Finite Group Databasebeta

← C5×#60320 #11983040

Subgroups — C5×#60320 #11983040

Order 1280.

1876 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3483C211yesmaximal, characteristic
2C5×#2990C212yesmaximal, complemented
3C5×#2989C214yesmaximal, complemented
4C5×#2981C214yesmaximal, complemented
5C5×#2980C214yesmaximal, complemented
6C5×#2979C211yesmaximal, characteristic, complemented
7C5×#2970C214yesmaximal, complemented
8C5×#2965C212yesmaximal, complemented
9C5×#2935C214yesmaximal, complemented
10C5×#2932C214yesmaximal, complemented
11C5×#2931C211yesmaximal, characteristic, complemented
12C2×C5×#131C2212yes—
13C2×C5×#131C2214yes—
14C5×Q82C411yescharacteristic
15C5×#555C411yescharacteristic
16C5×#555C414yes—
17C5×#555C414yes—
18C5×#550C412yes—
19C5×#550C414yes—
20C5×#532C2214yes—
21C5×#532C2211yescharacteristic
22C5×#532C2214yes—
23C4×C5×#41C2214yes—
24C4×C5×#41C2212yes—
25C5×#446C2212yes—
26C5×#446C2214yes—
27C5×#446C2212yes—
28C5×#436C2212yes—
29C5×#436C2214yes—
30C5×#436C2214yes—
31C5×#436C2212yes—
32C5×#435C2218yes—
33C5×#435C2218yes—
34C5×#435C2218yes—
35C5×#435C2218yes—
36C5×#435C2214yes—
37C5×#435C2218yes—
38C5×#435C2214yes—
39C5×C8×D4C2214yes—
40C5×C8×D4C2214yes—
41C5×C8×D4C2214yes—
42C5×#432C2214yes—
43C5×#432C2218yes—
44C5×#431C2214yes—
45C5×#431C2212yes—
46C5×#423C2214yes—
47C5×#423C2211yescharacteristic
48C2×C5×C4⋊C8C2214yes—
49C5×#408C2214yes—
50C5×#408C2218yes—
51C5×#408C2212yes—
52C5×#408C2214yes—
53C4×C5×M16C2214yes—
54C2×C5×#97C2214yes—
55C2×C4×C5×C8C2211yescharacteristic
56#60320C511yesmaximal, characteristic, direct product factor, Sylow
57C2×C5×#41C2×C414yes—
58C2×C5×#41C2×C412yes—
59C2×C5×#41C2314yes—
60C2×C5×#41C2312yes—
61C5×#131—44no—
62C5×#131—48no—
63C2×C5×M16C2314yes—
64C2×C5×M16C2314yes—
65C2×C5×M16C2312yes—
66C2×C5×M16C2314yes—
67C2×C5×M16C2314yes—
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2314yes—
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2314yes—
72C22×C5×C8C2318yes—
73C5×C4⋊Q8C2×C414yes—
74C5×C4⋊Q8C2×C411yescharacteristic
75C5×C4⋊Q8C2×C414yes—
76C5×#127C2×C411yescharacteristic
77C5×#127C2×C414yes—
78C5×#127C2×C414yes—
79C5×#124C2×C418yes—
80C5×#124C2×C412yes—
81C5×#124C2×C414yes—
82C5×#124C2×C414yes—
83C5×#121C2×C414yes—
84C5×#121C2×C414yes—
85C5×#121C2×C414yes—
86C5×#121C2×C418yes—
87C5×#121C2×C418yes—
88C5×#121C2×C418yes—
89C4×C5×Q8C2×C414yes—
