yes—
11C5×#563C2212yes—
12C5×#557—21no—
13C5×#554—21no—
14C5×#552—21no—
15C5×#552—22no—
16C5×#552—21no—
17C5×#544—21no—
18C5×#544—21no—
19C5×#541—21no—
20C5×#541—22no—
21C5×#539—21no—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#125C2211yescharacteristic
26C5×#501—22no—
27C5×#501C2212yes—
28C5×#501C2214yes—
29C5×#491C2214yes—
30C5×#489C2212yes—
31C5×#487—21no—
32C5×#487—21no—
33C5×#483—21no—
34C5×#480—21no—
35C5×#477—21no—
36C5×#476—21no—
37C5×#432C2211yescharacteristic
38C2×C5×#107—21no—
39C2×C5×#106—21no—
40C5×#419—22no—
41C4×C5×M16C2211yescharacteristic
42C2×C5×#97C2211yescharacteristic
43C5×#330C2212yes—
44C5×#330C2214yes—
45C5×#330C2214yes—
46C5×#329C2212yes—
47#19029C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C2×C5×M16—21no—
50C22×C5×C8—21no—
51C5×C4⋊Q8—22no—
52C5×C4⋊Q8—21no—
53C5×C4⋊Q8—22no—
54C5×C4⋊Q8—21no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8D411yescharacteristic
58C5×C4⋊Q8D411yescharacteristic
59C5×C4⋊Q8C2312yes—
60C5×#126—22no—
61C5×#126—22no—
62C5×#126—22no—
63C5×#126—22no—
64C5×#126—21no—
65C5×#125—22no—
66C5×#125—22no—
67C5×#125—21no—
68C5×#125—22no—
69C5×#125—22no—
70C5×#125—22no—
71C5×#125—22no—
72C5×#125—22no—
73C5×#125—22no—
74C5×#125—21no—
75C5×#125—21no—
76C5×#125D412yes—
77C5×#125C2312yes—
78C5×#125C2312yes—
79C5×#125C2311yescharacteristic
80C5×#124C2311yescharacteristic
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—21no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—21no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8D411yescharacteristic
93C5×#121D411yescharacteristic
94C4×C5×Q8—21no—
95C4×C5×Q8—22no—
96C4×C5×Q8—21no—
97C4×C5×Q8—21no—
98C4×C5×Q8—21no—
99C4×C5×Q8D411yescharacteristic
100C4×C5×D4—22no—
101C4×C5×D4—21no—
102C4×C5×D4D411yescharacteristic
103C5×#117—22no—
104C5×#117—21no—
105C5×#117—22no—
106C5×#117—21no—
107C5×#117D412yes—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C5×#107—24no—
117C5×#107—22no—
118C5×#106—24no—
119C5×#106—22no—
120C5×C4⋊C8—21no—
121C5×#103—22no—
122C5×#103—24no—
123C5×#103—24no—
124C5×#102—22no—
125C5×C22⋊C8—21no—
126C5×#97—21no—
127C5×#97C2312yes—
128C5×#97C2312yes—
129C5×#97C2312yes—
130C4×C5×C8—21no—
131#3563C2×C511yescharacteristic
132#3238C2×C511yescharacteristic
133C2×#501C2×C511yescharacteristic, complemented
134#3139C2×C511yescharacteristic, complemented
135#1664C2×C514yescomplemented
136#1663C2×C514yescomplemented
137#1531C2×C511yescharacteristic, complemented
138#1528C2×C511yescharacteristic, complemented
139#1524C2×C511yescharacteristic
140C2×C5×Q8—22no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8—22no—
144C2×C5×Q8—44no—
145C2×C5×Q8—41no—
146C2×C5×Q8C2×D411yescharacteristic
147C2×C5×D4—21no—
148C2×C5×D4C2×D411yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—41no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C5×M16—42no—
158C2×C5×C8—24no—
159C2×C5×C8—22no—
160C2×C5×C8—22no—
161C2×C5×C8—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—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—22no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—41no—
