Finite Group Databasebeta

← C5×#60338 #11983058

Subgroups — C5×#60338 #11983058

Order 1280.

1628 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3531C211yesmaximal, characteristic
2C5×#2995C212yesmaximal, complemented
3C5×#2994C214yesmaximal, complemented
4C5×#2992C214yesmaximal, complemented
5C5×#2987C211yesmaximal, characteristic, complemented
6C5×#2985C214yesmaximal, complemented
7C5×#2969C214yesmaximal, complemented
8C5×#2967C214yesmaximal, complemented
9C5×#2966C212yesmaximal, complemented
10C5×#2962C214yesmaximal, complemented
11C5×#2960C211yesmaximal, characteristic, complemented
12C5×#564C411yescharacteristic
13C5×#563C414yes—
14C5×#563C414yes—
15C5×#563C412yes—
16C5×#562C411yescharacteristic
17C5×#562C414yes—
18C5×#533C2214yes—
19C5×#533C2211yescharacteristic
20C5×#529C2214yes—
21C5×#529C2214yes—
22C5×#529C2212yes—
23C5×#446C2214yes—
24C5×#446C2214yes—
25C5×#446C2214yes—
26C5×#446C2214yes—
27C5×#446C2214yes—
28C5×#446C2214yes—
29C5×#446C2212yes—
30C5×#446C2214yes—
31C5×C8×Q8C2212yes—
32C5×C8×Q8C2214yes—
33C5×C8×Q8C2214yes—
34C5×#436C2214yes—
35C5×#436C2212yes—
36C5×#436C2214yes—
37C5×#435C2214yes—
38C5×#435C2214yes—
39C5×#435C2214yes—
40C5×#435C2214yes—
41C5×#435C2214yes—
42C5×C8×D4C2212yes—
43C5×C8×D4C2214yes—
44C5×C8×D4C2214yes—
45C5×#433C2214yes—
46C5×#433C2214yes—
47C5×#433C2214yes—
48C5×#433C2214yes—
49C5×#433C2214yes—
50C5×#432C2214yes—
51C5×#432C2212yes—
52C5×#431C2214yes—
53C5×#424C2214yes—
54C5×#424C2214yes—
55C5×#424C2212yes—
56C5×#423C2211yescharacteristic
57C2×C5×C4⋊C8C2214yes—
58C5×#405C2212yes—
59C5×#405C2214yes—
60C5×#405C2214yes—
61C4×C5×M16C2214yes—
62C2×C4×C5×C8C2211yescharacteristic
63#60338C511yesmaximal, characteristic, direct product factor, Sylow
64C2×C5×M16C2314yes—
65C2×C5×M16C2314yes—
66C2×C5×M16C2312yes—
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2314yes—
70C22×C5×C8C2314yes—
71C5×C4⋊Q8C2×C414yes—
72C5×C4⋊Q8C2×C414yes—
73C5×C4⋊Q8C2×C412yes—
74C5×#126C2×C414yes—
75C5×#126C2×C414yes—
76C5×#126C2×C414yes—
77C5×#126C2×C414yes—
78C5×#126C2×C414yes—
79C5×#125C2×C414yes—
80C5×#125C2×C414yes—
81C5×#125C2×C412yes—
82C5×#125C2×C414yes—
83C5×#125C2×C411yescharacteristic
84C5×#125C2×C414yes—
85C5×#125C2×C411yescharacteristic
86C5×#124C2×C414yes—
87C5×#124C2×C414yes—
88C5×#124C2×C412yes—
89C5×#123C2×C414yes—
90C5×#123C2×C414yes—
91C5×#123C2×C414yes—
92C5×#123C2×C414yes—
93C5×#123C2×C414yes—
94C5×C22⋊Q8C2×C414yes—
95C5×C22⋊Q8C2×C414yes—
96C5×C22⋊Q8C2×C412yes—
