Finite Group Databasebeta

← C5×#9377 #11932097

Subgroups — C5×#9377 #11932097

Order 1280.

434 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3239C211yesmaximal, characteristic
2C5×#2992C211yesmaximal, characteristic
3C5×#1981C211yesmaximal, characteristic, complemented
4C5×#1556C211yesmaximal, characteristic, complemented
5C5×#1509C211yesmaximal, characteristic
6C5×#1290C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C5×#529C2211yescharacteristic
10C5×#501C412yescomplemented
11C5×#489C412yescomplemented
12C5×#484—21no—
13C5×#481—21no—
14C5×#475—21no—
15C5×#474—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
26C2×C5×#103—21no—
27C2×C5×#103—21no—
28C4×C5×C4⋊C4C2211yescharacteristic
29C5×#332—21no—
30C5×#332—21no—
31C5×#328—21no—
32C5×#327—21no—
33#9377C511yesmaximal, characteristic, direct product factor, Sylow
34C22×C5×Q8—21no—
35C2×C5×M16—21no—
36C22×C5×C8—21no—
37C22×C5×C8D411yescharacteristic
38C22×C5×C8D411yescharacteristic
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8—21no—
42C5×C4⋊Q8C2×C412yes—
43C5×#126—21no—
44C5×#125C2×C411yescharacteristic
45C5×#124C2×C411yescharacteristic
46C5×#123—21no—
47C5×C22⋊Q8D411yescharacteristic
48C5×#121D411yescharacteristic
49C4×C5×Q8D411yescharacteristic
50C4×C5×D4—21no—
51C4×C5×D4D411yescharacteristic
52C5×#117—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C42×C5—21no—
57C2×C42×C5C2311yescharacteristic
58C5×#107—22no—
59C5×#106—22no—
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—42no—
70C5×#103—42no—
71C5×#102—22no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8—21no—
76C5×C22⋊C8—21no—
77C5×#97—21no—
78C5×#97—21no—
79C5×#97—21no—
80C5×#97C2×C412yes—
81C4×C5×C8—21no—
82C5×#95—21no—
83#3239C2×C511yescharacteristic
84#2992C2×C511yescharacteristic
85#1981C2×C511yescharacteristic, complemented
86#1556C2×C511yescharacteristic, complemented
87#1509C2×C511yescharacteristic
88#1290C2×C511yescharacteristic, complemented
89#1285C2×C511yescharacteristic, complemented
90C2×C5×Q8—22no—
91C2×C5×Q8—41no—
92C2×C5×Q8—41no—
93C2×C5×Q8—41no—
94C2×C5×Q8—41no—
95C2×C5×Q8—41no—
96C2×C5×Q8C22⋊C411yescharacteristic
97C2×C5×D4—21no—
98C2×C5×D4C22⋊C411yescharacteristic
99C22×C4×C5—21no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C22×C4×C5#4111yescharacteristic
105C5×M16—81no—
106C2×C5×C8—22no—
107C2×C5×C8—21no—
108C2×C5×C8—21no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C2×C5×C8—41no—
114C2×C5×C8—81no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—22no—
120C5×C4⋊C4—22no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C5×C4⋊C4C22⋊C411yescharacteristic
126C5×C4⋊C4C22⋊C411yescharacteristic
127C5×C22⋊C4—21no—
128C5×C22⋊C4—21no—
129C5×C22⋊C4—21no—
130C5×C22⋊C4—21no—
131C5×C22⋊C4—21no—
132C42×C5—21no—
133C42×C5—81no—
134C42×C5C22×C411yescharacteristic
135C42×C5C2×D411yescharacteristic
136C42×C5C2×D411yescharacteristic
137C42×C5#4111yescharacteristic
138C2×C4⋊Q8C22×C511yescharacteristic
139#529C22×C511yescharacteristic
140#501C4×C512yescomplemented
141#489C4×C512yescomplemented
142#484—21no—
143#481—21no—
144#475—21no—
145#474—21no—
146#446—21no—
147#435—21no—
148#435—21no—
149C8×D4—21no—
150#433—21no—
151#432C22×C511yescharacteristic
152#432C22×C511yescharacteristic
153#432C22×C511yescharacteristic
154#424—21no—
155C2×C4⋊C8C22×C511yescharacteristic
156C2×#103—21no—
157C2×#103—21no—
158C4×C4⋊C4C22×C511yescharacteristic
159#332—21no—
160#332—21no—
161#328—21no—
162#327—21no—
163C23×C5—21no—
164C23×C5#12111yescharacteristic
165C5×Q8—41no—
166C5×Q8—42no—
167C5×Q8—42no—
168C5×Q8—81no—
169C5×Q8—81no—
170C5×D4—41no—
171C5×D4—41no—
172C5×D4—41no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—81no—
186C2×C4×C5—81no—
187C2×C4×C5—81no—
188C2×C4×C5—81no—
189C2×C4×C5C2×C22⋊C411yescharacteristic
190C2×C4×C5C4×D411yescharacteristic
