Finite Group Databasebeta

← C5×#9181 #11931901

Subgroups — C5×#9181 #11931901

Order 1280.

548 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3036C211yesmaximal, characteristic
2C5×#2357C211yesmaximal, characteristic, complemented
3C5×#1517C211yesmaximal, characteristic, complemented
4C5×#1502C211yesmaximal, characteristic, complemented
5C5×#1478C211yesmaximal, characteristic, complemented
6C5×#1303C211yesmaximal, characteristic, complemented
7C5×#1286C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C5×#532C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#463—22no—
12C5×#461C412yescomplemented
13C5×#459C412yescomplemented
14C5×#431C2211yescharacteristic
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C5×#417—21no—
18C5×#390—21no—
19C5×#388—22no—
20C5×#382C2211yescharacteristic
21C5×#381—21no—
22C4×C5×C4⋊C4—21no—
23C4×C5×C4⋊C4C2211yescharacteristic
24C4×C5×C22⋊C4—21no—
25C5×#327—21no—
26C5×#327—21no—
27C5×#327—22no—
28C5×D4⋊C8—22no—
29#9181C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C22×C5×D4D411yescharacteristic
32C23×C4×C5—21no—
33C5×AGL(1,ℤ/8)—42no—
34C5×AGL(1,ℤ/8)—42no—
35C2×C5×SD16—22no—
36C2×C5×D8—22no—
37C2×C5×M16—21no—
38C5×C4⋊Q8C2×C411yescharacteristic
39C5×#127C2×C411yescharacteristic
40C5×#124—21no—
41C5×#121—21no—
42C5×#121—21no—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4C2×C412yes—
48C4×C5×D4D412yes—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4D411yescharacteristic
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—22no—
54C2×C5×C22⋊C4—22no—
55C2×C42×C5—21no—
56C2×C42×C5—22no—
57C2×C42×C5C2311yescharacteristic
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8C2×C412yes—
62C5×#103—22no—
63C5×#102—22no—
64C5×C22⋊C8—21no—
65C5×C22⋊C8—21no—
66C4×C5×C8—21no—
67C4×C5×C8—21no—
68C5×#95—22no—
69C5×#95—21no—
70C5×#95D411yescharacteristic
71C5×#95D411yescharacteristic
72C5×#95D412yes—
73#3036C2×C511yescharacteristic
74#2357C2×C511yescharacteristic, complemented
75#1517C2×C511yescharacteristic, complemented
76#1502C2×C511yescharacteristic, complemented
77#1478C2×C511yescharacteristic, complemented
78#1303C2×C511yescharacteristic, complemented
79#1286C2×C511yescharacteristic, complemented
80C24×C5—21no—
81C5×#41—41no—
82C5×#41—41no—
83C5×#41—41no—
84C5×#41—41no—
85C2×C5×Q8—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—21no—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—41no—
95C2×C5×D4C22⋊C412yes—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—41no—
103C22×C4×C5—82no—
104C22×C4×C5C2×D411yescharacteristic
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C5×SD16—44no—
108C5×D8—44no—
109C5×M16—41no—
110C5×M16—41no—
111C2×C5×C8—22no—
112C2×C5×C8—41no—
113C2×C5×C8—41no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—42no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4C22⋊C412yes—
121C5×C22⋊C4—22no—
122C5×C22⋊C4—22no—
123C5×C22⋊C4—44no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—82no—
127C42×C5—41no—
128C42×C5—41no—
129C42×C5—82no—
130C42×C5C22×C411yescharacteristic
131C42×C5C2×D411yescharacteristic
132C42×C5#4111yescharacteristic
133C42×C5#4111yescharacteristic
134C2×AGL(1,ℤ/8)—21no—
135#532C22×C511yescharacteristic
136C2×C4×D4C22×C511yescharacteristic
137#463—22no—
138#461C4×C512yescomplemented
139#459C4×C512yescomplemented
140#431C22×C511yescharacteristic
141#431C22×C511yescharacteristic
142#423C22×C511yescharacteristic
143#417—21no—
144#390—21no—
145#388—22no—
146#382C22×C511yescharacteristic
147#381—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4C22×C511yescharacteristic
150C4×C22⋊C4—21no—
151#327—21no—
152#327—21no—
153#327—22no—
154D4⋊C8—22no—
155C23×C5—22no—
156C23×C5—42no—
157C23×C5—42no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5#12011yescharacteristic
162C5×Q8—41no—
163C5×Q8—41no—
164C5×D4—22no—
165C5×D4—22no—
166C5×D4—41no—
167C5×D4—41no—
168C5×D4—41no—
169C5×D4—41no—
170C5×D4—81no—
171C5×D4—81no—
172C5×D4—81no—
173C5×D4—81no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—42no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—42no—
188C2×C4×C5—82no—
189C2×C4×C5—82no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5C2×C22⋊C411yescharacteristic
193C2×C4×C5C4×D411yescharacteristic