90C4×C5×Q8C2×C412yes—
91C4×C5×Q8C2312yes—
92C4×C5×D4C2×C412yes—
93C4×C5×D4C2×C414yes—
94C4×C5×D4C2×C414yes—
95C4×C5×D4C2×C418yes—
96C4×C5×D4C2312yes—
97C4×C5×D4C2314yes—
98C4×C5×D4C2318yes—
99C4×C5×D4C2314yes—
100C5×#117C2×C414yes—
101C5×#117C2×C412yes—
102C5×#117C2×C418yes—
103C5×#117C2×C414yes—
104C2×C42×C5C2311yescharacteristic
105C2×C42×C5C2314yes—
106C2×C42×C5C2314yes—
107C5×C4⋊C8C2312yes—
108C5×C4⋊C8C2314yes—
109C5×C4⋊C8C2318yes—
110C5×C4⋊C8C2314yes—
111C5×C4⋊C8C2312yes—
112C5×C4⋊C8C2314yes—
113C5×C22⋊C8C2314yes—
114C5×C22⋊C8C2314yes—
115C5×C22⋊C8C2314yes—
116C5×C22⋊C8C2318yes—
117C5×C22⋊C8C2318yes—
118C5×C22⋊C8C2318yes—
119C5×#97C2314yes—
120C5×#97C2318yes—
121C5×#97C2314yes—
122C4×C5×C8C2312yes—
123C4×C5×C8C2312yes—
124C4×C5×C8C2314yes—
125#3483C2×C511yescharacteristic
126#2990C2×C512yescomplemented
127#2989C2×C514yescomplemented
128#2981C2×C514yescomplemented
129#2980C2×C514yescomplemented
130#2979C2×C511yescharacteristic, complemented
131#2970C2×C514yescomplemented
132#2965C2×C512yescomplemented
133#2935C2×C514yescomplemented
134#2932C2×C514yescomplemented
135#2931C2×C511yescharacteristic, complemented
136C5×#41—42no—
137C5×#41—44no—
138C5×#41—42no—
139C5×#41—44no—
140C5×#41—48no—
141C5×#41—44no—
142C2×C5×Q8C22×C412yes—
143C2×C5×Q8C22×C414yes—
144C2×C5×Q8C22×C412yes—
145C2×C5×D4C22×C412yes—
146C2×C5×D4C22×C414yes—
147C2×C5×D4C22×C414yes—
148C2×C5×D4C22×C418yes—
149C2×C5×D4C22×C414yes—
150C2×C5×D4C22×C414yes—
151C2×C5×D4C22×C418yes—
152C2×C5×D4C22×C412yes—
153C22×C4×C5C22×C412yes—
154C22×C4×C5C22×C414yes—
155C22×C4×C5C22×C418yes—
156C22×C4×C5C22×C414yes—
157C22×C4×C5C2411yescharacteristic
158C22×C4×C5C2414yes—
159C22×C4×C5C2414yes—
160C5×M16—28no—
161C5×M16—44no—
162C5×M16—42no—
163C5×M16—44no—
164C5×M16—44no—
165C2×C5×C8—28no—
166C2×C5×C8—22no—
167C2×C5×C8—44no—
168C2×C5×C8—41no—
169C2×C5×C8—48no—
170C2×C5×C8C2414yes—
171C2×C5×C8C2414yes—
172C2×C5×C8C2414yes—
173C2×C5×C8C2411yescharacteristic
174C2×C5×C8C2412yes—
175C2×C5×C8C2411yescharacteristic
176C5×C4⋊C4C22×C414yes—
177C5×C4⋊C4C22×C412yes—
178C5×C4⋊C4C22×C418yes—
179C5×C4⋊C4C22×C414yes—
180C5×C4⋊C4C22×C414yes—
181C5×C4⋊C4C22×C412yes—
182C5×C22⋊C4C22×C414yes—
183C5×C22⋊C4C22×C418yes—
184C5×C22⋊C4C22×C414yes—
185C5×C22⋊C4C22×C418yes—
186C5×C22⋊C4C22×C414yes—
187C5×C22⋊C4C22×C418yes—
188C42×C5C22×C411yescharacteristic
189C42×C5C22×C414yes—
