Finite Group Databasebeta

← C5×#18998 #11941718

Subgroups — C5×#18998 #11941718

Order 1280.

926 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
1C2×C5×#562C211yesmaximal, characteristic
2C5×#3236C211yesmaximal, characteristic, complemented
3C5×#3215C211yesmaximal, characteristic, complemented
4C5×#3140C211yesmaximal, characteristic, complemented
5C5×#1662C214yesmaximal, complemented
6C5×#1661C214yesmaximal, complemented
7C5×#1533C211yesmaximal, characteristic, complemented
8C5×#1528C211yesmaximal, characteristic, complemented
9C5×#1527C211yesmaximal, characteristic, complemented
10C5×#562—22no—
11C5×#562—22no—
12C5×#562—22no—
13C5×#562C2214yes—
14C5×#533C2211yescharacteristic
15C2×C5×#125C2211yescharacteristic
16C2×C5×#124C2211yescharacteristic
17C2×C5×#124C2211yescharacteristic
18C2×C5×#123—21no—
19C2×C5×#123—21no—
20C2×C5×C22⋊Q8—21no—
21C2×C5×C22⋊Q8—21no—
22C2×C5×#121—21no—
23C2×C5×#121—21no—
24C5×#501C2212yescomplemented
25C5×#497C2212yescomplemented
26C5×#491C2212yescomplemented
27C5×#489C2212yescomplemented
28C5×#489C2212yescomplemented
29C5×#489C2212yescomplemented
30C5×#488—22no—
31C5×#484—21no—
32C5×#483—21no—
33C5×#479—22no—
34C5×#464—22no—
35C5×#451—21no—
36C5×#450—21no—
37C5×#432C2211yescharacteristic
38C5×#432C2211yescharacteristic
39C5×#419—21no—
40C5×#418—21no—
41C4×C5×M16C2211yescharacteristic
42C5×#330C2214yescomplemented
43C5×#329C2214yescomplemented
44C5×#329C2214yescomplemented
45#18998C511yesmaximal, characteristic, direct product factor, Sylow
46C22×C5×Q8D411yescharacteristic
47C22×C5×Q8D411yescharacteristic
48C22×C5×D4—21no—
49C22×C5×D4—21no—
50C22×C5×D4D411yescharacteristic
51C22×C5×D4D411yescharacteristic
52C23×C4×C5—21no—
53C23×C4×C5—21no—
54C2×C5×Q16—22no—
55C2×C5×SD16—22no—
56C2×C5×M16—21no—
57C5×C4⋊Q8C2311yescharacteristic
58C5×C4⋊Q8C2311yescharacteristic
59C5×#125—21no—
60C5×#125—21no—
61C5×#125—21no—
62C5×#125D412yes—
63C5×#125C2312yes—
64C5×#124—21no—
65C5×#124—21no—
66C5×#124—21no—
67C5×#124—21no—
68C5×#124D412yes—
69C5×#124D412yes—
70C5×#124C2312yes—
71C5×#124C2312yes—
72C5×#123—24no—
73C5×#123—24no—
74C5×#123—24no—
75C5×#123—24no—
76C5×C22⋊Q8—24no—
77C5×C22⋊Q8—24no—
78C5×C22⋊Q8—24no—
79C5×C22⋊Q8—24no—
80C5×C22⋊Q8—21no—
81C5×C22⋊Q8—21no—
82C5×#121—24no—
83C5×#121—24no—
84C5×#121—24no—
85C5×#121—24no—
86C4×C5×Q8—21no—
87C4×C5×Q8—21no—
88C5×#117—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4D411yescharacteristic
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C42×C5C2311yescharacteristic
102C5×#107—22no—
103C5×#106—22no—
104C5×C4⋊C8—21no—
105C5×C4⋊C8—21no—
106C5×#103—22no—
107C5×#103—22no—
108C5×#103—22no—
109C5×#103—22no—
110C5×#103—22no—
111C5×#102—22no—
112C5×#102—22no—
113C5×#102—22no—
114C5×C22⋊C8—21no—
115C5×C22⋊C8—21no—
116C5×#97C2312yes—
117C5×#97C2312yes—
118C5×#97C2312yes—
119C4×C5×C8—21no—
120C2×#562C2×C511yescharacteristic
121#3236C2×C511yescharacteristic, complemented
122#3215C2×C511yescharacteristic, complemented
123#3140C2×C511yescharacteristic, complemented
124#1662C2×C514yescomplemented
125#1661C2×C514yescomplemented
126#1533C2×C511yescharacteristic, complemented
127#1528C2×C511yescharacteristic, complemented
128#1527C2×C511yescharacteristic, complemented
129C24×C5—21no—
130C24×C5—21no—
131C2×C5×Q8—21no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—21no—
135C2×C5×Q8—42no—
136C2×C5×Q8—81no—
137C2×C5×Q8C2×D412yes—
138C2×C5×Q8C2×D412yes—
139C2×C5×D4—24no—
140C2×C5×D4—24no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—42no—
