Finite Group Databasebeta

← C5×#8336 #11931056

Subgroups — C5×#8336 #11931056

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#529C211yesmaximal, characteristic
2C5×#1749C211yesmaximal, characteristic, complemented
3C5×#1749C211yesmaximal, characteristic, complemented
4C2×C5×#330C212yesmaximal, complemented
5C2×C5×#329C212yesmaximal, complemented
6C5×#529—24no—
7C5×#529—24no—
8C2×C5×#126—21no—
9C2×C5×#125C2211yescharacteristic
10C2×C5×#124C2211yescharacteristic
11C2×C5×#123—21no—
12C2×C5×C22⋊Q8C411yescharacteristic
13C2×C5×#121C411yescharacteristic
14C2×C4×C5×Q8C411yescharacteristic
15C2×C4×C5×D4—21no—
16C2×C4×C5×D4C411yescharacteristic
17C2×C5×#117—21no—
18C22×C42×C5C2211yescharacteristic
19C2×C5×C22⋊C8—21no—
20C2×C5×C22⋊C8—21no—
21C2×C5×#97C2212yes—
22C2×C5×#97C2212yes—
23C5×#336—21no—
24C5×#336—21no—
25C5×#330—24no—
26C5×#329—24no—
27#8336C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8C2×C411yescharacteristic
29C22×C5×D4—21no—
30C22×C5×D4C2×C411yescharacteristic
31C23×C4×C5—21no—
32C23×C4×C5C2×C411yescharacteristic
33C23×C4×C5D411yescharacteristic
34C23×C4×C5D411yescharacteristic
35C22×C5×C8—22no—
36C22×C5×C8—22no—
37C5×#126—28no—
38C5×#125—22no—
39C5×#125D414yes—
40C5×#124—22no—
41C5×#124D414yes—
42C5×#123—28no—
43C5×C22⋊Q8—22no—
44C5×C22⋊Q8—22no—
45C5×#121—22no—
46C5×#121—22no—
47C4×C5×Q8—22no—
48C4×C5×Q8—22no—
49C4×C5×D4—28no—
50C4×C5×D4—22no—
51C4×C5×D4—22no—
52C5×#117—28no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4C2×C411yescharacteristic
58C2×C5×C4⋊C4C2×C411yescharacteristic
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C42×C5—21no—
65C2×C42×C5—22no—
66C2×C42×C5—22no—
67C2×C42×C5C2×C411yescharacteristic
68C2×C42×C5D411yescharacteristic
69C2×C42×C5D411yescharacteristic
70C2×C42×C5C2311yescharacteristic
71C5×C22⋊C8—24no—
72C5×C22⋊C8—24no—
73C5×#97—22no—
74C5×#97—22no—
75C5×#97—22no—
76C5×#97—22no—
77C2×#529C2×C511yescharacteristic
78#1749C2×C511yescharacteristic, complemented
79#1749C2×C511yescharacteristic, complemented
80C2×#330C2×C512yescomplemented
81C2×#329C2×C512yescomplemented
82C24×C5—21no—
83C24×C5C22⋊C411yescharacteristic
84C2×C5×Q8—21no—
85C2×C5×Q8—41no—
86C2×C5×Q8—41no—
87C2×C5×Q8C22⋊C412yes—
88C2×C5×D4—24no—
89C2×C5×D4—21no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—42no—
93C2×C5×D4—42no—
94C2×C5×D4C22⋊C412yes—
95C22×C4×C5—24no—
96C22×C4×C5—22no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5—42no—
110C22×C4×C5—42no—
111C22×C4×C5C22⋊C411yescharacteristic
112C22×C4×C5C22⋊C411yescharacteristic
113C22×C4×C5C22⋊C411yescharacteristic
114C22×C4×C5C22×C411yescharacteristic
115C22×C4×C5C2×D411yescharacteristic
116C22×C4×C5C2×D411yescharacteristic
117C2×C5×C8—24no—
118C2×C5×C8—24no—
119C2×C5×C8—42no—
120C2×C5×C8—42no—
121C2×C5×C8—42no—
122C2×C5×C8—42no—
123C5×C4⋊C4—24no—
124C5×C4⋊C4—24no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—24no—
128C5×C4⋊C4—24no—
129C5×C4⋊C4C22⋊C412yes—
130C5×C4⋊C4C22⋊C412yes—
131C5×C22⋊C4—24no—
132C5×C22⋊C4—24no—
133C5×C22⋊C4—24no—
134C5×C22⋊C4—24no—
135C5×C22⋊C4—24no—
136C42×C5—24no—
137C42×C5—21no—
138C42×C5—21no—
139C42×C5—22no—
140C42×C5—22no—
141C42×C5C2×D412yes—
142C42×C5C2×D412yes—
143#529—24no—
144#529—24no—
145C2×#126—21no—
146C2×#125C22×C511yescharacteristic
147C2×#124C22×C511yescharacteristic
148C2×#123—21no—
149C2×C22⋊Q8C4×C511yescharacteristic
150C2×#121C4×C511yescharacteristic
151C2×C4×Q8C4×C511yescharacteristic
152C2×C4×D4—21no—
153C2×C4×D4C4×C511yescharacteristic
154C2×#117—21no—
155C22×C42C22×C511yescharacteristic
156C2×C22⋊C8—21no—
157C2×C22⋊C8—21no—
158C2×#97C22×C512yes—
159C2×#97C22×C512yes—
160#336—21no—
161#336—21no—
162#330—24no—
163#329—24no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—21no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—21no—
170C23×C5—22no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5#10412yes—
178C23×C5C2×C22⋊C411yescharacteristic
179C5×Q8—42no—
180C5×Q8—42no—
181C5×D4—42no—
182C5×D4—42no—
183C5×D4—48no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—22no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—44no—
202C2×C4×C5—44no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—48no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5#10412yes—
213C2×C4×C5C2×C22⋊C411yescharacteristic
