Finite Group Databasebeta

← C5×#9082 #11931802

Subgroups — C5×#9082 #11931802

Order 1280.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#431C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic
3C5×#1817C211yesmaximal, characteristic
4C2×C5×#324C212yesmaximal
5C5×#1280C212yesmaximal
6C22×C5×C4⋊C4C411yescharacteristic
7C22×C5×C4⋊C4C2211yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C5×#431—24no—
10C2×C5×C4⋊C8—21no—
11C2×C5×C22⋊C8C2212yes—
12C2×C5×C22⋊C8C2212yes—
13C2×C4×C5×C8—21no—
14C5×#387—21no—
15C5×#387—21no—
16C5×#387—21no—
17C5×#387—21no—
18C2×C5×#95C411yescharacteristic
19C2×C5×#95C411yescharacteristic
20C2×C5×#95C411yescharacteristic
21C2×C5×#95C2211yescharacteristic
22C5×#336—21no—
23C5×#336—21no—
24C5×#324—24no—
25#9082C511yesmaximal, characteristic, direct product factor, Sylow
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5C2×C411yescharacteristic
31C23×C4×C5C2×C411yescharacteristic
32C23×C4×C5C2311yescharacteristic
33C22×C5×C8—22no—
34C22×C5×C8—22no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—22no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—22no—
41C2×C5×C4⋊C4—22no—
42C2×C5×C4⋊C4C814yescomplemented
43C2×C42×C5—22no—
44C2×C42×C5—22no—
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C2×C42×C5D411yescharacteristic
49C5×C4⋊C8—24no—
50C5×C22⋊C8—22no—
51C5×C22⋊C8—22no—
52C5×C22⋊C8—22no—
53C5×C22⋊C8D414yes—
54C4×C5×C8—24no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95—21no—
60C5×#95—21no—
61C5×#95—21no—
62C5×#95—21no—
63C2×#431C2×C511yescharacteristic
64C2×#387C2×C511yescharacteristic
65#1817C2×C511yescharacteristic
66C2×#324C2×C512yes—
67#1280C2×C512yes—
68C24×C5C22×C411yescharacteristic
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—22no—
78C22×C4×C5—22no—
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—22no—
82C22×C4×C5—22no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5C22⋊C411yescharacteristic
94C22×C4×C5C22⋊C411yescharacteristic
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C2×C812yes—
97C22×C4×C5C2×C812yes—
98C22×C4×C5C2×C812yes—
99C22×C4×C5M1612yes—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D412yes—
103C22×C4×C5#4112yes—
104C2×C5×C8—24no—
105C2×C5×C8—42no—
106C2×C5×C8—42no—
107C2×C5×C8—42no—
108C2×C5×C8—42no—
109C2×C5×C8—42no—
110C5×C4⋊C4—24no—
111C5×C4⋊C4—24no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—42no—
114C5×C4⋊C4—41no—
115C42×C5—21no—
116C42×C5—21no—
117C42×C5—22no—
118C42×C5—22no—
119C42×C5—21no—
120C42×C5—21no—
121C22×C4⋊C4C4×C511yescharacteristic
122C22×C4⋊C4C22×C511yescharacteristic
123C22×C42C22×C511yescharacteristic
124#431—24no—
125C2×C4⋊C8—21no—
126C2×C22⋊C8C22×C512yes—
127C2×C22⋊C8C22×C512yes—
128C2×C4×C8—21no—
129#387—21no—
130#387—21no—
131#387—21no—
132#387—21no—
133C2×#95C4×C511yescharacteristic
134C2×#95C4×C511yescharacteristic
135C2×#95C4×C511yescharacteristic
136C2×#95C22×C511yescharacteristic
137#336—21no—
138#336—21no—
139#324—24no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5C2×C22⋊C411yescharacteristic
145C23×C5C4×D412yes—