190C42×C5C22×C414yes—
191C42×C5C22×C414yes—
192C42×C5C22×C414yes—
193C42×C5C22×C411yescharacteristic
194C42×C5C2412yes—
195C42×C5C2414yes—
196C2×#131C22×C512yes—
197C2×#131C22×C514yes—
198Q82C4×C511yescharacteristic
199#555C4×C514yes—
200#555C4×C511yescharacteristic
201#555C4×C514yes—
202#550C4×C512yes—
203#550C4×C514yes—
204#532C22×C511yescharacteristic
205#532C22×C514yes—
206#532C22×C514yes—
207C4×#41C22×C512yes—
208C4×#41C22×C514yes—
209#446C22×C512yes—
210#446C22×C512yes—
211#446C22×C514yes—
212#436C22×C514yes—
213#436C22×C512yes—
214#436C22×C514yes—
215#436C22×C512yes—
216#435C22×C514yes—
217#435C22×C518yes—
218#435C22×C518yes—
219#435C22×C518yes—
220#435C22×C518yes—
221#435C22×C514yes—
222#435C22×C518yes—
223C8×D4C22×C514yes—
224C8×D4C22×C514yes—
225C8×D4C22×C514yes—
226#432C22×C518yes—
227#432C22×C514yes—
228#431C22×C512yes—
229#431C22×C514yes—
230#423C22×C511yescharacteristic
231#423C22×C514yes—
232C2×C4⋊C8C22×C514yes—
233#408C22×C512yes—
234#408C22×C514yes—
235#408C22×C514yes—
236#408C22×C518yes—
237C4×M16C22×C514yes—
238C2×#97C22×C514yes—
239C2×C4×C8C22×C511yescharacteristic
240C23×C5C23×C411yescharacteristic
241C23×C5C23×C414yes—
242C23×C5C23×C414yes—
243C5×Q8—24no—
244C5×Q8—42no—
245C5×Q8—44no—
246C5×D4—24no—
247C5×D4—28no—
248C5×D4—44no—
249C5×D4—42no—
250C5×D4—44no—
251C5×D4—48no—
252C5×D4—44no—
253C5×D4—48no—
254C2×C4×C5—24no—
255C2×C4×C5—28no—
256C2×C4×C5—24no—
257C2×C4×C5—21no—
258C2×C4×C5—24no—
259C2×C4×C5—24no—
260C2×C4×C5—21no—
261C2×C4×C5—24no—
262C2×C4×C5—48no—
263C2×C4×C5—44no—
264C2×C4×C5C23×C412yes—
265C2×C4×C5C23×C414yes—
266C2×C4×C5C23×C414yes—
267C2×C4×C5C23×C411yescharacteristic
268C2×C4×C5C23×C414yes—
269C2×C4×C5C23×C414yes—
270C2×C4×C5C23×C412yes—
271C2×C4×C5C2511yescharacteristic
272C5×C8—24no—
273C5×C8—21no—
274C5×C8—24no—
275C5×C8—24no—
276C5×C8—22no—
277C5×C8H(5,𝔽2)12yes—
278C2×#41C2×C4×C512yes—
279C2×#41C2×C4×C514yes—
280C2×#41C23×C512yes—
281C2×#41C23×C514yes—
282#131—44no—
283#131—48no—
284C2×M16C23×C514yes—
285C2×M16C23×C512yes—
286C2×M16C23×C514yes—
287C2×M16C23×C514yes—
288C2×M16C23×C514yes—
289C22×C8C23×C511yescharacteristic
290C22×C8C23×C514yes—
291C22×C8C23×C518yes—
292C22×C8C23×C511yescharacteristic
293C22×C8C23×C514yes—
294C4⋊Q8C2×C4×C511yescharacteristic
295C4⋊Q8C2×C4×C514yes—
296C4⋊Q8C2×C4×C514yes—
297#127C2×C4×C511yescharacteristic
298#127C2×C4×C514yes—
