Finite Group Databasebeta

← C5×#60334 #11983054

Subgroups — C5×#60334 #11983054

Order 1280.

1710 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3461C211yesmaximal, characteristic
2C5×#2994C214yesmaximal, complemented
3C5×#2992C214yesmaximal, complemented
4C5×#2988C212yesmaximal, complemented
5C5×#2986C214yesmaximal, complemented
6C5×#2983C211yesmaximal, characteristic, complemented
7C5×#2969C214yesmaximal, complemented
8C5×#2966C214yesmaximal, complemented
9C5×#2965C212yesmaximal, complemented
10C5×#2962C214yesmaximal, complemented
11C2×C5×C8×Q8C211yesmaximal, characteristic, complemented
12C5×#544C411yescharacteristic
13C5×#542C414yes—
14C5×#541C414yes—
15C5×#539C414yes—
16C5×#537C411yescharacteristic
17C5×#536C412yes—
18C5×#533C2214yes—
19C5×#529C2214yes—
20C5×#529C2214yes—
21C4×C5×#41C2212yes—
22C2×C4×C5×Q8C2211yescharacteristic
23C5×#446C2214yes—
24C5×#446C2214yes—
25C5×#446C2212yes—
26C5×#446C2218yes—
27C5×#446C2212yes—
28C5×#446C2214yes—
29C5×C8×Q8C2214yes—
30C5×C8×Q8C2214yes—
31C5×C8×Q8C2214yes—
32C5×C8×Q8C2214yes—
33C5×#436C2212yes—
34C5×#436C2212yes—
35C5×#436C2214yes—
36C5×#435C2214yes—
37C5×#435C2218yes—
38C5×#435C2214yes—
39C5×C8×D4C2218yes—
40C5×C8×D4C2214yes—
41C5×C8×D4C2214yes—
42C5×#433C2218yes—
43C5×#433C2218yes—
44C5×#432C2214yes—
45C5×#431C2212yes—
46C5×#431C2214yes—
47C5×#431C2214yes—
48C5×#424C2218yes—
49C2×C5×C4⋊C8C2211yescharacteristic
50C2×C5×C4⋊C8C2214yes—
51C2×C5×C4⋊C8C2212yes—
52C5×#405C2218yes—
53C4×C5×M16C2214yes—
54C2×C4×C5×C8C2211yescharacteristic
55C2×C4×C5×C8C2212yes—
56#60334C511yesmaximal, characteristic, direct product factor, Sylow
57C2×C5×#41C2×C412yes—
58C22×C5×Q8C2×C411yescharacteristic
59C2×C5×M16C2314yes—
60C2×C5×M16C2314yes—
61C22×C5×C8C2311yescharacteristic
62C22×C5×C8C2312yes—
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2318yes—
65C5×C4⋊Q8C2×C414yes—
66C5×C4⋊Q8C2×C414yes—
67C5×#126C2×C418yes—
68C5×#126C2×C418yes—
69C5×#125C2×C414yes—
70C5×#125C2×C414yes—
71C5×#125C2×C418yes—
72C5×#124C2×C414yes—
73C5×#124C2×C414yes—
74C5×#123C2×C418yes—
75C5×#123C2×C418yes—
76C5×C22⋊Q8C2×C414yes—
77C5×C22⋊Q8C2×C414yes—
78C5×C22⋊Q8C2×C414yes—
79C5×C22⋊Q8C2×C414yes—
80C5×C22⋊Q8C2×C418yes—
81C5×#121C2×C414yes—
82C5×#121C2×C414yes—
83C4×C5×Q8C2×C414yes—
84C4×C5×Q8C2×C412yes—
85C4×C5×Q8C2314yes—
86C4×C5×Q8C2312yes—
87C4×C5×Q8C2314yes—
88C4×C5×D4C2×C414yes—
89C4×C5×D4C2×C412yes—
90C4×C5×D4C2314yes—
91C4×C5×D4C2312yes—
92C4×C5×D4C2314yes—
93C5×#117C2×C412yes—
94C5×#117C2×C414yes—
95C5×#117C2318yes—
96C2×C5×C4⋊C4C2×C411yescharacteristic
97C2×C5×C4⋊C4C2×C412yes—
98C2×C42×C5C2311yescharacteristic
99C2×C42×C5C2312yes—
100C2×C42×C5C2314yes—
101C5×C4⋊C8C2314yes—
102C5×C4⋊C8C2312yes—
103C5×C4⋊C8C2318yes—
104C5×C4⋊C8C2318yes—
105C5×C4⋊C8C2314yes—
106C5×C4⋊C8C2314yes—
107C5×C4⋊C8C2312yes—
108C5×C4⋊C8C2314yes—
109C5×C4⋊C8C2314yes—
110C5×C22⋊C8C2314yes—
111C5×C22⋊C8C2318yes—
112C5×C22⋊C8C2314yes—