194C2×C4×C5C4×D411yescharacteristic
195C2×C4×C5#12111yescharacteristic
196C2×C4×C5#12111yescharacteristic
197C2×C4×C5#12311yescharacteristic
198C2×C4×C5#13511yescharacteristic
199C2×C4×C5#13511yescharacteristic
200C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
202C5×C8—42no—
203C5×C8—81no—
204C5×C8—81no—
205C2×#41—21no—
206C22×D4C5×D411yescharacteristic
207C23×C4—21no—
208AGL(1,ℤ/8)—42no—
209AGL(1,ℤ/8)—42no—
210C2×SD16—22no—
211C2×D8—22no—
212C2×M16—21no—
213C4⋊Q8C2×C4×C511yescharacteristic
214#127C2×C4×C511yescharacteristic
215#124—21no—
216#121—21no—
217#121—21no—
218C4×D4—21no—
219C4×D4—21no—
220C4×D4—21no—
221C4×D4—21no—
222C4×D4C2×C4×C512yes—
223C4×D4C5×D412yes—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C5×D411yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C42—21no—
231C2×C42—22no—
232C2×C42C23×C511yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8C2×C4×C512yes—
237#103—22no—
238#102—22no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243#95—22no—
244#95—21no—
245#95C5×D411yescharacteristic
246#95C5×D411yescharacteristic
247#95C5×D412yes—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—42no—
251C22×C5—42no—
252C22×C5—42no—
253C22×C5—82no—
254C22×C5—82no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5#38611yescharacteristic
259C22×C5#44911yescharacteristic
260C22×C5#44911yescharacteristic
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—42no—
266C4×C5—42no—
267C4×C5—81no—
268C4×C5—82no—
269C4×C5—81no—
270C4×C5#41611yescharacteristic
271C4×C5#41811yescharacteristic
272C4×C5#48211yescharacteristic
273C4×C5#48211yescharacteristic
274C24—21no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C5×C22⋊C412yes—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—82no—
298C22×C4C2×C5×D411yescharacteristic
299C22×C4C2×C5×D411yescharacteristic
300C22×C4C2×C5×D411yescharacteristic
301SD16—44no—
302D8—44no—
303M16—41no—
304M16—41no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4C5×C22⋊C412yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—44no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—82no—
321C42—41no—
322C42—41no—
323C42—82no—
324C42C22×C4×C511yescharacteristic
325C42C2×C5×D411yescharacteristic
326C42C5×#4111yescharacteristic
327C42C5×#4111yescharacteristic
328C2×C5—21no—
329C2×C5—21no—
330C2×C5—82no—
331C2×C5—161no—
332C2×C5#187511yescharacteristic
333C2×C5#190411yescharacteristic
334C2×C5#190611yescharacteristic
335C23—22no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C5×#12011yescharacteristic
342Q8—41no—
343Q8—41no—
344D4—22no—
345D4—22no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4C2×C5×C22⋊C411yescharacteristic
373C2×C4C4×C5×D411yescharacteristic
374C2×C4C4×C5×D411yescharacteristic
375C2×C4C5×#12111yescharacteristic
376C2×C4C5×#12111yescharacteristic
377C2×C4C5×#12311yescharacteristic
378C2×C4C5×#13511yescharacteristic
379C2×C4C5×#13511yescharacteristic
380C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
381C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
382C8—42no—
383C8—81no—
384C8—81no—
385C5#918111yescharacteristic, direct product factor, Sylow
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C5×#38611yescharacteristic
397C22C5×#44911yescharacteristic
398C22C5×#44911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4—81no—
408C4C5×#41611yescharacteristic
409C4C5×#41811yescharacteristic
410C4C5×#48211yescharacteristic
411C4C5×#48211yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—161no—
416C2C5×#187511yescharacteristic
417C2C5×#190411yescharacteristic
418C2C5×#190611yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3036C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2357C2semidirect
3. C5×#1517C2semidirect
4. C5×#1502C2semidirect
5. C5×#1478C2semidirect
6. C5×#1303C2semidirect
7. C5×#1286C2semidirect
12. C5×#461C4semidirect
13. C5×#459C4semidirect
29. #9181C5direct (N × H)
74. #2357C2×C5semidirect
75. #1517C2×C5semidirect
76. #1502C2×C5semidirect
77. #1478C2×C5semidirect
78. #1303C2×C5semidirect
79. #1286C2×C5semidirect
138. #461C4×C5semidirect
139. #459C4×C5semidirect
385. C5#9181direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30362
C5×#23572
C5×#15172
C5×#15022
C5×#14782
C5×#13032
C5×#12862
#91815