Finite Group Databasebeta

← C5×#9352 #11932072

Subgroups — C5×#9352 #11932072

Order 1280.

414 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3080C211yesmaximal, characteristic
2C5×#2971C211yesmaximal, characteristic
3C5×#1528C211yesmaximal, characteristic, complemented
4C5×#1488C211yesmaximal, characteristic
5C5×#1470C211yesmaximal, characteristic, complemented
6C5×#1307C211yesmaximal, characteristic, complemented
7C5×#1299C211yesmaximal, characteristic, complemented
8C2×C5×#125C2211yescharacteristic
9C4×C5×#41C2211yescharacteristic
10C5×#479—21no—
11C5×#479—21no—
12C5×#478—21no—
13C5×#478—21no—
14C5×C8×Q8—21no—
15C5×#436—22no—
16C5×#436—21no—
17C5×#432—21no—
18C5×#432C2211yescharacteristic
19C5×#432C2211yescharacteristic
20C5×#431C2211yescharacteristic
21C5×#428C411yescharacteristic
22C5×#428C411yescharacteristic
23C5×#423C2211yescharacteristic
24C5×#417C411yescharacteristic
25C5×#417C411yescharacteristic
26C4×C5×M16—21no—
27C4×C5×M16C2211yescharacteristic
28C5×#330—21no—
29C5×#330—21no—
30C5×Q8⋊C8—21no—
31C5×D4⋊C8—21no—
32C5×#324—22no—
33#9352C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41C2×C411yescharacteristic
35C2×C5×M16—22no—
36C2×C5×M16—21no—
37C2×C5×M16C2×C411yescharacteristic
38C2×C5×M16C2×C411yescharacteristic
39C5×#125—21no—
40C5×#125—21no—
41C5×#125—21no—
42C5×#125—21no—
43C4×C5×Q8D411yescharacteristic
44C4×C5×Q8D411yescharacteristic
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4D411yescharacteristic
48C4×C5×D4D411yescharacteristic
49C5×#117—21no—
50C5×#117C2×C411yescharacteristic
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4C2×C411yescharacteristic
54C2×C5×C4⋊C4C2×C411yescharacteristic
55C2×C42×C5—21no—
56C2×C42×C5C2311yescharacteristic
57C5×#107—21no—
58C5×#107—21no—
59C5×#106—21no—
60C5×#106—21no—
61C5×C4⋊C8—22no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8—21no—
67C5×#103—21no—
68C5×#103—21no—
69C5×#102—21no—
70C5×#102—21no—
71C5×C22⋊C8—22no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8D412yes—
75C5×#97—21no—
76C5×#97—21no—
77C5×#97D411yescharacteristic
78C5×#97D411yescharacteristic
79C4×C5×C8—22no—
80C4×C5×C8—21no—
81C4×C5×C8—21no—
82#3080C2×C511yescharacteristic
83#2971C2×C511yescharacteristic
84#1528C2×C511yescharacteristic, complemented
85#1488C2×C511yescharacteristic
86#1470C2×C511yescharacteristic, complemented
87#1307C2×C511yescharacteristic, complemented
88#1299C2×C511yescharacteristic, complemented
89C5×#41—22no—
90C5×#41—41no—
91C2×C5×Q8C22⋊C411yescharacteristic
92C2×C5×D4—21no—
93C2×C5×D4C22⋊C411yescharacteristic
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5C22×C411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5#4111yescharacteristic
102C5×M16—42no—
103C5×M16—44no—
104C5×M16—41no—
105C5×M16—41no—
106C2×C5×C8—21no—
107C2×C5×C8—21no—
108C2×C5×C8—21no—
109C2×C5×C8—22no—
110C2×C5×C8—21no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4C22⋊C411yescharacteristic
124C5×C4⋊C4C22⋊C411yescharacteristic
125C5×C22⋊C4—21no—
126C5×C22⋊C4—21no—
127C5×C22⋊C4—21no—
128C42×C5—21no—
129C42×C5—21no—
130C42×C5—21no—
131C42×C5C2×D411yescharacteristic
132C42×C5C2×D411yescharacteristic
133C42×C5C2×D411yescharacteristic
134C42×C5#4111yescharacteristic
135C2×#125C22×C511yescharacteristic
136C4×#41C22×C511yescharacteristic
137#479—21no—
138#479—21no—
139#478—21no—
140#478—21no—
141C8×Q8—21no—
142#436—21no—
143#436—22no—
144#432—21no—
145#432C22×C511yescharacteristic
146#432C22×C511yescharacteristic
147#431C22×C511yescharacteristic
148#428C4×C511yescharacteristic
149#428C4×C511yescharacteristic
150#423C22×C511yescharacteristic
151#417C4×C511yescharacteristic
152#417C4×C511yescharacteristic
153C4×M16—21no—
154C4×M16C22×C511yescharacteristic
155#330—21no—
156#330—21no—
157Q8⋊C8—21no—
158D4⋊C8—21no—
159#324—22no—
160C23×C5—21no—
