Finite Group Databasebeta

← C5×#29699 #11952419

Subgroups — C5×#29699 #11952419

Order 1280.

948 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#541C211yesmaximal, characteristic
2C2×C5×#477C211yesmaximal, characteristic, complemented
3C2×C5×#475C211yesmaximal, characteristic, complemented
4C5×#2628C211yesmaximal, characteristic
5C5×#2059C212yesmaximal, complemented
6C5×#2043C212yesmaximal, complemented
7C5×#2036C212yesmaximal
8C5×#2035C212yesmaximal
9C5×#1805C211yesmaximal, characteristic, complemented
10C5×#1805C211yesmaximal, characteristic, complemented
11C5×#1798C211yesmaximal, characteristic
12C5×#541—24no—
13C5×#541—24no—
14C2×C5×C4⋊Q8C2211yescharacteristic
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C5×#126—21no—
17C2×C5×#126—21no—
18C2×C5×#125—21no—
19C2×C5×#125—21no—
20C2×C5×#125C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C4×C5×Q8C2211yescharacteristic
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C5×#117C2211yescharacteristic
26C5×#477—24no—
27C5×#475—24no—
28C2×C5×#107C2212yes—
29C2×C5×#106C2212yes—
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×#103C2212yes—
33C2×C5×#103C2212yes—
34C2×C5×#103C2212yes—
35C2×C5×#103C2212yes—
36C2×C5×C22⋊C8C2212yes—
37C5×#400—21no—
38C5×#399—21no—
39C5×#395—21no—
40C5×#393—21no—
41C5×#389C2212yes—
42C5×#382C2211yescharacteristic
43C5×#380C2212yes—
44C5×#340C2212yes—
45C5×#340C2212yes—
46C5×#336C2212yes—
47#29699C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C22×C5×Q8C2311yescharacteristic
50C22×C5×Q8C2311yescharacteristic
51C23×C4×C5C2311yescharacteristic
52C22×C5×C8C2312yes—
53C22×C5×C8C2312yes—
54C5×C4⋊Q8—22no—
55C5×C4⋊Q8—22no—
56C5×C4⋊Q8—22no—
57C5×C4⋊Q8—22no—
58C5×#126—28no—
59C5×#126—28no—
60C5×#125—28no—
61C5×#125—28no—
62C5×#125—22no—
63C5×#125—22no—
64C5×C22⋊Q8—22no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8—22no—
67C5×C22⋊Q8—22no—
68C4×C5×Q8—22no—
69C4×C5×Q8—22no—
70C4×C5×Q8D414yes—
71C4×C5×Q8D414yes—
72C5×#117—22no—
73C5×#117—22no—
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—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4D411yescharacteristic
85C2×C5×C4⋊C4D411yescharacteristic
86C2×C5×C4⋊C4C2312yes—
87C2×C5×C4⋊C4C2312yes—
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4D411yescharacteristic
94C2×C5×C22⋊C4D411yescharacteristic
95C2×C42×C5—21no—
96C2×C42×C5—21no—
97C2×C42×C5C2311yescharacteristic
98C2×C42×C5C2311yescharacteristic
99C5×#107—24no—
100C5×#106—24no—
101C5×C4⋊C8—22no—
102C5×C4⋊C8—22no—
103C5×#103—24no—
104C5×#103—24no—
105C5×#103—42no—
106C5×#103—42no—
107C5×C22⋊C8—42no—
108C5×#95—22no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95—22no—
112C2×#541C2×C511yescharacteristic
113C2×#477C2×C511yescharacteristic, complemented
114C2×#475C2×C511yescharacteristic, complemented
115#2628C2×C511yescharacteristic
116#2059C2×C512yescomplemented
117#2043C2×C512yescomplemented
118#2036C2×C512yes—
119#2035C2×C512yes—
120#1805C2×C511yescharacteristic, complemented
121#1805C2×C511yescharacteristic, complemented
122#1798C2×C511yescharacteristic
123C24×C5C2×D411yescharacteristic
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129C2×C5×Q8—21no—