214C2×C4×C5C2×C22⋊C411yescharacteristic
215C2×C4×C5#12012yes—
216C2×C4×C5#12012yes—
217C5×C8—44no—
218C5×C8—44no—
219C22×Q8C2×C4×C511yescharacteristic
220C22×D4—21no—
221C22×D4C2×C4×C511yescharacteristic
222C23×C4—21no—
223C23×C4C2×C4×C511yescharacteristic
224C23×C4C5×D411yescharacteristic
225C23×C4C5×D411yescharacteristic
226C22×C8—22no—
227C22×C8—22no—
228#126—28no—
229#125—22no—
230#125C5×D414yes—
231#124—22no—
232#124C5×D414yes—
233#123—28no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236#121—22no—
237#121—22no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×D4—28no—
241C4×D4—22no—
242C4×D4—22no—
243#117—28no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×C4×C511yescharacteristic
249C2×C4⋊C4C2×C4×C511yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42C2×C4×C511yescharacteristic
259C2×C42C5×D411yescharacteristic
260C2×C42C5×D411yescharacteristic
261C2×C42C23×C511yescharacteristic
262C22⋊C8—24no—
263C22⋊C8—24no—
264#97—22no—
265#97—22no—
266#97—22no—
267#97—22no—
268C22×C5—22no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5—42no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5#37911yescharacteristic
283C22×C5#41311yescharacteristic
284C22×C5#41311yescharacteristic
285C22×C5C2×#10411yescharacteristic
286C22×C5C2×#10411yescharacteristic
287C22×C5#42111yescharacteristic
288C22×C5#42111yescharacteristic
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—22no—
292C4×C5—22no—
293C4×C5—22no—
294C4×C5—41no—
295C4×C5—42no—
296C4×C5—41no—
297C4×C5—42no—
298C4×C5—42no—
299C24—21no—
300C24C5×C22⋊C411yescharacteristic
301C2×Q8—21no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8C5×C22⋊C412yes—
305C2×D4—24no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4C5×C22⋊C412yes—
312C22×C4—24no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C5×C22⋊C411yescharacteristic
329C22×C4C5×C22⋊C411yescharacteristic
330C22×C4C5×C22⋊C411yescharacteristic
331C22×C4C22×C4×C511yescharacteristic
332C22×C4C2×C5×D411yescharacteristic
333C22×C4C2×C5×D411yescharacteristic
334C2×C8—24no—
335C2×C8—24no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C2×C8—42no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—24no—
345C4⋊C4—24no—
346C4⋊C4C5×C22⋊C412yes—
347C4⋊C4C5×C22⋊C412yes—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C42—24no—
354C42—21no—
355C42—21no—
356C42—22no—
357C42—22no—
358C42C2×C5×D412yes—
359C42C2×C5×D412yes—
360C2×C5—42no—
361C2×C5—82no—
362C2×C5#152411yescharacteristic
363C2×C5#152911yescharacteristic
364C2×C5#153211yescharacteristic
365C2×C5#153511yescharacteristic
366C2×C5#178511yescharacteristic
367C2×C5#178911yescharacteristic
368C2×C5#178911yescharacteristic
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—22no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23C5×#10412yes—
383C23C2×C5×C22⋊C411yescharacteristic
384Q8—42no—
385Q8—42no—
386D4—42no—
387D4—42no—
388D4—48no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—48no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4C5×#10412yes—
418C2×C4C2×C5×C22⋊C411yescharacteristic
419C2×C4C2×C5×C22⋊C411yescharacteristic
420C2×C4C5×#12012yes—
421C2×C4C5×#12012yes—
422C8—44no—
423C8—44no—
424C5#833611yescharacteristic, direct product factor, Sylow
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C5×#37911yescharacteristic
440C22C5×#41311yescharacteristic
441C22C5×#41311yescharacteristic
442C22C2×C5×#10411yescharacteristic
443C22C2×C5×#10411yescharacteristic
444C22C5×#42111yescharacteristic
445C22C5×#42111yescharacteristic
446C4—21no—
447C4—21no—
448C4—22no—
449C4—22no—
450C4—22no—
451C4—41no—
452C4—42no—
453C4—41no—
454C4—42no—
455C4—42no—
456C2—42no—
457C2—82no—
458C2C5×#152411yescharacteristic
459C2C5×#152911yescharacteristic
460C2C5×#153211yescharacteristic
461C2C5×#153511yescharacteristic
462C2C5×#178511yescharacteristic
463C2C5×#178911yescharacteristic
464C2C5×#178911yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1749C2semidirect
3. C5×#1749C2semidirect
4. C2×C5×#330C2semidirect
5. C2×C5×#329C2semidirect
27. #8336C5direct (N × H)
78. #1749C2×C5semidirect
79. #1749C2×C5semidirect
80. C2×#330C2×C5semidirect
81. C2×#329C2×C5semidirect
424. C5#8336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5292
C5×#17492
C2×C5×#3302
C2×C5×#3292
#83365