161C23×C5C4×D411yescharacteristic
162C5×Q8—21no—
163C5×Q8#10112yes—
164C5×D4—21no—
165C5×D4—21no—
166C5×D4—42no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—42no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—81no—
180C2×C4×C5—81no—
181C2×C4×C5C2×C22⋊C411yescharacteristic
182C2×C4×C5C4×D411yescharacteristic
183C2×C4×C5#12011yescharacteristic
184C2×C4×C5#12111yescharacteristic
185C2×C4×C5#12111yescharacteristic
186C2×C4×C5#12311yescharacteristic
187C5×C8—22no—
188C5×C8—42no—
189C5×C8—41no—
190C5×C8—41no—
191C5×C8—41no—
192C5×C8—81no—
193C5×C8—81no—
194C2×#41C2×C4×C511yescharacteristic
195C2×M16—22no—
196C2×M16—21no—
197C2×M16C2×C4×C511yescharacteristic
198C2×M16C2×C4×C511yescharacteristic
199#125—21no—
200#125—21no—
201#125—21no—
202#125—21no—
203C4×Q8C5×D411yescharacteristic
204C4×Q8C5×D411yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C5×D411yescharacteristic
208C4×D4C5×D411yescharacteristic
209#117—21no—
210#117C2×C4×C511yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C511yescharacteristic
214C2×C4⋊C4C2×C4×C511yescharacteristic
215C2×C42—21no—
216C2×C42C23×C511yescharacteristic
217#107—21no—
218#107—21no—
219#106—21no—
220#106—21no—
221C4⋊C8—22no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227#103—21no—
228#103—21no—
229#102—21no—
230#102—21no—
231C22⋊C8—22no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8C5×D412yes—
235#97—21no—
236#97—21no—
237#97C5×D411yescharacteristic
238#97C5×D411yescharacteristic
239C4×C8—22no—
240C4×C8—21no—
241C4×C8—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5—41no—
248C22×C5#38611yescharacteristic
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—22no—
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—81no—
258C4×C5—81no—
259C4×C5C2×#10111yescharacteristic
260C4×C5#41311yescharacteristic
261#41—22no—
262#41—41no—
263C2×Q8C5×C22⋊C411yescharacteristic
264C2×D4—21no—
265C2×D4C5×C22⋊C411yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4C22×C4×C511yescharacteristic
272C22×C4C2×C5×D411yescharacteristic
273C22×C4C5×#4111yescharacteristic
274M16—42no—
275M16—44no—
276M16—41no—
277M16—41no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C5×C22⋊C411yescharacteristic
296C4⋊C4C5×C22⋊C411yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42C2×C5×D411yescharacteristic
304C42C2×C5×D411yescharacteristic
305C42C2×C5×D411yescharacteristic
306C42C5×#4111yescharacteristic
307C2×C5—41no—
308C2×C5—81no—
309C2×C5#188111yescharacteristic
310C2×C5#190111yescharacteristic
311C2×C5#190611yescharacteristic
312C23—21no—
313C23C4×C5×D411yescharacteristic
314Q8—21no—
315Q8C5×#10112yes—
316D4—21no—
317D4—21no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4C2×C5×C22⋊C411yescharacteristic
334C2×C4C4×C5×D411yescharacteristic
335C2×C4C5×#12011yescharacteristic
336C2×C4C5×#12111yescharacteristic
337C2×C4C5×#12111yescharacteristic
338C2×C4C5×#12311yescharacteristic
339C8—22no—
340C8—42no—
341C8—41no—
342C8—41no—
343C8—41no—
344C8—81no—
345C8—81no—
346C5#935211yescharacteristic, direct product factor, Sylow
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C5×#38611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×C5×#10111yescharacteristic
365C4C5×#41311yescharacteristic
366C2—41no—
367C2—81no—
368C2C5×#188111yescharacteristic
369C2C5×#190111yescharacteristic
370C2C5×#190611yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#41C2×C4
LCSG ▷ C22×C4 ▷ 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×#1528C2semidirect
5. C5×#1470C2semidirect
6. C5×#1307C2semidirect
7. C5×#1299C2semidirect
33. #9352C5direct (N × H)
84. #1528C2×C5semidirect
86. #1470C2×C5semidirect
87. #1307C2×C5semidirect
88. #1299C2×C5semidirect
346. C5#9352direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30802
C5×#29712
C5×#15282
C5×#14882
C5×#14702
C5×#13072
C5×#12992
#93525