130C2×C5×Q8—21no—
131C2×C5×Q8—21no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—42no—
135C2×C5×Q8—82no—
136C2×C5×Q8C2×D412yes—
137C2×C5×Q8C2×D412yes—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
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—24no—
166C5×C4⋊C4—24no—
167C5×C4⋊C4—24no—
168C5×C4⋊C4—24no—
169C5×C4⋊C4—24no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—42no—
179C5×C4⋊C4—82no—
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—82no—
187C42×C5—24no—
188C42×C5—24no—
189C42×C5—21no—
190C42×C5—21no—
191C42×C5C2×D412yes—
192C42×C5C2×D412yes—
193#541—24no—
194#541—24no—
195C2×C4⋊Q8C22×C511yescharacteristic
196C2×C4⋊Q8C22×C511yescharacteristic
197C2×#126—21no—
198C2×#126—21no—
199C2×#125—21no—
200C2×#125—21no—
201C2×#125C22×C511yescharacteristic
202C2×C22⋊Q8C22×C511yescharacteristic
203C2×C22⋊Q8C22×C511yescharacteristic
204C2×C4×Q8C22×C511yescharacteristic
205C2×C4×Q8C22×C511yescharacteristic
206C2×#117C22×C511yescharacteristic
207#477—24no—
208#475—24no—
209C2×#107C22×C512yes—
210C2×#106C22×C512yes—
211C2×C4⋊C8C22×C511yescharacteristic
212C2×C4⋊C8C22×C511yescharacteristic
213C2×#103C22×C512yes—
214C2×#103C22×C512yes—
215C2×#103C22×C512yes—
216C2×#103C22×C512yes—
217C2×C22⋊C8C22×C512yes—
218#400—21no—
219#399—21no—
220#395—21no—
221#393—21no—
222#389C22×C512yes—
223#382C22×C511yescharacteristic
224#380C22×C512yes—
225#340C22×C512yes—
226#340C22×C512yes—
227#336C22×C512yes—
228C23×C5—21no—
229C23×C5—21no—
230C23×C5—21no—
231C23×C5—22no—
232C23×C5—22no—
233C23×C5C22×D411yescharacteristic
234C5×Q8—22no—
235C5×Q8—22no—
236C5×Q8—22no—
237C5×Q8—22no—
238C5×Q8—41no—
239C5×Q8—41no—
240C5×Q8—41no—
241C5×Q8—41no—
242C5×Q8—84no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—22no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
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#12012yes—
273C2×C4×C5#12012yes—
274C2×C4×C5C22×D411yescharacteristic
275C2×C4×C5C22×D411yescharacteristic
276C2×C4×C5H(5,𝔽2)11yescharacteristic
277C2×C4×C52−1+411yescharacteristic
278C2×C4×C52−1+411yescharacteristic
279C2×C4×C52−1+411yescharacteristic
280C5×C8—42no—
281C5×C8—42no—
282C22×Q8—21no—
283C22×Q8C23×C511yescharacteristic
284C22×Q8C23×C511yescharacteristic
285C23×C4C23×C511yescharacteristic
286C22×C8C23×C512yes—
287C22×C8C23×C512yes—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292#126—28no—
293#126—28no—
294#125—28no—
295#125—28no—
296#125—22no—
297#125—22no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8C5×D414yes—
305C4×Q8C5×D414yes—
306#117—22no—
307#117—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4C5×D411yescharacteristic
319C2×C4⋊C4C5×D411yescharacteristic
320C2×C4⋊C4C23×C512yes—
321C2×C4⋊C4C23×C512yes—
322C2×C4⋊C4C23×C511yescharacteristic
323C2×C4⋊C4C23×C511yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4C5×D411yescharacteristic
328C2×C22⋊C4C5×D411yescharacteristic
329C2×C42—21no—
330C2×C42—21no—
331C2×C42C23×C511yescharacteristic
332C2×C42C23×C511yescharacteristic
333#107—24no—
334#106—24no—
335C4⋊C8—22no—
336C4⋊C8—22no—
337#103—24no—
338#103—24no—
339#103—42no—
340#103—42no—
341C22⋊C8—42no—
342#95—22no—
343#95—21no—
344#95—21no—