113C5×C22⋊C8C2314yes—
114C5×#97C2314yes—
115C5×#97C2314yes—
116C5×#97C2318yes—
117C4×C5×C8C2312yes—
118C4×C5×C8C2314yes—
119C4×C5×C8C2312yes—
120C4×C5×C8C2314yes—
121C4×C5×C8C2314yes—
122C4×C5×C8C2318yes—
123#3461C2×C511yescharacteristic
124#2994C2×C514yescomplemented
125#2992C2×C514yescomplemented
126#2988C2×C512yescomplemented
127#2986C2×C514yescomplemented
128#2983C2×C511yescharacteristic, complemented
129#2969C2×C514yescomplemented
130#2966C2×C514yescomplemented
131#2965C2×C512yescomplemented
132#2962C2×C514yescomplemented
133C2×C8×Q8C2×C511yescharacteristic, complemented
134C5×#41—28no—
135C2×C5×Q8—24no—
136C2×C5×Q8C22×C414yes—
137C2×C5×Q8C22×C412yes—
138C2×C5×Q8C22×C414yes—
139C2×C5×D4C22×C414yes—
140C2×C5×D4C22×C412yes—
141C2×C5×D4C22×C414yes—
142C22×C4×C5C22×C412yes—
143C22×C4×C5C22×C414yes—
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5C22×C412yes—
146C22×C4×C5C22×C414yes—
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C2411yescharacteristic
149C22×C4×C5C2414yes—
150C5×M16—28no—
151C5×M16—44no—
152C2×C5×C8—22no—
153C2×C5×C8—42no—
154C2×C5×C8—48no—
155C2×C5×C8—41no—
156C2×C5×C8C2414yes—
157C2×C5×C8C2414yes—
158C2×C5×C8C2412yes—
159C2×C5×C8C2411yescharacteristic
160C2×C5×C8C2414yes—
161C2×C5×C8C2411yescharacteristic
162C5×C4⋊C4C22×C414yes—
163C5×C4⋊C4C22×C418yes—
164C5×C4⋊C4C22×C414yes—
165C5×C4⋊C4C22×C412yes—
166C5×C4⋊C4C22×C412yes—
167C5×C4⋊C4C22×C414yes—
168C5×C4⋊C4C22×C418yes—
169C5×C4⋊C4C22×C418yes—
170C5×C4⋊C4C22×C414yes—
171C5×C4⋊C4C22×C414yes—
172C5×C4⋊C4C22×C418yes—
173C5×C22⋊C4C22×C414yes—
174C5×C22⋊C4C22×C414yes—
175C5×C22⋊C4C22×C414yes—
176C5×C22⋊C4C22×C418yes—
177C5×C22⋊C4C22×C418yes—
178C5×C22⋊C4C22×C418yes—
179C42×C5C22×C412yes—
180C42×C5C22×C414yes—
181C42×C5C22×C414yes—
182C42×C5C22×C414yes—
183C42×C5C2412yes—
184C42×C5C2414yes—
185C42×C5C2414yes—
186#544C4×C511yescharacteristic
187#542C4×C514yes—
188#541C4×C514yes—
189#539C4×C514yes—
190#537C4×C511yescharacteristic
191#536C4×C512yes—
192#533C22×C514yes—
193#529C22×C514yes—
194#529C22×C514yes—
195C4×#41C22×C512yes—
196C2×C4×Q8C22×C511yescharacteristic
197#446C22×C512yes—
198#446C22×C514yes—
199#446C22×C514yes—
200#446C22×C518yes—
201#446C22×C512yes—
202#446C22×C514yes—
203C8×Q8C22×C514yes—
204C8×Q8C22×C514yes—
205C8×Q8C22×C514yes—
206C8×Q8C22×C514yes—
207#436C22×C512yes—
208#436C22×C512yes—
209#436C22×C514yes—
210#435C22×C514yes—
211#435C22×C514yes—
212#435C22×C518yes—
213C8×D4C22×C518yes—
214C8×D4C22×C514yes—
215C8×D4C22×C514yes—
216#433C22×C518yes—
217#433C22×C518yes—
218#432C22×C514yes—
219#431C22×C512yes—
220#431C22×C514yes—
221#431C22×C514yes—
222#424C22×C518yes—
223C2×C4⋊C8C22×C511yescharacteristic
224C2×C4⋊C8C22×C512yes—
225C2×C4⋊C8C22×C514yes—
226#405C22×C518yes—
227C4×M16C22×C514yes—
228C2×C4×C8C22×C511yescharacteristic
229C2×C4×C8C22×C512yes—
230C23×C5C23×C414yes—
231C23×C5C23×C411yescharacteristic
232C5×Q8—28no—
233C5×Q8—24no—