191C2×C4×C5C4×D411yescharacteristic
192C2×C4×C5#12011yescharacteristic
193C2×C4×C5#12111yescharacteristic
194C2×C4×C5#12311yescharacteristic
195C5×C8—42no—
196C5×C8—41no—
197C5×C8—41no—
198C5×C8—41no—
199C5×C8—41no—
200C5×C8—81no—
201C22×Q8—21no—
202C2×M16—21no—
203C22×C8—21no—
204C22×C8C5×D411yescharacteristic
205C22×C8C5×D411yescharacteristic
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8C2×C4×C512yes—
210#126—21no—
211#125C2×C4×C511yescharacteristic
212#124C2×C4×C511yescharacteristic
213#123—21no—
214C22⋊Q8C5×D411yescharacteristic
215#121C5×D411yescharacteristic
216C4×Q8C5×D411yescharacteristic
217C4×D4—21no—
218C4×D4C5×D411yescharacteristic
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C42—21no—
224C2×C42C23×C511yescharacteristic
225#107—22no—
226#106—22no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8C5×D411yescharacteristic
234C4⋊C8C5×D411yescharacteristic
235#103—22no—
236#103—42no—
237#103—42no—
238#102—22no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244#97—21no—
245#97—21no—
246#97—21no—
247#97C2×C4×C512yes—
248C4×C8—21no—
249#95—21no—
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—41no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5#38611yescharacteristic
256C22×C5#47111yescharacteristic
257C22×C5#47311yescharacteristic
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—41no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—82no—
267C4×C5—82no—
268C4×C5#45311yescharacteristic
269C4×C5#45411yescharacteristic
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8C5×C22⋊C411yescharacteristic
277C2×D4—21no—
278C2×D4C5×C22⋊C411yescharacteristic
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×C5×D411yescharacteristic
283C22×C4C2×C5×D411yescharacteristic
284C22×C4C5×#4111yescharacteristic
285M16—81no—
286C2×C8—22no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—81no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C5×C22⋊C411yescharacteristic
306C4⋊C4C5×C22⋊C411yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C42—21no—
313C42—81no—
314C42C22×C4×C511yescharacteristic
315C42C2×C5×D411yescharacteristic
316C42C2×C5×D411yescharacteristic
317C42C5×#4111yescharacteristic
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—81no—
321C2×C5#188311yescharacteristic
322C2×C5#190811yescharacteristic
323C2×C5#190911yescharacteristic
324C23—21no—
325C23C5×#12111yescharacteristic
326Q8—41no—
327Q8—42no—
328Q8—42no—
329Q8—81no—
330Q8—81no—
331D4—41no—
332D4—41no—
333D4—41no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4C2×C5×C22⋊C411yescharacteristic
351C2×C4C4×C5×D411yescharacteristic
352C2×C4C4×C5×D411yescharacteristic
353C2×C4C5×#12011yescharacteristic
354C2×C4C5×#12111yescharacteristic
355C2×C4C5×#12311yescharacteristic
356C8—42no—
357C8—41no—
358C8—41no—
359C8—41no—
360C8—41no—
361C8—81no—
362C5#937711yescharacteristic, direct product factor, Sylow
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C5×#38611yescharacteristic
369C22C5×#47111yescharacteristic
370C22C5×#47311yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—82no—
380C4—82no—
381C4C5×#45311yescharacteristic
382C4C5×#45411yescharacteristic
383C2—21no—
384C2—21no—
385C2—81no—
386C2C5×#188311yescharacteristic
387C2C5×#190811yescharacteristic
388C2C5×#190911yescharacteristic
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×#1981C2semidirect
4. C5×#1556C2semidirect
6. C5×#1290C2semidirect
7. C5×#1285C2semidirect
10. C5×#501C4semidirect
11. C5×#489C4semidirect
33. #9377C5direct (N × H)
85. #1981C2×C5semidirect
86. #1556C2×C5semidirect
88. #1290C2×C5semidirect
89. #1285C2×C5semidirect
140. #501C4×C5semidirect
141. #489C4×C5semidirect
362. C5#9377direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32392
C5×#29922
C5×#19812
C5×#15562
C5×#15092
C5×#12902
C5×#12852
#93775