144C2×C5×D4—81no—
145C2×C5×D4—82no—
146C2×C5×D4—82no—
147C2×C5×D4C2×D412yes—
148C2×C5×D4C2×D412yes—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—24no—
154C22×C4×C5—24no—
155C22×C4×C5—82no—
156C22×C4×C5—82no—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C5×Q16—82no—
161C5×SD16—82no—
162C5×M16—42no—
163C2×C5×C8—22no—
164C2×C5×C8—22no—
165C2×C5×C8—22no—
166C5×C4⋊C4—24no—
167C5×C4⋊C4—24no—
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—41no—
179C5×C4⋊C4—41no—
180C5×C4⋊C4C2×D412yes—
181C5×C4⋊C4C2×D412yes—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—24no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—41no—
193C42×C5—41no—
194C42×C5C2×D411yescharacteristic
195C42×C5C2×D411yescharacteristic
196C42×C5C2×D411yescharacteristic
197C42×C5C2411yescharacteristic
198#562—22no—
199#562—22no—
200#562—22no—
201#562C22×C514yes—
202#533C22×C511yescharacteristic
203C2×#125C22×C511yescharacteristic
204C2×#124C22×C511yescharacteristic
205C2×#124C22×C511yescharacteristic
206C2×#123—21no—
207C2×#123—21no—
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8—21no—
210C2×#121—21no—
211C2×#121—21no—
212#501C22×C512yescomplemented
213#497C22×C512yescomplemented
214#491C22×C512yescomplemented
215#489C22×C512yescomplemented
216#489C22×C512yescomplemented
217#489C22×C512yescomplemented
218#488—22no—
219#484—21no—
220#483—21no—
221#479—22no—
222#464—22no—
223#451—21no—
224#450—21no—
225#432C22×C511yescharacteristic
226#432C22×C511yescharacteristic
227#419—21no—
228#418—21no—
229C4×M16C22×C511yescharacteristic
230#330C22×C514yescomplemented
231#329C22×C514yescomplemented
232#329C22×C514yescomplemented
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5#12011yescharacteristic
242C5×Q8—42no—
243C5×Q8—42no—
244C5×Q8—42no—
245C5×Q8—42no—
246C5×Q8—81no—
247C5×Q8—81no—
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—81no—
251C5×D4—81no—
252C5×D4—84no—
253C5×D4—84no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—84no—
268C2×C4×C5—84no—
269C2×C4×C5#12011yescharacteristic
270C2×C4×C5#12011yescharacteristic
271C2×C4×C5#12011yescharacteristic
272C2×C4×C5C22×D411yescharacteristic
273C2×C4×C5C22×D411yescharacteristic
274C2×C4×C5C22×D411yescharacteristic
275C5×C8—42no—
276C5×C8—42no—
277C5×C8—42no—
278C22×Q8C5×D411yescharacteristic
279C22×Q8C5×D411yescharacteristic
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C5×D411yescharacteristic
283C22×D4C5×D411yescharacteristic
284C23×C4—21no—
285C23×C4—21no—
286C2×Q16—22no—
287C2×SD16—22no—
288C2×M16—21no—
289C4⋊Q8C23×C511yescharacteristic
290C4⋊Q8C23×C511yescharacteristic
291#125—21no—
292#125—21no—
293#125—21no—
294#125C5×D412yes—
295#125C23×C512yes—
296#124—21no—
297#124—21no—
298#124—21no—
299#124—21no—
300#124C5×D412yes—
301#124C5×D412yes—
302#124C23×C512yes—
303#124C23×C512yes—
304#123—24no—
305#123—24no—
306#123—24no—
307#123—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C22⋊Q8—24no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314#121—24no—
315#121—24no—
316#121—24no—
317#121—24no—
318C4×Q8—21no—
319C4×Q8—21no—
320#117—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4C5×D411yescharacteristic
326C2×C4⋊C4C5×D411yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42C23×C511yescharacteristic
334#107—22no—
335#106—22no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338#103—22no—
339#103—22no—
340#103—22no—
341#103—22no—
342#103—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348#97C23×C512yes—
349#97C23×C512yes—