299#127C2×C4×C514yes—
300#124C2×C4×C512yes—
301#124C2×C4×C514yes—
302#124C2×C4×C514yes—
303#124C2×C4×C518yes—
304#121C2×C4×C514yes—
305#121C2×C4×C514yes—
306#121C2×C4×C514yes—
307#121C2×C4×C518yes—
308#121C2×C4×C518yes—
309#121C2×C4×C518yes—
310C4×Q8C2×C4×C512yes—
311C4×Q8C2×C4×C514yes—
312C4×Q8C23×C512yes—
313C4×D4C2×C4×C512yes—
314C4×D4C2×C4×C514yes—
315C4×D4C2×C4×C514yes—
316C4×D4C2×C4×C518yes—
317C4×D4C23×C512yes—
318C4×D4C23×C514yes—
319C4×D4C23×C514yes—
320C4×D4C23×C518yes—
321#117C2×C4×C512yes—
322#117C2×C4×C514yes—
323#117C2×C4×C514yes—
324#117C2×C4×C518yes—
325C2×C42C23×C511yescharacteristic
326C2×C42C23×C514yes—
327C2×C42C23×C514yes—
328C4⋊C8C23×C512yes—
329C4⋊C8C23×C514yes—
330C4⋊C8C23×C518yes—
331C4⋊C8C23×C514yes—
332C4⋊C8C23×C512yes—
333C4⋊C8C23×C514yes—
334C22⋊C8C23×C514yes—
335C22⋊C8C23×C514yes—
336C22⋊C8C23×C514yes—
337C22⋊C8C23×C518yes—
338C22⋊C8C23×C518yes—
339C22⋊C8C23×C518yes—
340#97C23×C514yes—
341#97C23×C518yes—
342#97C23×C514yes—
343C4×C8C23×C512yes—
344C4×C8C23×C512yes—
345C4×C8C23×C514yes—
346C22×C5—21no—
347C22×C5—24no—
348C22×C5—24no—
349C22×C5—22no—
350C22×C5—24no—
351C22×C5—24no—
352C22×C5—28no—
353C22×C5C24×C411yescharacteristic
354C4×C5—24no—
355C4×C5—21no—
356C4×C5—24no—
357C4×C5—22no—
358C4×C5—24no—
359C4×C5—24no—
360C4×C5#56814yes—
361C4×C5C2×H(5,𝔽2)11yescharacteristic
362C4×C5#58511yescharacteristic
363#41—42no—
364#41—44no—
365#41—42no—
366#41—44no—
367#41—44no—
368#41—48no—
369C2×Q8C22×C4×C512yes—
370C2×Q8C22×C4×C512yes—
371C2×Q8C22×C4×C514yes—
372C2×D4C22×C4×C512yes—
373C2×D4C22×C4×C514yes—
374C2×D4C22×C4×C514yes—
375C2×D4C22×C4×C518yes—
376C2×D4C22×C4×C514yes—
377C2×D4C22×C4×C514yes—
378C2×D4C22×C4×C518yes—
379C2×D4C22×C4×C512yes—
380C22×C4C22×C4×C512yes—
381C22×C4C22×C4×C514yes—
382C22×C4C22×C4×C518yes—
383C22×C4C22×C4×C514yes—
384C22×C4C24×C511yescharacteristic
385C22×C4C24×C514yes—
386C22×C4C24×C514yes—
387M16—28no—
388M16—42no—
389M16—44no—
390M16—44no—
391M16—44no—
392C2×C8—28no—
393C2×C8—22no—
394C2×C8—48no—
395C2×C8—44no—
396C2×C8—41no—
397C2×C8C24×C512yes—
398C2×C8C24×C511yescharacteristic
399C2×C8C24×C514yes—
400C2×C8C24×C514yes—
401C2×C8C24×C514yes—
402C2×C8C24×C511yescharacteristic
403C4⋊C4C22×C4×C514yes—
404C4⋊C4C22×C4×C512yes—
405C4⋊C4C22×C4×C514yes—
406C4⋊C4C22×C4×C518yes—
407C4⋊C4C22×C4×C512yes—
408C4⋊C4C22×C4×C514yes—
409C22⋊C4C22×C4×C514yes—
410C22⋊C4C22×C4×C518yes—
