Finite Group Databasebeta

← C5×#9376 #11932096

Subgroups — C5×#9376 #11932096

Order 1280.

430 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3218C211yesmaximal, characteristic
2C5×#2992C211yesmaximal, characteristic
3C5×#1987C211yesmaximal, characteristic, complemented
4C5×#1556C211yesmaximal, characteristic, complemented
5C5×#1509C211yesmaximal, characteristic
6C5×#1290C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C5×#529C2211yescharacteristic
10C5×#497C412yescomplemented
11C5×#491C412yescomplemented
12C5×#462—21no—
13C5×#461—21no—
14C5×#451—21no—
15C5×#448—21no—
16C5×#446—21no—
17C5×#435—21no—
18C5×#435—21no—
19C5×C8×D4—21no—
20C5×#433—21no—
21C5×#432C2211yescharacteristic
22C5×#432C2211yescharacteristic
23C5×#432C2211yescharacteristic
24C5×#424—21no—
25C2×C5×C4⋊C8C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C5×#340—21no—
28C5×#340—21no—
29C5×#332—21no—
30C5×#332—21no—
31C5×#328—21no—
32C5×#327—21no—
33#9376C511yesmaximal, characteristic, direct product factor, Sylow
34C22×C5×Q8—21no—
35C2×C5×Q16—22no—
36C2×C5×SD16—22no—
37C2×C5×M16—21no—
38C22×C5×C8—21no—
39C22×C5×C8D411yescharacteristic
40C22×C5×C8D411yescharacteristic
41C5×C4⋊Q8—21no—
42C5×C4⋊Q8—21no—
43C5×C4⋊Q8—21no—
44C5×C4⋊Q8C2×C412yes—
45C5×#126—21no—
46C5×#125C2×C411yescharacteristic
47C5×#124C2×C411yescharacteristic
48C5×#123—21no—
49C5×C22⋊Q8D411yescharacteristic
50C5×#121D411yescharacteristic
51C4×C5×Q8D411yescharacteristic
52C4×C5×D4—21no—
53C4×C5×D4D411yescharacteristic
54C5×#117—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—21no—
58C2×C42×C5—21no—
59C2×C42×C5C2311yescharacteristic
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8D411yescharacteristic
67C5×C4⋊C8D411yescharacteristic
68C5×#103—22no—
69C5×#103—22no—
70C5×C22⋊C8—21no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C5×#97—21no—
76C5×#97—21no—
77C5×#97—21no—
78C5×#97C2×C412yes—
79C4×C5×C8—21no—
80C5×#95—21no—
81#3218C2×C511yescharacteristic
82#2992C2×C511yescharacteristic
83#1987C2×C511yescharacteristic, complemented
84#1556C2×C511yescharacteristic, complemented
85#1509C2×C511yescharacteristic
86#1290C2×C511yescharacteristic, complemented
87#1285C2×C511yescharacteristic, complemented
88C2×C5×Q8—22no—
89C2×C5×Q8—41no—
90C2×C5×Q8—82no—
91C2×C5×Q8C22⋊C411yescharacteristic
92C2×C5×D4—21no—
93C2×C5×D4C22⋊C411yescharacteristic
94C22×C4×C5—21no—
95C22×C4×C5—41no—
96C22×C4×C5—41no—
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5#4111yescharacteristic
100C5×Q16—82no—
101C5×SD16—82no—
102C5×M16—81no—
103C2×C5×C8—22no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8—21no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C2×C5×C8—81no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4C22⋊C411yescharacteristic
123C5×C4⋊C4C22⋊C411yescharacteristic
124C5×C22⋊C4—21no—
125C5×C22⋊C4—21no—
126C5×C22⋊C4—21no—
127C5×C22⋊C4—21no—
128C5×C22⋊C4—21no—
129C42×C5—21no—
130C42×C5—81no—
131C42×C5C22×C411yescharacteristic
132C42×C5C2×D411yescharacteristic
133C42×C5C2×D411yescharacteristic
134C42×C5#4111yescharacteristic
135C2×C4⋊Q8C22×C511yescharacteristic
136#529C22×C511yescharacteristic
137#497C4×C512yescomplemented
138#491C4×C512yescomplemented
139#462—21no—
140#461—21no—
141#451—21no—
142#448—21no—
143#446—21no—
144#435—21no—
145#435—21no—
146C8×D4—21no—
147#433—21no—
148#432C22×C511yescharacteristic
149#432C22×C511yescharacteristic
150#432C22×C511yescharacteristic
151#424—21no—
152C2×C4⋊C8C22×C511yescharacteristic
153C4×C4⋊C4C22×C511yescharacteristic
154#340—21no—
155#340—21no—
156#332—21no—
157#332—21no—
158#328—21no—
159#327—21no—
160C23×C5—21no—
161C23×C5#12111yescharacteristic
162C5×Q8—41no—
163C5×Q8—42no—
164C5×Q8—42no—
165C5×Q8—82no—
166C5×D4—41no—
167C5×D4—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—42no—
181C2×C4×C5—81no—
182C2×C4×C5—82no—
183C2×C4×C5—81no—
184C2×C4×C5C2×C22⋊C411yescharacteristic
