Finite Group Databasebeta

← C5×#9291 #11932011

Subgroups — C5×#9291 #11932011

Order 1280.

494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3226C211yesmaximal, characteristic
2C5×#2932C211yesmaximal, characteristic
3C5×#1960C211yesmaximal, characteristic, complemented
4C5×#1546C211yesmaximal, characteristic, complemented
5C5×#1517C211yesmaximal, characteristic
6C5×#1286C211yesmaximal, characteristic, complemented
7C5×#1275C211yesmaximal, characteristic, complemented
8C2×C5×#131—21no—
9C5×#532C2211yescharacteristic
10C2×C5×C4⋊Q8C2211yescharacteristic
11C5×#500C412yescomplemented
12C5×#486C412yescomplemented
13C5×#480—22no—
14C5×#474—22no—
15C5×#435—22no—
16C5×#435—22no—
17C5×#431C2211yescharacteristic
18C5×#431C2211yescharacteristic
19C5×#423C2211yescharacteristic
20C2×C5×#103—21no—
21C2×C5×#103—21no—
22C5×#408—21no—
23C2×C5×#97C2211yescharacteristic
24C5×#382C2211yescharacteristic
25C5×#332—22no—
26C5×#327—22no—
27#9291C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×Q8—21no—
30C5×#131—42no—
31C5×#131—42no—
32C2×C5×M16—22no—
33C2×C5×M16—21no—
34C22×C5×C8—22no—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8D411yescharacteristic
37C5×C4⋊Q8—21no—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8C2×C412yes—
41C5×C4⋊Q8C2×C411yescharacteristic
42C5×#127C2×C411yescharacteristic
43C5×#124—21no—
44C5×#121—21no—
45C5×#121D412yes—
46C4×C5×D4—21no—
47C4×C5×D4D412yes—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C42×C5C2311yescharacteristic
52C5×#107—24no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8D412yes—
57C5×#103—42no—
58C5×#103—42no—
59C5×#102—24no—
60C5×C22⋊C8—24no—
61C5×C22⋊C8—21no—
62C5×C22⋊C8—21no—
63C5×#97—21no—
64C5×#97—21no—
65C4×C5×C8—21no—
66C4×C5×C8C2×C412yes—
67C5×#95—21no—
68C5×#95—21no—
69#3226C2×C511yescharacteristic
70#2932C2×C511yescharacteristic
71#1960C2×C511yescharacteristic, complemented
72#1546C2×C511yescharacteristic, complemented
73#1517C2×C511yescharacteristic
74#1286C2×C511yescharacteristic, complemented
75#1275C2×C511yescharacteristic, complemented
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C2×C5×Q8—21no—
81C2×C5×Q8—22no—
82C2×C5×Q8—41no—
83C2×C5×Q8—41no—
84C2×C5×Q8—41no—
85C2×C5×Q8—41no—
86C2×C5×Q8—41no—
87C2×C5×D4—22no—
88C2×C5×D4—21no—
89C2×C5×D4—21no—
90C2×C5×D4C22⋊C412yes—
91C22×C4×C5—22no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5#4111yescharacteristic
97C5×M16—44no—
98C5×M16—41no—
99C5×M16—41no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—22no—
103C2×C5×C8—22no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8—44no—
108C2×C5×C8—41no—
109C2×C5×C8D812yes—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4—41no—
116C5×C4⋊C4—41no—
117C5×C4⋊C4C22⋊C412yes—
118C5×C22⋊C4—22no—
119C5×C22⋊C4—22no—
120C42×C5C22×C411yescharacteristic
121C42×C5C2×D411yescharacteristic
122C42×C5C2×D411yescharacteristic
123C42×C5#4111yescharacteristic
124C2×#131—21no—
125#532C22×C511yescharacteristic
126C2×C4⋊Q8C22×C511yescharacteristic
127#500C4×C512yescomplemented
128#486C4×C512yescomplemented
129#480—22no—
130#474—22no—
131#435—22no—
132#435—22no—
133#431C22×C511yescharacteristic
134#431C22×C511yescharacteristic
135#423C22×C511yescharacteristic
136C2×#103—21no—
137C2×#103—21no—
138#408—21no—
139C2×#97C22×C511yescharacteristic
140#382C22×C511yescharacteristic
141#332—22no—
142#327—22no—
143C23×C5—22no—
144C23×C5#12111yescharacteristic
145C5×Q8—41no—
146C5×Q8—41no—
147C5×Q8—42no—
148C5×Q8—42no—
149C5×Q8—81no—
150C5×Q8—81no—
151C5×D4—42no—
152C5×D4—42no—
153C5×D4—42no—
154C5×D4—41no—
155C5×D4—41no—
156C5×D4—81no—
157C2×C4×C5—22no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—42no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5—81no—
167C2×C4×C5—81no—
168C2×C4×C5C2×C22⋊C411yescharacteristic
169C2×C4×C5C4×D411yescharacteristic
170C2×C4×C5C4×D411yescharacteristic
171C2×C4×C5#12011yescharacteristic
172C2×C4×C5#12111yescharacteristic
173C2×C4×C5#12311yescharacteristic
174C2×C4×C5C2×D811yescharacteristic