97C5×C22⋊Q8C2×C414yes—
98C5×C22⋊Q8C2×C414yes—
99C5×C22⋊Q8C2×C414yes—
100C5×C22⋊Q8C2×C414yes—
101C5×C22⋊Q8C2×C414yes—
102C5×#121C2×C414yes—
103C5×#121C2×C414yes—
104C5×#121C2×C412yes—
105C4×C5×Q8C2312yes—
106C4×C5×Q8C2314yes—
107C4×C5×Q8C2314yes—
108C4×C5×D4C2312yes—
109C4×C5×D4C2314yes—
110C4×C5×D4C2314yes—
111C5×#117C2312yes—
112C5×#117C2314yes—
113C5×#117C2314yes—
114C2×C42×C5C2311yescharacteristic
115C2×C42×C5C2314yes—
116C5×C4⋊C8C2314yes—
117C5×C4⋊C8C2314yes—
118C5×C4⋊C8C2314yes—
119C5×C4⋊C8C2314yes—
120C5×C4⋊C8C2314yes—
121C5×C4⋊C8C2314yes—
122C5×C4⋊C8C2312yes—
123C5×C4⋊C8C2314yes—
124C5×C4⋊C8C2314yes—
125C5×C4⋊C8C2314yes—
126C5×C4⋊C8C2312yes—
127C5×C22⋊C8C2314yes—
128C5×C22⋊C8C2314yes—
129C5×C22⋊C8C2314yes—
130C5×C22⋊C8C2314yes—
131C5×C22⋊C8C2314yes—
132C5×#97C2314yes—
133C5×#97C2314yes—
134C5×#97C2314yes—
135C5×#97C2314yes—
136C5×#97C2314yes—
137C4×C5×C8C2312yes—
138C4×C5×C8C2312yes—
139C4×C5×C8C2314yes—
140C4×C5×C8C2314yes—
141C4×C5×C8C2314yes—
142C4×C5×C8C2314yes—
143#3531C2×C511yescharacteristic
144#2995C2×C512yescomplemented
145#2994C2×C514yescomplemented
146#2992C2×C514yescomplemented
147#2987C2×C511yescharacteristic, complemented
148#2985C2×C514yescomplemented
149#2969C2×C514yescomplemented
150#2967C2×C514yescomplemented
151#2966C2×C512yescomplemented
152#2962C2×C514yescomplemented
153#2960C2×C511yescharacteristic, complemented
154C2×C5×Q8C22×C412yes—
155C2×C5×Q8C22×C414yes—
156C2×C5×Q8C22×C414yes—
157C2×C5×D4C22×C412yes—
158C2×C5×D4C22×C414yes—
159C2×C5×D4C22×C414yes—
160C22×C4×C5C22×C412yes—
161C22×C4×C5C22×C414yes—
162C22×C4×C5C22×C414yes—
163C22×C4×C5C2411yescharacteristic
164C22×C4×C5C2414yes—
165C5×M16—28no—
166C5×M16—44no—
167C5×M16—42no—
168C2×C5×C8—22no—
169C2×C5×C8—41no—
170C2×C5×C8—44no—
171C2×C5×C8—44no—
172C2×C5×C8C2412yes—
173C2×C5×C8C2414yes—
174C2×C5×C8C2414yes—
175C2×C5×C8C2411yescharacteristic
176C2×C5×C8C2414yes—
177C2×C5×C8C2411yescharacteristic
178C5×C4⋊C4C22×C412yes—
179C5×C4⋊C4C22×C414yes—
180C5×C4⋊C4C22×C414yes—
181C5×C4⋊C4C22×C412yes—
182C5×C4⋊C4C22×C414yes—
183C5×C4⋊C4C22×C414yes—
184C5×C4⋊C4C22×C412yes—
185C5×C4⋊C4C22×C414yes—
186C5×C4⋊C4C22×C414yes—
187C5×C4⋊C4C22×C412yes—
188C5×C4⋊C4C22×C414yes—
189C5×C4⋊C4C22×C414yes—
190C5×C4⋊C4C22×C414yes—
191C5×C4⋊C4C22×C414yes—
192C5×C4⋊C4C22×C414yes—
193C5×C4⋊C4C22×C414yes—
194C5×C4⋊C4C22×C414yes—
195C5×C22⋊C4C22×C414yes—
196C5×C22⋊C4C22×C414yes—
197C5×C22⋊C4C22×C414yes—
198C5×C22⋊C4C22×C414yes—
199C5×C22⋊C4C22×C414yes—
200C5×C22⋊C4C22×C414yes—