411C22⋊C4C22×C4×C514yes—
412C22⋊C4C22×C4×C518yes—
413C22⋊C4C22×C4×C514yes—
414C22⋊C4C22×C4×C518yes—
415C42C22×C4×C511yescharacteristic
416C42C22×C4×C514yes—
417C42C22×C4×C514yes—
418C42C22×C4×C514yes—
419C42C22×C4×C514yes—
420C42C22×C4×C511yescharacteristic
421C42C24×C512yes—
422C42C24×C514yes—
423C2×C5—41no—
424C2×C5—44no—
425C2×C5—44no—
426C2×C5C4×H(5,𝔽2)11yescharacteristic
427C2×C5C2×#56812yes—
428C23C23×C4×C511yescharacteristic
429C23C23×C4×C514yes—
430C23C23×C4×C514yes—
431Q8—24no—
432Q8—42no—
433Q8—44no—
434D4—24no—
435D4—28no—
436D4—44no—
437D4—42no—
438D4—44no—
439D4—48no—
440D4—44no—
441D4—48no—
442C2×C4—24no—
443C2×C4—28no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—48no—
451C2×C4—44no—
452C2×C4C23×C4×C512yes—
453C2×C4C23×C4×C514yes—
454C2×C4C23×C4×C514yes—
455C2×C4C23×C4×C511yescharacteristic
456C2×C4C23×C4×C514yes—
457C2×C4C23×C4×C514yes—
458C2×C4C23×C4×C512yes—
459C2×C4C25×C511yescharacteristic
460C8—24no—
461C8—21no—
462C8—24no—
463C8—24no—
464C8—22no—
465C8C5×H(5,𝔽2)12yes—
466C5#6032011yescharacteristic, direct product factor, Sylow
467C22—21no—
468C22—24no—
469C22—24no—
470C22—22no—
471C22—24no—
472C22—24no—
473C22—28no—
474C22C24×C4×C511yescharacteristic
475C4—24no—
476C4—21no—
477C4—24no—
478C4—22no—
479C4—24no—
480C4—24no—
481C4C5×#56814yes—
482C4C2×C5×H(5,𝔽2)11yescharacteristic
483C4C5×#58511yescharacteristic
484C2—41no—
485C2—44no—
486C2—44no—
487C2C4×C5×H(5,𝔽2)11yescharacteristic
488C2C2×C5×#56812yes—
subgroupG/H
centerC2×C4×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC2×C4C25×C5
socleC22×C5C24×C4
prime radicalC5×#3483C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2990C2semidirect
3. C5×#2989C2semidirect
4. C5×#2981C2semidirect
5. C5×#2980C2semidirect
6. C5×#2979C2semidirect
7. C5×#2970C2semidirect
8. C5×#2965C2semidirect
9. C5×#2935C2semidirect
10. C5×#2932C2semidirect
11. C5×#2931C2semidirect
56. #60320C5direct (N × H)
126. #2990C2×C5semidirect
127. #2989C2×C5semidirect
128. #2981C2×C5semidirect
129. #2980C2×C5semidirect
130. #2979C2×C5semidirect
131. #2970C2×C5semidirect
132. #2965C2×C5semidirect
133. #2935C2×C5semidirect
134. #2932C2×C5semidirect
135. #2931C2×C5semidirect
466. C5#60320direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34832
C5×#29902
C5×#29892
C5×#29812
C5×#29802
C5×#29792
C5×#29702
C5×#29652
C5×#29352
C5×#29322
C5×#29312
#603205