350#97C23×C512yes—
351C4×C8—21no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—42no—
355C22×C5—42no—
356C22×C5—42no—
357C22×C5—42no—
358C22×C5—42no—
359C22×C5—42no—
360C22×C5—84no—
361C22×C5—84no—
362C22×C5#45512yes—
363C22×C5C2×#12011yescharacteristic
364C4×C5—21no—
365C4×C5—21no—
366C4×C5—21no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—21no—
370C4×C5—42no—
371C4×C5—42no—
372C4×C5—42no—
373C4×C5—42no—
374C4×C5—81no—
375C4×C5—81no—
376C24—21no—
377C24—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—81no—
384C2×Q8C2×C5×D412yes—
385C2×Q8C2×C5×D412yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—81no—
392C2×D4—82no—
393C2×D4—82no—
394C2×D4C2×C5×D412yes—
395C2×D4C2×C5×D412yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—82no—
403C22×C4—82no—
404C22×C4C2×C5×D411yescharacteristic
405C22×C4C2×C5×D411yescharacteristic
406C22×C4C2×C5×D411yescharacteristic
407Q16—82no—
408SD16—82no—
409M16—42no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4C2×C5×D412yes—
428C4⋊C4C2×C5×D412yes—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—41no—
440C42—41no—
441C42C2×C5×D411yescharacteristic
442C42C2×C5×D411yescharacteristic
443C42C2×C5×D411yescharacteristic
444C42C24×C511yescharacteristic
445C2×C5—22no—
446C2×C5—82no—
447C2×C5—82no—
448C2×C5C2×#45511yescharacteristic
449C2×C5#301911yescharacteristic
450C2×C5#302011yescharacteristic
451C23—22no—
452C23—22no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23C5×#12011yescharacteristic
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—81no—
465Q8—81no—
466D4—42no—
467D4—42no—
468D4—81no—
469D4—81no—
470D4—84no—
471D4—84no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—84no—
486C2×C4—84no—
487C2×C4C5×#12011yescharacteristic
488C2×C4C5×#12011yescharacteristic
489C2×C4C5×#12011yescharacteristic
490C2×C4C22×C5×D411yescharacteristic
491C2×C4C22×C5×D411yescharacteristic
492C2×C4C22×C5×D411yescharacteristic
493C8—42no—
494C8—42no—
495C8—42no—
496C5#1899811yescharacteristic, direct product factor, Sylow
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—84no—
507C22C5×#45512yes—
508C22C2×C5×#12011yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—81no—
520C4—81no—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×C5×#45511yescharacteristic
525C2C5×#301911yescharacteristic
526C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC2×C5×#562C2
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
2. C5×#3236C2semidirect
3. C5×#3215C2semidirect
4. C5×#3140C2semidirect
5. C5×#1662C2semidirect
6. C5×#1661C2semidirect
7. C5×#1533C2semidirect
8. C5×#1528C2semidirect
9. C5×#1527C2semidirect
24. C5×#501C22semidirect
25. C5×#497C22semidirect
26. C5×#491C22semidirect
27. C5×#489C22semidirect
28. C5×#489C22semidirect
29. C5×#489C22semidirect
42. C5×#330C22semidirect
43. C5×#329C22semidirect
44. C5×#329C22semidirect
45. #18998C5direct (N × H)
121. #3236C2×C5semidirect
122. #3215C2×C5semidirect
123. #3140C2×C5semidirect
124. #1662C2×C5semidirect
125. #1661C2×C5semidirect
126. #1533C2×C5semidirect
127. #1528C2×C5semidirect
128. #1527C2×C5semidirect
212. #501C22×C5semidirect
213. #497C22×C5semidirect
214. #491C22×C5semidirect
215. #489C22×C5semidirect
216. #489C22×C5semidirect
217. #489C22×C5semidirect
230. #330C22×C5semidirect
231. #329C22×C5semidirect
232. #329C22×C5semidirect
496. C5#18998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5622
C5×#32362
C5×#32152
C5×#31402
C5×#16622
C5×#16612
C5×#15332
C5×#15282
C5×#15272
#189985