201C5×C22⋊C4C22×C414yes—
202C5×C22⋊C4C22×C414yes—
203C5×C22⋊C4C22×C414yes—
204C5×C22⋊C4C22×C414yes—
205C42×C5C22×C411yescharacteristic
206C42×C5C22×C414yes—
207C42×C5C22×C411yescharacteristic
208C42×C5C22×C414yes—
209C42×C5C2412yes—
210C42×C5C2414yes—
211C42×C5C2414yes—
212#564C4×C511yescharacteristic
213#563C4×C514yes—
214#563C4×C512yes—
215#563C4×C514yes—
216#562C4×C514yes—
217#562C4×C511yescharacteristic
218#533C22×C511yescharacteristic
219#533C22×C514yes—
220#529C22×C512yes—
221#529C22×C514yes—
222#529C22×C514yes—
223#446C22×C514yes—
224#446C22×C512yes—
225#446C22×C514yes—
226#446C22×C514yes—
227#446C22×C514yes—
228#446C22×C514yes—
229#446C22×C514yes—
230#446C22×C514yes—
231C8×Q8C22×C514yes—
232C8×Q8C22×C514yes—
233C8×Q8C22×C512yes—
234#436C22×C512yes—
235#436C22×C514yes—
236#436C22×C514yes—
237#435C22×C514yes—
238#435C22×C514yes—
239#435C22×C514yes—
240#435C22×C514yes—
241#435C22×C514yes—
242C8×D4C22×C512yes—
243C8×D4C22×C514yes—
244C8×D4C22×C514yes—
245#433C22×C514yes—
246#433C22×C514yes—
247#433C22×C514yes—
248#433C22×C514yes—
249#433C22×C514yes—
250#432C22×C512yes—
251#432C22×C514yes—
252#431C22×C514yes—
253#424C22×C512yes—
254#424C22×C514yes—
255#424C22×C514yes—
256#423C22×C511yescharacteristic
257C2×C4⋊C8C22×C514yes—
258#405C22×C512yes—
259#405C22×C514yes—
260#405C22×C514yes—
261C4×M16C22×C514yes—
262C2×C4×C8C22×C511yescharacteristic
263C23×C5C23×C411yescharacteristic
264C23×C5C23×C414yes—
265C5×Q8—42no—
266C5×Q8—44no—
267C5×Q8—44no—
268C5×D4—42no—
269C5×D4—44no—
270C5×D4—44no—
271C2×C4×C5—21no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—21no—
275C2×C4×C5—42no—
276C2×C4×C5—44no—
277C2×C4×C5—44no—
278C2×C4×C5C23×C411yescharacteristic
279C2×C4×C5C23×C414yes—
280C2×C4×C5C23×C412yes—
281C2×C4×C5C23×C414yes—
282C2×C4×C5C23×C414yes—
283C2×C4×C5C23×C412yes—
284C2×C4×C5C23×C414yes—
285C2×C4×C5C23×C414yes—
286C2×C4×C5C2511yescharacteristic
287C5×C8—21no—
288C5×C8—24no—
289C5×C8—22no—
290C5×C8—24no—
291C5×C8—24no—
292C5×C82−1+412yes—
293C2×M16C23×C514yes—
294C2×M16C23×C514yes—
295C2×M16C23×C512yes—
296C22×C8C23×C511yescharacteristic
297C22×C8C23×C511yescharacteristic
298C22×C8C23×C514yes—
299C22×C8C23×C514yes—
300C4⋊Q8C2×C4×C512yes—
301C4⋊Q8C2×C4×C514yes—
302C4⋊Q8C2×C4×C514yes—
303#126C2×C4×C514yes—
304#126C2×C4×C514yes—
305#126C2×C4×C514yes—
306#126C2×C4×C514yes—
307#126C2×C4×C514yes—
308#125C2×C4×C512yes—
309#125C2×C4×C514yes—
310#125C2×C4×C514yes—
311#125C2×C4×C511yescharacteristic