185C2×C4×C5C4×D411yescharacteristic
186C2×C4×C5C4×D411yescharacteristic
187C2×C4×C5#12011yescharacteristic
188C2×C4×C5#12111yescharacteristic
189C2×C4×C5#12311yescharacteristic
190C5×C8—42no—
191C5×C8—41no—
192C5×C8—41no—
193C5×C8—41no—
194C5×C8—41no—
195C5×C8—81no—
196C22×Q8—21no—
197C2×Q16—22no—
198C2×SD16—22no—
199C2×M16—21no—
200C22×C8—21no—
201C22×C8C5×D411yescharacteristic
202C22×C8C5×D411yescharacteristic
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8C2×C4×C512yes—
207#126—21no—
208#125C2×C4×C511yescharacteristic
209#124C2×C4×C511yescharacteristic
210#123—21no—
211C22⋊Q8C5×D411yescharacteristic
212#121C5×D411yescharacteristic
213C4×Q8C5×D411yescharacteristic
214C4×D4—21no—
215C4×D4C5×D411yescharacteristic
216#117—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C42—21no—
221C2×C42C23×C511yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8C5×D411yescharacteristic
229C4⋊C8C5×D411yescharacteristic
230#103—22no—
231#103—22no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237#97—21no—
238#97—21no—
239#97—21no—
240#97C2×C4×C512yes—
241C4×C8—21no—
242#95—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5—41no—
248C22×C5#38611yescharacteristic
249C22×C5#47111yescharacteristic
250C22×C5#47311yescharacteristic
251C4×C5—21no—
252C4×C5—21no—
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—21no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—41no—
259C4×C5—82no—
260C4×C5—82no—
261C4×C5#45511yescharacteristic
262C4×C5#45611yescharacteristic
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—82no—
266C2×Q8C5×C22⋊C411yescharacteristic
267C2×D4—21no—
268C2×D4C5×C22⋊C411yescharacteristic
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×C5×D411yescharacteristic
273C22×C4C2×C5×D411yescharacteristic
274C22×C4C5×#4111yescharacteristic
275Q16—82no—
276SD16—82no—
277M16—81no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—81no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4C5×C22⋊C411yescharacteristic
298C4⋊C4C5×C22⋊C411yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C42—21no—
305C42—81no—
306C42C22×C4×C511yescharacteristic
307C42C2×C5×D411yescharacteristic
308C42C2×C5×D411yescharacteristic
309C42C5×#4111yescharacteristic
310C2×C5—21no—
311C2×C5—21no—
312C2×C5—81no—
313C2×C5#188211yescharacteristic
314C2×C5#190811yescharacteristic
315C2×C5#191011yescharacteristic
316C23—21no—
317C23C5×#12111yescharacteristic
318Q8—41no—
319Q8—42no—
320Q8—42no—
321Q8—82no—
322D4—41no—
323D4—41no—
324D4—41no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4C2×C5×C22⋊C411yescharacteristic
341C2×C4C4×C5×D411yescharacteristic
342C2×C4C4×C5×D411yescharacteristic
343C2×C4C5×#12011yescharacteristic
344C2×C4C5×#12111yescharacteristic
345C2×C4C5×#12311yescharacteristic
346C8—42no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C5#937611yescharacteristic, direct product factor, Sylow
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C5×#38611yescharacteristic
359C22C5×#47111yescharacteristic
360C22C5×#47311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—82no—
370C4—82no—
371C4C5×#45511yescharacteristic
372C4C5×#45611yescharacteristic
373C2—21no—
374C2—21no—
375C2—81no—
376C2C5×#188211yescharacteristic
377C2C5×#190811yescharacteristic
378C2C5×#191011yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#121D4
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×#1987C2semidirect
4. C5×#1556C2semidirect
6. C5×#1290C2semidirect
7. C5×#1285C2semidirect
10. C5×#497C4semidirect
11. C5×#491C4semidirect
33. #9376C5direct (N × H)
83. #1987C2×C5semidirect
84. #1556C2×C5semidirect
86. #1290C2×C5semidirect
87. #1285C2×C5semidirect
137. #497C4×C5semidirect
138. #491C4×C5semidirect
352. C5#9376direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32182
C5×#29922
C5×#19872
C5×#15562
C5×#15092
C5×#12902
C5×#12852
#93765