Finite Group Databasebeta

← C5×#60343 #11983063

Subgroups — C5×#60343 #11983063

Order 1280.

1930 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×2−1+4C211yesmaximal, characteristic
2C5×#2990C216yesmaximal, complemented
3C5×#2989C213yesmaximal, complemented
4C5×#2988C211yesmaximal, characteristic, complemented
5C5×#2984C212yesmaximal, complemented
6C5×#2983C213yesmaximal, complemented
7C5×#2970C216yesmaximal, complemented
8C5×#2965C213yesmaximal, complemented
9C5×C8×#41C211yesmaximal, characteristic, complemented
10C5×Q8×M16C212yesmaximal, complemented
11C2×C5×#446C213yesmaximal, complemented
12C2×C5×2−1+4C411yescharacteristic
13C5×#520C416yes—
14C5×#520C413yes—
15C5×#520C411yescharacteristic
16C5×#519C412yes—
17C5×#519C413yes—
18C4×C5×#41C2211yescharacteristic
19C4×C5×#41C2213yes—
20C4×C5×#41C2216yes—
21C2×C4×C5×Q8C2213yes—
22C2×C4×C5×Q8C2212yes—
23C5×#446C2213yes—
24C5×#446C2216yes—
25C5×#446C2216yes—
26C5×#446C2216yes—
27C5×#446C2216yes—
28C5×#446C2213yes—
29C5×#446C2216yes—
30C5×C8×Q8C2211yescharacteristic
31C5×C8×Q8C2212yes—
32C5×C8×Q8C2211yescharacteristic
33C5×#436C2213yes—
34C5×#436C2211yescharacteristic
35C5×#435C22112yes—
36C5×#435C2216yes—
37C5×#435C2216yes—
38C5×C8×D4C2216yes—
39C5×C8×D4C2213yes—
40C5×C8×D4C2213yes—
41C5×#432C22112yes—
42C5×#432C2216yes—
43C5×#431C2213yes—
44C5×#431C2213yes—
45C5×#431C2216yes—
46C5×#423C2216yes—
47C2×C5×C4⋊C8C2213yes—
48C2×C5×C4⋊C8C2216yes—
49C4×C5×M16C2216yes—
50C2×C5×#97C2216yes—
51C2×C4×C5×C8C2213yes—
52#60343C511yesmaximal, characteristic, direct product factor, Sylow
53C5×2−1+4—28no—
54C2×C5×#41C2×C416yes—
55C2×C5×#41C2×C413yes—
56C2×C5×#41C2×C411yescharacteristic
57C22×C5×Q8C2×C412yes—
58C22×C5×Q8C2×C413yes—
59C2×C5×M16C2312yes—
60C2×C5×M16C2316yes—
61C22×C5×C8C2313yes—
62C22×C5×C8C2313yes—
63C22×C5×C8C2316yes—
64C4×C5×Q8C2×C416yes—
65C4×C5×Q8C2×C416yes—
66C4×C5×Q8C2×C416yes—
67C4×C5×Q8C2×C412yes—
68C4×C5×Q8C2×C413yes—
69C4×C5×Q8C2×C416yes—
70C4×C5×Q8C2×C411yescharacteristic
71C4×C5×Q8C2311yescharacteristic
72C4×C5×Q8C2313yes—
73C4×C5×Q8C2316yes—
74C4×C5×D4C2×C416yes—
75C4×C5×D4C2×C413yes—
76C4×C5×D4C2×C4112yes—
77C4×C5×D4C2×C413yes—
78C4×C5×D4C2×C416yes—
79C4×C5×D4C2313yes—
80C4×C5×D4C2316yes—
81C4×C5×D4C2311yescharacteristic
82C5×#117C2×C416yes—
83C5×#117C2×C416yes—
84C5×#117C2×C4112yes—
85C5×#117C2×C413yes—
86C5×#117C2×C413yes—
87C2×C5×C4⋊C4C2×C416yes—
88C2×C5×C4⋊C4C2×C416yes—
89C2×C5×C4⋊C4C2×C413yes—
90C2×C42×C5C2313yes—
91C2×C42×C5C2316yes—
92C2×C42×C5C2316yes—
93C5×C4⋊C8C2316yes—
94C5×C4⋊C8C2313yes—
95C5×C4⋊C8C2316yes—
96C5×C4⋊C8C23112yes—
97C5×C4⋊C8C2313yes—
98C5×C4⋊C8C2311yescharacteristic
99C5×C4⋊C8C2313yes—
100C5×C4⋊C8C2316yes—
101C5×C22⋊C8C2312yes—
102C5×C22⋊C8C2316yes—
103C5×C22⋊C8C2316yes—
104C5×C22⋊C8C2316yes—
105C5×#97C2316yes—
106C5×#97C23112yes—
107C5×#97C2316yes—
108C4×C5×C8C2311yescharacteristic