234C5×Q8—44no—
235C5×D4—28no—
236C5×D4—24no—
237C5×D4—44no—
238C2×C4×C5—24no—
239C2×C4×C5—28no—
240C2×C4×C5—21no—
241C2×C4×C5—24no—
242C2×C4×C5—21no—
243C2×C4×C5—24no—
244C2×C4×C5—41no—
245C2×C4×C5—44no—
246C2×C4×C5—42no—
247C2×C4×C5#13114yes—
248C2×C4×C5C23×C411yescharacteristic
249C2×C4×C5C23×C412yes—
250C2×C4×C5C23×C414yes—
251C2×C4×C5C23×C414yes—
252C2×C4×C5C23×C414yes—
253C2×C4×C5C23×C414yes—
254C2×C4×C5C23×C414yes—
255C2×C4×C5C23×C412yes—
256C2×C4×C5C2511yescharacteristic
257C5×C8—21no—
258C5×C8—24no—
259C5×C8—24no—
260C5×C8—24no—
261C5×C8—22no—
262C5×C82−1+412yes—
263C2×#41C2×C4×C512yes—
264C22×Q8C2×C4×C511yescharacteristic
265C2×M16C23×C514yes—
266C2×M16C23×C514yes—
267C22×C8C23×C511yescharacteristic
268C22×C8C23×C512yes—
269C22×C8C23×C511yescharacteristic
270C22×C8C23×C518yes—
271C4⋊Q8C2×C4×C514yes—
272C4⋊Q8C2×C4×C514yes—
273#126C2×C4×C518yes—
274#126C2×C4×C518yes—
275#125C2×C4×C514yes—
276#125C2×C4×C514yes—
277#125C2×C4×C518yes—
278#124C2×C4×C514yes—
279#124C2×C4×C514yes—
280#123C2×C4×C518yes—
281#123C2×C4×C518yes—
282C22⋊Q8C2×C4×C514yes—
283C22⋊Q8C2×C4×C514yes—
284C22⋊Q8C2×C4×C514yes—
285C22⋊Q8C2×C4×C514yes—
286C22⋊Q8C2×C4×C518yes—
287#121C2×C4×C514yes—
288#121C2×C4×C514yes—
289C4×Q8C2×C4×C514yes—
290C4×Q8C2×C4×C512yes—
291C4×Q8C23×C514yes—
292C4×Q8C23×C512yes—
293C4×Q8C23×C514yes—
294C4×D4C2×C4×C514yes—
295C4×D4C2×C4×C512yes—
296C4×D4C23×C514yes—
297C4×D4C23×C512yes—
298C4×D4C23×C514yes—
299#117C2×C4×C512yes—
300#117C2×C4×C514yes—
301#117C23×C518yes—
302C2×C4⋊C4C2×C4×C511yescharacteristic
303C2×C4⋊C4C2×C4×C512yes—
304C2×C42C23×C511yescharacteristic
305C2×C42C23×C512yes—
306C2×C42C23×C514yes—
307C4⋊C8C23×C514yes—
308C4⋊C8C23×C512yes—
309C4⋊C8C23×C518yes—
310C4⋊C8C23×C518yes—
311C4⋊C8C23×C514yes—
312C4⋊C8C23×C514yes—
313C4⋊C8C23×C512yes—
314C4⋊C8C23×C514yes—
315C4⋊C8C23×C514yes—
316C22⋊C8C23×C514yes—
317C22⋊C8C23×C514yes—
318C22⋊C8C23×C518yes—
319C22⋊C8C23×C514yes—
320#97C23×C514yes—
321#97C23×C514yes—
322#97C23×C518yes—
323C4×C8C23×C512yes—
324C4×C8C23×C514yes—
325C4×C8C23×C512yes—
326C4×C8C23×C514yes—
327C4×C8C23×C514yes—
328C4×C8C23×C518yes—
329C22×C5—21no—
330C22×C5—21no—
331C22×C5—24no—
332C22×C5—24no—
333C22×C5—24no—
334C22×C5C2×#13112yes—
335C22×C5C24×C411yescharacteristic
336C4×C5—21no—
337C4×C5—24no—
338C4×C5—24no—
339C4×C5—24no—
340C4×C5—22no—
341C4×C5—24no—
342C4×C5—24no—
343C4×C5C2×#13114yes—
344C4×C5C2×2−1+411yescharacteristic
345C4×C5#58511yescharacteristic
346#41—28no—
347C2×Q8—24no—
348C2×Q8C22×C4×C514yes—
349C2×Q8C22×C4×C512yes—
350C2×Q8C22×C4×C514yes—
351C2×D4C22×C4×C514yes—
352C2×D4C22×C4×C512yes—
353C2×D4C22×C4×C514yes—
354C22×C4C22×C4×C512yes—
355C22×C4C22×C4×C514yes—
356C22×C4C22×C4×C511yescharacteristic
357C22×C4C22×C4×C512yes—
358C22×C4C22×C4×C514yes—
359C22×C4C22×C4×C511yescharacteristic
360C22×C4C24×C511yescharacteristic
361C22×C4C24×C514yes—
362M16—28no—
363M16—44no—
364C2×C8—22no—