175C2×C4×C5#13511yescharacteristic
176C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
178C5×C8—22no—
179C5×C8—42no—
180C5×C8—42no—
181C5×C8—41no—
182C5×C8—81no—
183C2×#41—21no—
184C22×Q8—21no—
185#131—42no—
186#131—42no—
187C2×M16—22no—
188C2×M16—21no—
189C22×C8—22no—
190C22×C8C5×D411yescharacteristic
191C22×C8C5×D411yescharacteristic
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C2×C4×C512yes—
196C4⋊Q8C2×C4×C511yescharacteristic
197#127C2×C4×C511yescharacteristic
198#124—21no—
199#121—21no—
200#121C5×D412yes—
201C4×D4—21no—
202C4×D4C5×D412yes—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C42C23×C511yescharacteristic
207#107—24no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8C5×D412yes—
212#103—42no—
213#103—42no—
214#102—24no—
215C22⋊C8—24no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218#97—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8C2×C4×C512yes—
222#95—21no—
223#95—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—42no—
227C22×C5—42no—
228C22×C5—42no—
229C22×C5#38611yescharacteristic
230C22×C5#45911yescharacteristic
231C22×C5#46311yescharacteristic
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—42no—
237C4×C5—82no—
238C4×C5—161no—
239C4×C5C4×D811yescharacteristic
240C4×C5#44211yescharacteristic
241C4×C5#44711yescharacteristic
242C4×C5#44911yescharacteristic
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4C5×C22⋊C412yes—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C2×C5×D411yescharacteristic
262C22×C4C2×C5×D411yescharacteristic
263C22×C4C5×#4111yescharacteristic
264M16—44no—
265M16—41no—
266M16—41no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—22no—
270C2×C8—21no—
271C2×C8—22no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—44no—
275C2×C8—41no—
276C2×C8C5×D812yes—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4C5×C22⋊C412yes—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C42C22×C4×C511yescharacteristic
288C42C2×C5×D411yescharacteristic
289C42C2×C5×D411yescharacteristic
290C42C5×#4111yescharacteristic
291C2×C5—21no—
292C2×C5—21no—
293C2×C5—82no—
294C2×C5#187911yescharacteristic
295C2×C5#190211yescharacteristic
296C2×C5#190911yescharacteristic
297C23—22no—
298C23C5×#12111yescharacteristic
299Q8—41no—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—81no—
304Q8—81no—
305D4—42no—
306D4—42no—
307D4—42no—
308D4—41no—
309D4—41no—
310D4—81no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C2×C5×C22⋊C411yescharacteristic
323C2×C4C4×C5×D411yescharacteristic
324C2×C4C4×C5×D411yescharacteristic
325C2×C4C5×#12011yescharacteristic
326C2×C4C5×#12111yescharacteristic
327C2×C4C5×#12311yescharacteristic
328C2×C4C2×C5×D811yescharacteristic
329C2×C4C5×#13511yescharacteristic
330C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
331C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
332C8—22no—
333C8—42no—
334C8—42no—
335C8—41no—
336C8—81no—
337C5#929111yescharacteristic, direct product factor, Sylow
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22C5×#38611yescharacteristic
344C22C5×#45911yescharacteristic
345C22C5×#46311yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—82no—
352C4—161no—
353C4C4×C5×D811yescharacteristic
354C4C5×#44211yescharacteristic
355C4C5×#44711yescharacteristic
356C4C5×#44911yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C5×#187911yescharacteristic
361C2C5×#190211yescharacteristic
362C2C5×#190911yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#532C22
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
3. C5×#1960C2semidirect
4. C5×#1546C2semidirect
6. C5×#1286C2semidirect
7. C5×#1275C2semidirect
11. C5×#500C4semidirect
12. C5×#486C4semidirect
27. #9291C5direct (N × H)
71. #1960C2×C5semidirect
72. #1546C2×C5semidirect
74. #1286C2×C5semidirect
75. #1275C2×C5semidirect
127. #500C4×C5semidirect
128. #486C4×C5semidirect
337. C5#9291direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32262
C5×#29322
C5×#19602
C5×#15462
C5×#15172
C5×#12862
C5×#12752
#92915