109C4×C5×C8C2313yes—
110C4×C5×C8C2313yes—
111C4×C5×C8C2313yes—
112C4×C5×C8C2316yes—
113C4×2−1+4C2×C511yescharacteristic
114#2990C2×C516yescomplemented
115#2989C2×C513yescomplemented
116#2988C2×C511yescharacteristic, complemented
117#2984C2×C512yescomplemented
118#2983C2×C513yescomplemented
119#2970C2×C516yescomplemented
120#2965C2×C513yescomplemented
121C8×#41C2×C511yescharacteristic, complemented
122Q8×M16C2×C512yescomplemented
123C2×#446C2×C513yescomplemented
124C5×#41—224no—
125C5×#41—212no—
126C5×#41M1618yescomplemented
127C2×C5×Q8—28no—
128C2×C5×Q8—212no—
129C2×C5×Q8C22×C416yes—
130C2×C5×Q8C22×C413yes—
131C2×C5×Q8C22×C411yescharacteristic
132C2×C5×D4C22×C416yes—
133C2×C5×D4C22×C411yescharacteristic
134C2×C5×D4C22×C413yes—
135C22×C4×C5C22×C416yes—
136C22×C4×C5C22×C416yes—
137C22×C4×C5C22×C416yes—
138C22×C4×C5C22×C413yes—
139C22×C4×C5C22×C416yes—
140C22×C4×C5C22×C413yes—
141C22×C4×C5C2413yes—
142C22×C4×C5C2412yes—
143C5×M16—24no—
144C5×M16—46no—
145C2×C5×C8—26no—
146C2×C5×C8—43no—
147C2×C5×C8—46no—
148C2×C5×C8C2411yescharacteristic
149C2×C5×C8C2416yes—
150C2×C5×C8C2413yes—
151C2×C5×C8C2413yes—
152C2×C5×C8C2412yes—
153C2×C5×C8C2411yescharacteristic
154C5×C4⋊C4C22×C416yes—
155C5×C4⋊C4C22×C4112yes—
156C5×C4⋊C4C22×C413yes—
157C5×C4⋊C4C22×C416yes—
158C5×C4⋊C4C22×C413yes—
159C5×C4⋊C4C22×C416yes—
160C5×C4⋊C4C22×C413yes—
161C5×C4⋊C4C22×C411yescharacteristic
162C5×C22⋊C4C22×C416yes—
163C5×C22⋊C4C22×C412yes—
164C5×C22⋊C4C22×C416yes—
165C5×C22⋊C4C22×C416yes—
166C42×C5C22×C4112yes—
167C42×C5C22×C416yes—
168C42×C5C22×C413yes—
169C42×C5C22×C413yes—
170C42×C5C22×C416yes—
171C42×C5C2411yescharacteristic
172C42×C5C2413yes—
173C42×C5C2416yes—
174C2×2−1+4C4×C511yescharacteristic
175#520C4×C516yes—
176#520C4×C513yes—
177#520C4×C511yescharacteristic
178#519C4×C512yes—
179#519C4×C513yes—
180C4×#41C22×C511yescharacteristic
181C4×#41C22×C513yes—
182C4×#41C22×C516yes—
183C2×C4×Q8C22×C513yes—
184C2×C4×Q8C22×C512yes—
185#446C22×C513yes—
186#446C22×C516yes—
187#446C22×C516yes—
188#446C22×C516yes—
189#446C22×C516yes—
190#446C22×C513yes—
191#446C22×C516yes—
192C8×Q8C22×C511yescharacteristic
193C8×Q8C22×C512yes—
194C8×Q8C22×C511yescharacteristic
195#436C22×C511yescharacteristic
196#436C22×C513yes—
197#435C22×C516yes—
198#435C22×C516yes—
199#435C22×C5112yes—
200C8×D4C22×C513yes—
201C8×D4C22×C513yes—
202C8×D4C22×C516yes—
203#432C22×C5112yes—
204#432C22×C516yes—
205#431C22×C513yes—
206#431C22×C513yes—
207#431C22×C516yes—
208#423C22×C516yes—
209C2×C4⋊C8C22×C513yes—
210C2×C4⋊C8C22×C516yes—
211C4×M16C22×C516yes—
212C2×#97C22×C516yes—
213C2×C4×C8C22×C513yes—
214C23×C5C23×C412yes—
215C23×C5C23×C413yes—
216C5×Q8—212no—
217C5×Q8—26no—
218C5×Q8C2×M1614yes—
219C5×D4—212no—
220C5×D4—22no—
221C5×D4C2×M16112yes—
222C2×C4×C5—212no—
223C2×C4×C5—212no—
224C2×C4×C5—23no—
225C2×C4×C5—22no—