312#125C2×C4×C514yes—
313#125C2×C4×C511yescharacteristic
314#125C2×C4×C514yes—
315#124C2×C4×C512yes—
316#124C2×C4×C514yes—
317#124C2×C4×C514yes—
318#123C2×C4×C514yes—
319#123C2×C4×C514yes—
320#123C2×C4×C514yes—
321#123C2×C4×C514yes—
322#123C2×C4×C514yes—
323C22⋊Q8C2×C4×C512yes—
324C22⋊Q8C2×C4×C514yes—
325C22⋊Q8C2×C4×C514yes—
326C22⋊Q8C2×C4×C514yes—
327C22⋊Q8C2×C4×C514yes—
328C22⋊Q8C2×C4×C514yes—
329C22⋊Q8C2×C4×C514yes—
330C22⋊Q8C2×C4×C514yes—
331#121C2×C4×C512yes—
332#121C2×C4×C514yes—
333#121C2×C4×C514yes—
334C4×Q8C23×C512yes—
335C4×Q8C23×C514yes—
336C4×Q8C23×C514yes—
337C4×D4C23×C514yes—
338C4×D4C23×C512yes—
339C4×D4C23×C514yes—
340#117C23×C514yes—
341#117C23×C512yes—
342#117C23×C514yes—
343C2×C42C23×C511yescharacteristic
344C2×C42C23×C514yes—
345C4⋊C8C23×C514yes—
346C4⋊C8C23×C514yes—
347C4⋊C8C23×C514yes—
348C4⋊C8C23×C514yes—
349C4⋊C8C23×C514yes—
350C4⋊C8C23×C514yes—
351C4⋊C8C23×C512yes—
352C4⋊C8C23×C514yes—
353C4⋊C8C23×C514yes—
354C4⋊C8C23×C514yes—
355C4⋊C8C23×C512yes—
356C22⋊C8C23×C514yes—
357C22⋊C8C23×C514yes—
358C22⋊C8C23×C514yes—
359C22⋊C8C23×C514yes—
360C22⋊C8C23×C514yes—
361#97C23×C514yes—
362#97C23×C514yes—
363#97C23×C514yes—
364#97C23×C514yes—
365#97C23×C514yes—
366C4×C8C23×C512yes—
367C4×C8C23×C512yes—
368C4×C8C23×C514yes—
369C4×C8C23×C514yes—
370C4×C8C23×C514yes—
371C4×C8C23×C514yes—
372C22×C5—21no—
373C22×C5—24no—
374C22×C5—22no—
375C22×C5—24no—
376C22×C5—24no—
377C22×C5C24×C411yescharacteristic
378C4×C5—21no—
379C4×C5—24no—
380C4×C5—22no—
381C4×C5—24no—
382C4×C5—24no—
383C4×C5—22no—
384C4×C5—24no—
385C4×C5—24no—
386C4×C5C2×2−1+411yescharacteristic
387C4×C5#58511yescharacteristic
388C2×Q8C22×C4×C512yes—
389C2×Q8C22×C4×C514yes—
390C2×Q8C22×C4×C514yes—
391C2×D4C22×C4×C514yes—
392C2×D4C22×C4×C512yes—
393C2×D4C22×C4×C514yes—
394C22×C4C22×C4×C512yes—
395C22×C4C22×C4×C514yes—
396C22×C4C22×C4×C514yes—
397C22×C4C24×C511yescharacteristic
398C22×C4C24×C514yes—
399M16—28no—
400M16—44no—
401M16—42no—
402C2×C8—22no—
403C2×C8—41no—
404C2×C8—44no—
405C2×C8—44no—
406C2×C8C24×C512yes—
407C2×C8C24×C514yes—
408C2×C8C24×C511yescharacteristic
409C2×C8C24×C514yes—
410C2×C8C24×C514yes—
411C2×C8C24×C511yescharacteristic
412C4⋊C4C22×C4×C514yes—
413C4⋊C4C22×C4×C512yes—
414C4⋊C4C22×C4×C514yes—
415C4⋊C4C22×C4×C514yes—
416C4⋊C4C22×C4×C512yes—
417C4⋊C4C22×C4×C514yes—
418C4⋊C4C22×C4×C514yes—
419C4⋊C4C22×C4×C512yes—
420C4⋊C4C22×C4×C514yes—
421C4⋊C4C22×C4×C512yes—
422C4⋊C4C22×C4×C514yes—
423C4⋊C4C22×C4×C514yes—
424C4⋊C4C22×C4×C514yes—