365C2×C8—42no—
366C2×C8—48no—
367C2×C8—41no—
368C2×C8C24×C511yescharacteristic
369C2×C8C24×C514yes—
370C2×C8C24×C514yes—
371C2×C8C24×C512yes—
372C2×C8C24×C514yes—
373C2×C8C24×C511yescharacteristic
374C4⋊C4C22×C4×C514yes—
375C4⋊C4C22×C4×C518yes—
376C4⋊C4C22×C4×C514yes—
377C4⋊C4C22×C4×C512yes—
378C4⋊C4C22×C4×C512yes—
379C4⋊C4C22×C4×C514yes—
380C4⋊C4C22×C4×C518yes—
381C4⋊C4C22×C4×C518yes—
382C4⋊C4C22×C4×C514yes—
383C4⋊C4C22×C4×C514yes—
384C4⋊C4C22×C4×C518yes—
385C22⋊C4C22×C4×C514yes—
386C22⋊C4C22×C4×C514yes—
387C22⋊C4C22×C4×C514yes—
388C22⋊C4C22×C4×C518yes—
389C22⋊C4C22×C4×C518yes—
390C22⋊C4C22×C4×C518yes—
391C42C22×C4×C512yes—
392C42C22×C4×C514yes—
393C42C22×C4×C514yes—
394C42C22×C4×C514yes—
395C42C24×C512yes—
396C42C24×C514yes—
397C42C24×C514yes—
398C2×C5—22no—
399C2×C5—44no—
400C2×C5C4×2−1+411yescharacteristic
401C2×C5C22×#13111yescharacteristic
402C2×C5#357311yescharacteristic
403C23C23×C4×C514yes—
404C23C23×C4×C511yescharacteristic
405Q8—28no—
406Q8—24no—
407Q8—44no—
408D4—28no—
409D4—24no—
410D4—44no—
411C2×C4—24no—
412C2×C4—28no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—41no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4C5×#13114yes—
421C2×C4C23×C4×C511yescharacteristic
422C2×C4C23×C4×C512yes—
423C2×C4C23×C4×C514yes—
424C2×C4C23×C4×C514yes—
425C2×C4C23×C4×C514yes—
426C2×C4C23×C4×C514yes—
427C2×C4C23×C4×C514yes—
428C2×C4C23×C4×C512yes—
429C2×C4C25×C511yescharacteristic
430C8—21no—
431C8—24no—
432C8—24no—
433C8—24no—
434C8—22no—
435C8C5×2−1+412yes—
436C5#6033411yescharacteristic, direct product factor, Sylow
437C22—21no—
438C22—21no—
439C22—24no—
440C22—24no—
441C22—24no—
442C22C2×C5×#13112yes—
443C22C24×C4×C511yescharacteristic
444C4—21no—
445C4—24no—
446C4—24no—
447C4—24no—
448C4—22no—
449C4—24no—
450C4—24no—
451C4C2×C5×#13114yes—
452C4C2×C5×2−1+411yescharacteristic
453C4C5×#58511yescharacteristic
454C2—22no—
455C2—44no—
456C2C4×C5×2−1+411yescharacteristic
457C2C22×C5×#13111yescharacteristic
458C2C5×#357311yescharacteristic
subgroupG/H
centerC2×C4×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC2×C4C25×C5
socleC22×C5C24×C4
prime radicalC5×#537C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2994C2semidirect
3. C5×#2992C2semidirect
4. C5×#2988C2semidirect
5. C5×#2986C2semidirect
6. C5×#2983C2semidirect
7. C5×#2969C2semidirect
8. C5×#2966C2semidirect
9. C5×#2965C2semidirect
10. C5×#2962C2semidirect
11. C2×C5×C8×Q8C2semidirect
56. #60334C5direct (N × H)
124. #2994C2×C5semidirect
125. #2992C2×C5semidirect
126. #2988C2×C5semidirect
127. #2986C2×C5semidirect
128. #2983C2×C5semidirect
129. #2969C2×C5semidirect
130. #2966C2×C5semidirect
131. #2965C2×C5semidirect
132. #2962C2×C5semidirect
133. C2×C8×Q8C2×C5semidirect
436. C5#60334direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34612
C5×#29942
C5×#29922
C5×#29882
C5×#29862
C5×#29832
C5×#29692
C5×#29662
C5×#29652
C5×#29622
C2×C5×C8×Q82
#603345