226C2×C4×C5—23no—
227C2×C4×C5—22no—
228C2×C4×C5—43no—
229C2×C4×C5—46no—
230C2×C4×C5—46no—
231C2×C4×C5C2×M16112yes—
232C2×C4×C5C23×C413yes—
233C2×C4×C5C23×C412yes—
234C2×C4×C5C23×C413yes—
235C2×C4×C5C23×C411yescharacteristic
236C2×C4×C5C23×C416yes—
237C2×C4×C5C23×C416yes—
238C2×C4×C5C23×C413yes—
239C2×C4×C5C23×C411yescharacteristic
240C2×C4×C5C2511yescharacteristic
241C5×C8—23no—
242C5×C8—22no—
243C5×C8—21no—
244C5×C8—26no—
245C5×C8—23no—
246C5×C82−1+412yescomplemented
2472−1+4—28no—
248C2×#41C2×C4×C516yes—
249C2×#41C2×C4×C513yes—
250C2×#41C2×C4×C511yescharacteristic
251C22×Q8C2×C4×C512yes—
252C22×Q8C2×C4×C513yes—
253C2×M16C23×C512yes—
254C2×M16C23×C516yes—
255C22×C8C23×C513yes—
256C22×C8C23×C513yes—
257C22×C8C23×C516yes—
258C4×Q8C2×C4×C516yes—
259C4×Q8C2×C4×C516yes—
260C4×Q8C2×C4×C516yes—
261C4×Q8C2×C4×C512yes—
262C4×Q8C2×C4×C513yes—
263C4×Q8C2×C4×C516yes—
264C4×Q8C2×C4×C511yescharacteristic
265C4×Q8C23×C511yescharacteristic
266C4×Q8C23×C513yes—
267C4×Q8C23×C516yes—
268C4×D4C2×C4×C516yes—
269C4×D4C2×C4×C513yes—
270C4×D4C2×C4×C5112yes—
271C4×D4C2×C4×C513yes—
272C4×D4C2×C4×C516yes—
273C4×D4C23×C513yes—
274C4×D4C23×C516yes—
275C4×D4C23×C511yescharacteristic
276#117C2×C4×C516yes—
277#117C2×C4×C516yes—
278#117C2×C4×C5112yes—
279#117C2×C4×C513yes—
280#117C2×C4×C513yes—
281C2×C4⋊C4C2×C4×C516yes—
282C2×C4⋊C4C2×C4×C516yes—
283C2×C4⋊C4C2×C4×C513yes—
284C2×C42C23×C513yes—
285C2×C42C23×C516yes—
286C2×C42C23×C516yes—
287C4⋊C8C23×C516yes—
288C4⋊C8C23×C513yes—
289C4⋊C8C23×C516yes—
290C4⋊C8C23×C5112yes—
291C4⋊C8C23×C513yes—
292C4⋊C8C23×C511yescharacteristic
293C4⋊C8C23×C513yes—
294C4⋊C8C23×C516yes—
295C22⋊C8C23×C512yes—
296C22⋊C8C23×C516yes—
297C22⋊C8C23×C516yes—
298C22⋊C8C23×C516yes—
299#97C23×C516yes—
300#97C23×C5112yes—
301#97C23×C516yes—
302C4×C8C23×C511yescharacteristic
303C4×C8C23×C513yes—
304C4×C8C23×C513yes—
305C4×C8C23×C513yes—
306C4×C8C23×C516yes—
307C22×C5—23no—
308C22×C5—23no—
309C22×C5—22no—
310C22×C5—22no—
311C22×C5—22no—
312C22×C5C22×M1616yes—
313C22×C5C24×C411yescharacteristic
314C4×C5—23no—
315C4×C5—22no—
316C4×C5—26no—
317C4×C5—21no—
318C4×C5—26no—
319C4×C5—23no—
320C4×C5C22×M1616yes—
321C4×C5C22×M1612yes—
322C4×C5C2×2−1+411yescharacteristic
323C4×C5#58511yescharacteristic
324#41—224no—
325#41—212no—
326#41C5×M1618yescomplemented
327C2×Q8—28no—
328C2×Q8—212no—
329C2×Q8C22×C4×C516yes—
330C2×Q8C22×C4×C513yes—
331C2×Q8C22×C4×C511yescharacteristic
332C2×D4C22×C4×C516yes—
333C2×D4C22×C4×C511yescharacteristic
334C2×D4C22×C4×C513yes—
335C22×C4C22×C4×C516yes—
336C22×C4C22×C4×C516yes—
337C22×C4C22×C4×C516yes—
338C22×C4C22×C4×C513yes—
339C22×C4C22×C4×C516yes—
340C22×C4C22×C4×C513yes—
341C22×C4C24×C513yes—
342C22×C4C24×C512yes—
343M16—24no—
344M16—46no—
345C2×C8—26no—
346C2×C8—43no—
347C2×C8—46no—
348C2×C8C24×C511yescharacteristic
349C2×C8C24×C512yes—
350C2×C8C24×C513yes—