425C4⋊C4C22×C4×C514yes—
426C4⋊C4C22×C4×C514yes—
427C4⋊C4C22×C4×C514yes—
428C4⋊C4C22×C4×C514yes—
429C22⋊C4C22×C4×C514yes—
430C22⋊C4C22×C4×C514yes—
431C22⋊C4C22×C4×C514yes—
432C22⋊C4C22×C4×C514yes—
433C22⋊C4C22×C4×C514yes—
434C22⋊C4C22×C4×C514yes—
435C22⋊C4C22×C4×C514yes—
436C22⋊C4C22×C4×C514yes—
437C22⋊C4C22×C4×C514yes—
438C22⋊C4C22×C4×C514yes—
439C42C22×C4×C511yescharacteristic
440C42C22×C4×C514yes—
441C42C22×C4×C511yescharacteristic
442C42C22×C4×C514yes—
443C42C24×C512yes—
444C42C24×C514yes—
445C42C24×C514yes—
446C2×C5—41no—
447C2×C5—44no—
448C2×C5C4×2−1+411yescharacteristic
449C2×C5#357312yes—
450C23C23×C4×C511yescharacteristic
451C23C23×C4×C514yes—
452Q8—42no—
453Q8—44no—
454Q8—44no—
455D4—44no—
456D4—42no—
457D4—44no—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—21no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4C23×C4×C511yescharacteristic
466C2×C4C23×C4×C514yes—
467C2×C4C23×C4×C512yes—
468C2×C4C23×C4×C514yes—
469C2×C4C23×C4×C514yes—
470C2×C4C23×C4×C512yes—
471C2×C4C23×C4×C514yes—
472C2×C4C23×C4×C514yes—
473C2×C4C25×C511yescharacteristic
474C8—21no—
475C8—24no—
476C8—22no—
477C8—24no—
478C8—24no—
479C8C5×2−1+412yes—
480C5#6033811yescharacteristic, direct product factor, Sylow
481C22—21no—
482C22—24no—
483C22—22no—
484C22—24no—
485C22—24no—
486C22C24×C4×C511yescharacteristic
487C4—21no—
488C4—24no—
489C4—22no—
490C4—24no—
491C4—24no—
492C4—22no—
493C4—24no—
494C4—24no—
495C4C2×C5×2−1+411yescharacteristic
496C4C5×#58511yescharacteristic
497C2—41no—
498C2—44no—
499C2C4×C5×2−1+411yescharacteristic
500C2C5×#357312yes—
subgroupG/H
centerC2×C4×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC2×C4C25×C5
socleC22×C5C24×C4
prime radicalC5×#3531C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2995C2semidirect
3. C5×#2994C2semidirect
4. C5×#2992C2semidirect
5. C5×#2987C2semidirect
6. C5×#2985C2semidirect
7. C5×#2969C2semidirect
8. C5×#2967C2semidirect
9. C5×#2966C2semidirect
10. C5×#2962C2semidirect
11. C5×#2960C2semidirect
63. #60338C5direct (N × H)
144. #2995C2×C5semidirect
145. #2994C2×C5semidirect
146. #2992C2×C5semidirect
147. #2987C2×C5semidirect
148. #2985C2×C5semidirect
149. #2969C2×C5semidirect
150. #2967C2×C5semidirect
151. #2966C2×C5semidirect
152. #2962C2×C5semidirect
153. #2960C2×C5semidirect
480. C5#60338direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35312
C5×#29952
C5×#29942
C5×#29922
C5×#29872
C5×#29852
C5×#29692
C5×#29672
C5×#29662
C5×#29622
C5×#29602
#603385