187C5×C4⋊C4—41no—
188C5×C4⋊C4C2×D412yes—
189C5×C4⋊C4C2×D412yes—
190C5×C4⋊C4C2×D412yes—
191C5×C4⋊C4C2×D412yes—
192C5×C4⋊C4C2×D411yescharacteristic
193C5×C4⋊C4C2×D411yescharacteristic
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4—21no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—21no—
203C42×C5—22no—
204C42×C5—22no—
205C42×C5—22no—
206C42×C5—22no—
207C42×C5—21no—
208C42×C5C2×D411yescharacteristic
209C42×C5C2×D411yescharacteristic
210C42×C5C2×D411yescharacteristic
211C42×C5C2411yescharacteristic
212#564C22×C512yes—
213#563C22×C512yes—
214#557—21no—
215#554—21no—
216#552—21no—
217#552—22no—
218#552—21no—
219#544—21no—
220#544—21no—
221#541—21no—
222#541—22no—
223#539—21no—
224#533C22×C511yescharacteristic
225C2×C4⋊Q8C22×C511yescharacteristic
226#529C22×C511yescharacteristic
227C2×#125C22×C511yescharacteristic
228#501—22no—
229#501C22×C514yes—
230#501C22×C512yes—
231#491C22×C514yes—
232#489C22×C512yes—
233#487—21no—
234#487—21no—
235#483—21no—
236#480—21no—
237#477—21no—
238#476—21no—
239#432C22×C511yescharacteristic
240C2×#107—21no—
241C2×#106—21no—
242#419—22no—
243C4×M16C22×C511yescharacteristic
244C2×#97C22×C511yescharacteristic
245#330C22×C512yes—
246#330C22×C514yes—
247#330C22×C514yes—
248#329C22×C512yes—
249C23×C5—21no—
250C23×C5#12011yescharacteristic
251C5×Q8—41no—
252C5×Q8—44no—
253C5×Q8—42no—
254C5×Q8—81no—
255C5×Q8—82no—
256C5×Q8—82no—
257C5×D4—41no—
258C5×D4—42no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—22no—
265C2×C4×C5—21no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—41no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—81no—
273C2×C4×C5—82no—
274C2×C4×C5—82no—
275C2×C4×C5#12011yescharacteristic
276C2×C4×C5#12011yescharacteristic
277C2×C4×C5#12011yescharacteristic
278C2×C4×C5C22×D411yescharacteristic
279C2×C4×C5C22×D411yescharacteristic
280C2×C4×C5C22×D411yescharacteristic
281C5×C8—24no—
282C5×C8—42no—
283C5×C8—42no—
284C22×Q8—21no—
285C2×M16—21no—
286C22×C8—21no—
287C4⋊Q8—22no—
288C4⋊Q8—21no—
289C4⋊Q8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C5×D411yescharacteristic
294C4⋊Q8C5×D411yescharacteristic
295C4⋊Q8C23×C512yes—
296#126—22no—
297#126—22no—
298#126—22no—
299#126—22no—
300#126—21no—
301#125—22no—
302#125—22no—
303#125—21no—
304#125—22no—
305#125—22no—
306#125—22no—
307#125—22no—
308#125—22no—
309#125—22no—
310#125—21no—
311#125—21no—
312#125C5×D412yes—
313#125C23×C512yes—
314#125C23×C511yescharacteristic
315#125C23×C512yes—
316#124C23×C511yescharacteristic
317#123—22no—
318#123—22no—
319#123—21no—
320C22⋊Q8—22no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8C5×D411yescharacteristic
329#121C5×D411yescharacteristic
330C4×Q8—21no—
331C4×Q8—22no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8C5×D411yescharacteristic
336C4×D4—22no—
337C4×D4—21no—
338C4×D4C5×D411yescharacteristic
339#117—22no—
340#117—21no—
341#117—22no—
342#117—21no—
343#117C5×D412yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C5×D411yescharacteristic