351C2×C8C24×C513yes—
352C2×C8C24×C516yes—
353C2×C8C24×C511yescharacteristic
354C4⋊C4C22×C4×C516yes—
355C4⋊C4C22×C4×C5112yes—
356C4⋊C4C22×C4×C513yes—
357C4⋊C4C22×C4×C516yes—
358C4⋊C4C22×C4×C513yes—
359C4⋊C4C22×C4×C516yes—
360C4⋊C4C22×C4×C513yes—
361C4⋊C4C22×C4×C511yescharacteristic
362C22⋊C4C22×C4×C516yes—
363C22⋊C4C22×C4×C512yes—
364C22⋊C4C22×C4×C516yes—
365C22⋊C4C22×C4×C516yes—
366C42C22×C4×C5112yes—
367C42C22×C4×C516yes—
368C42C22×C4×C513yes—
369C42C22×C4×C513yes—
370C42C22×C4×C516yes—
371C42C24×C511yescharacteristic
372C42C24×C513yes—
373C42C24×C516yes—
374C2×C5—26no—
375C2×C5—42no—
376C2×C5C4×2−1+411yescharacteristic
377C2×C5C23×M1611yescharacteristic
378C2×C5#357311yescharacteristic
379C23C23×C4×C512yes—
380C23C23×C4×C513yes—
381Q8—212no—
382Q8—26no—
383Q8C2×C5×M1614yes—
384D4—212no—
385D4—22no—
386D4C2×C5×M16112yes—
387C2×C4—212no—
388C2×C4—212no—
389C2×C4—23no—
390C2×C4—22no—
391C2×C4—23no—
392C2×C4—22no—
393C2×C4—43no—
394C2×C4—46no—
395C2×C4—46no—
396C2×C4C2×C5×M16112yes—
397C2×C4C23×C4×C513yes—
398C2×C4C23×C4×C512yes—
399C2×C4C23×C4×C513yes—
400C2×C4C23×C4×C511yescharacteristic
401C2×C4C23×C4×C516yes—
402C2×C4C23×C4×C516yes—
403C2×C4C23×C4×C513yes—
404C2×C4C23×C4×C511yescharacteristic
405C2×C4C25×C511yescharacteristic
406C8—23no—
407C8—22no—
408C8—21no—
409C8—26no—
410C8—23no—
411C8C5×2−1+412yescomplemented
412C5#6034311yescharacteristic, direct product factor, Sylow
413C22—23no—
414C22—23no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22C22×C5×M1616yes—
419C22C24×C4×C511yescharacteristic
420C4—23no—
421C4—22no—
422C4—26no—
423C4—21no—
424C4—26no—
425C4—23no—
426C4C22×C5×M1616yes—
427C4C22×C5×M1612yes—
428C4C2×C5×2−1+411yescharacteristic
429C4C5×#58511yescharacteristic
430C2—26no—
431C2—42no—
432C2C4×C5×2−1+411yescharacteristic
433C2C23×C5×M1611yescharacteristic
434C2C5×#357311yescharacteristic
subgroupG/H
centerC2×C4×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC2×C4C25×C5
socleC22×C5C24×C4
prime radicalC2×C5×2−1+4C4
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×#2988C2semidirect
5. C5×#2984C2semidirect
6. C5×#2983C2semidirect
7. C5×#2970C2semidirect
8. C5×#2965C2semidirect
9. C5×C8×#41C2semidirect
10. C5×Q8×M16C2semidirect
11. C2×C5×#446C2semidirect
52. #60343C5direct (N × H)
114. #2990C2×C5semidirect
115. #2989C2×C5semidirect
116. #2988C2×C5semidirect
117. #2984C2×C5semidirect
118. #2983C2×C5semidirect
119. #2970C2×C5semidirect
120. #2965C2×C5semidirect
121. C8×#41C2×C5semidirect
122. Q8×M16C2×C5semidirect
123. C2×#446C2×C5semidirect
126. C5×#41M16semidirect
246. C5×C82−1+4semidirect
326. #41C5×M16semidirect
411. C8C5×2−1+4semidirect
412. C5#60343direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×2−1+42
C5×#29902
C5×#29892
C5×#29882
C5×#29842
C5×#29832
C5×#29702
C5×#29652
C5×C8×#412
C5×Q8×M162
C2×C5×#4462
#603435