345#95—22no—
346C22×C5—41no—
347C22×C5—42no—
348C22×C5—42no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C2×#12011yescharacteristic
352C22×C5#53611yescharacteristic
353C22×C5#53711yescharacteristic
354C22×C5#57712yes—
355C22×C5#57812yes—
356C4×C5—22no—
357C4×C5—22no—
358C4×C5—41no—
359C4×C5—42no—
360C4×C5—42no—
361C4×C5—41no—
362C4×C5—42no—
363C4×C5—41no—
364C4×C5—42no—
365C4×C5—82no—
366C4×C5—82no—
367C4×C5#53611yescharacteristic
368C4×C5#53611yescharacteristic
369C4×C5#53711yescharacteristic
370C4×C5#53711yescharacteristic
371C24C2×C5×D411yescharacteristic
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—82no—
384C2×Q8C2×C5×D412yes—
385C2×Q8C2×C5×D412yes—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4C2×C5×D411yescharacteristic
399C22×C4C2×C5×D411yescharacteristic
400C22×C4C2×C5×D411yescharacteristic
401C22×C4C2×C5×D411yescharacteristic
402C22×C4C2×C5×D411yescharacteristic
403C22×C4C24×C511yescharacteristic
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—82no—
428C4⋊C4C2×C5×D412yes—
429C4⋊C4C2×C5×D412yes—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—82no—
435C42—24no—
436C42—24no—
437C42—21no—
438C42—21no—
439C42C2×C5×D412yes—
440C42C2×C5×D412yes—
441C2×C5—81no—
442C2×C5#261611yescharacteristic
443C2×C5#301011yescharacteristic
444C2×C5#301111yescharacteristic
445C2×C5#324212yes—
446C2×C5#325812yes—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—22no—
451C23—22no—
452C23C22×C5×D411yescharacteristic
453Q8—22no—
454Q8—22no—
455Q8—22no—
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—41no—
460Q8—41no—
461Q8—84no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4C5×#12012yes—
492C2×C4C5×#12012yes—
493C2×C4C22×C5×D411yescharacteristic
494C2×C4C22×C5×D411yescharacteristic
495C2×C4C5×H(5,𝔽2)11yescharacteristic
496C2×C4C5×2−1+411yescharacteristic
497C2×C4C5×2−1+411yescharacteristic
498C2×C4C5×2−1+411yescharacteristic
499C8—42no—
500C8—42no—
501C5#2969911yescharacteristic, direct product factor, Sylow
502C22—42no—
503C22—42no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22C2×C5×#12011yescharacteristic
508C22C5×#53611yescharacteristic
509C22C5×#53711yescharacteristic
510C22C5×#57712yes—
511C22C5×#57812yes—
512C4—22no—
513C4—22no—
514C4—41no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—42no—
521C4—82no—
522C4—82no—
523C4C5×#53611yescharacteristic
524C4C5×#53611yescharacteristic
525C4C5×#53711yescharacteristic
526C4C5×#53711yescharacteristic
527C2—81no—
528C2C5×#261611yescharacteristic
529C2C5×#301011yescharacteristic
530C2C5×#301111yescharacteristic
531C2C5×#324212yes—
532C2C5×#325812yes—
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
2. C2×C5×#477C2semidirect
3. C2×C5×#475C2semidirect
5. C5×#2059C2semidirect
6. C5×#2043C2semidirect
9. C5×#1805C2semidirect
10. C5×#1805C2semidirect
47. #29699C5direct (N × H)
113. C2×#477C2×C5semidirect
114. C2×#475C2×C5semidirect
116. #2059C2×C5semidirect
117. #2043C2×C5semidirect
120. #1805C2×C5semidirect
121. #1805C2×C5semidirect
501. C5#29699direct (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×#4772
C2×C5×#4752
C5×#26282
C5×#20592
C5×#20432
C5×#20362
C5×#20352
C5×#18052
C5×#17982
#296995