350C2×C4⋊C4C5×D411yescharacteristic
351C2×C42C23×C511yescharacteristic
352#107—24no—
353#107—22no—
354#106—24no—
355#106—22no—
356C4⋊C8—21no—
357#103—22no—
358#103—24no—
359#103—24no—
360#102—22no—
361C22⋊C8—21no—
362#97—21no—
363#97C23×C512yes—
364#97C23×C512yes—
365#97C23×C512yes—
366C4×C8—21no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—41no—
370C22×C5—41no—
371C22×C5—41no—
372C22×C5#45412yes—
373C22×C5C2×#12011yescharacteristic
374C4×C5—21no—
375C4×C5—21no—
376C4×C5—21no—
377C4×C5—21no—
378C4×C5—21no—
379C4×C5—42no—
380C4×C5—41no—
381C4×C5—41no—
382C4×C5—42no—
383C4×C5—42no—
384C4×C5—42no—
385C4×C5—41no—
386C4×C5—82no—
387C4×C5#45612yes—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—41no—
394C2×Q8C2×C5×D411yescharacteristic
395C2×D4—21no—
396C2×D4C2×C5×D411yescharacteristic
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—41no—
402C22×C4C2×C5×D411yescharacteristic
403C22×C4C2×C5×D411yescharacteristic
404C22×C4C2×C5×D411yescharacteristic
405M16—42no—
406C2×C8—24no—
407C2×C8—22no—
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—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4C2×C5×D412yes—
437C4⋊C4C2×C5×D412yes—
438C4⋊C4C2×C5×D412yes—
439C4⋊C4C2×C5×D411yescharacteristic
440C4⋊C4C2×C5×D412yes—
441C4⋊C4C2×C5×D411yescharacteristic
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—22no—
455C42—21no—
456C42C2×C5×D411yescharacteristic
457C42C2×C5×D411yescharacteristic
458C42C2×C5×D411yescharacteristic
459C42C24×C511yescharacteristic
460C2×C5—22no—
461C2×C5—81no—
462C2×C5C2×#45411yescharacteristic
463C2×C5C2×#45611yescharacteristic
464C2×C5#302211yescharacteristic
465C23—21no—
466C23C5×#12011yescharacteristic
467Q8—41no—
468Q8—44no—
469Q8—42no—
470Q8—81no—
471Q8—82no—
472Q8—82no—
473D4—41no—
474D4—42no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4C5×#12011yescharacteristic
492C2×C4C5×#12011yescharacteristic
493C2×C4C5×#12011yescharacteristic
494C2×C4C22×C5×D411yescharacteristic
495C2×C4C22×C5×D411yescharacteristic
496C2×C4C22×C5×D411yescharacteristic
497C8—24no—
498C8—42no—
499C8—42no—
500C5#1902911yescharacteristic, direct product factor, Sylow
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22C5×#45412yes—
507C22C2×C5×#12011yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—42no—
514C4—41no—
515C4—41no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4C5×#45612yes—
522C2—22no—
523C2—81no—
524C2C2×C5×#45411yescharacteristic
525C2C2×C5×#45611yescharacteristic
526C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#501C2semidirect
4. C5×#3139C2semidirect
5. C5×#1664C2semidirect
6. C5×#1663C2semidirect
7. C5×#1531C2semidirect
8. C5×#1528C2semidirect
47. #19029C5direct (N × H)
133. C2×#501C2×C5semidirect
134. #3139C2×C5semidirect
135. #1664C2×C5semidirect
136. #1663C2×C5semidirect
137. #1531C2×C5semidirect
138. #1528C2×C5semidirect
500. C5#19029direct (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×#32382
C2×C5×#5012
C5×#31392
C5×#16642
C5×#16632
C5×#15312
C5×#15282
C5×#15242
#190295