146C23×C5C22×C811yescharacteristic
147C23×C5C2×M1611yescharacteristic
148C23×C5#13112yes—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—24no—
160C2×C4×C5—24no—
161C2×C4×C5—21no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—24no—
167C2×C4×C5—42no—
168C2×C4×C5—42no—
169C2×C4×C5—44no—
170C2×C4×C5—42no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—82no—
184C2×C4×C5—82no—
185C2×C4×C5C22⋊C812yes—
186C2×C4×C5C22⋊C812yes—
187C2×C4×C5#10112yes—
188C2×C4×C5#12011yescharacteristic
189C2×C4×C5#12112yes—
190C2×C4×C5#12311yescharacteristic
191C5×C8—44no—
192C5×C8—82no—
193C23×C4C2×C4×C511yescharacteristic
194C23×C4C2×C4×C511yescharacteristic
195C23×C4C2×C4×C511yescharacteristic
196C23×C4C2×C4×C511yescharacteristic
197C23×C4C2×C4×C511yescharacteristic
198C23×C4C2×C4×C511yescharacteristic
199C23×C4C23×C511yescharacteristic
200C22×C8—22no—
201C22×C8—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4C5×C814yescomplemented
210C2×C42—22no—
211C2×C42—22no—
212C2×C42C5×D411yescharacteristic
213C2×C42C5×D411yescharacteristic
214C2×C42C5×D411yescharacteristic
215C2×C42C5×D411yescharacteristic
216C4⋊C8—24no—
217C22⋊C8—22no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8C5×D414yes—
221C4×C8—24no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230C22×C5—22no—
231C22×C5—22no—
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—22no—
237C22×C5—22no—
238C22×C5#38611yescharacteristic
239C22×C5C2×C22⋊C811yescharacteristic
240C22×C5#40811yescharacteristic
241C22×C5#41011yescharacteristic
242C22×C5#41011yescharacteristic
243C22×C5C2×#10111yescharacteristic
244C22×C5#41311yescharacteristic
245C22×C5C8×D412yes—
246C22×C5#43512yes—
247C4×C5—22no—
248C4×C5—22no—
249C4×C5—21no—
250C4×C5—22no—
251C4×C5—21no—
252C4×C5—22no—
253C4×C5—42no—
254C4×C5—41no—
255C4×C5—42no—
256C4×C5—81no—
257C4×C5—81no—
258C24C22×C4×C511yescharacteristic
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C5×C22⋊C411yescharacteristic
283C22×C4C5×C22⋊C411yescharacteristic
284C22×C4C5×C22⋊C411yescharacteristic
285C22×C4C5×C22⋊C411yescharacteristic
286C22×C4C2×C5×C812yes—
287C22×C4C2×C5×C812yes—
288C22×C4C2×C5×C812yes—
289C22×C4C5×M1612yes—
290C22×C4C2×C5×D411yescharacteristic
291C22×C4C2×C5×D411yescharacteristic
292C22×C4C2×C5×D412yes—
293C22×C4C5×#4112yes—
294C2×C8—24no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C42—21no—
306C42—21no—
307C42—22no—
308C42—22no—
309C42—21no—
310C42—21no—
311C2×C5—22no—
312C2×C5—22no—
313C2×C5#145811yescharacteristic
314C2×C5#146111yescharacteristic
315C2×C5#147011yescharacteristic
316C2×C5#147311yescharacteristic
317C2×C5#186911yescharacteristic
318C2×C5#189911yescharacteristic
319C2×C5#190111yescharacteristic
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23C2×C5×C22⋊C411yescharacteristic
325C23C4×C5×D412yes—
326C23C22×C5×C811yescharacteristic
327C23C2×C5×M1611yescharacteristic
328C23C5×#13112yes—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4C5×C22⋊C812yes—
366C2×C4C5×C22⋊C812yes—
367C2×C4C5×#10112yes—
368C2×C4C5×#12011yescharacteristic
369C2×C4C5×#12112yes—
370C2×C4C5×#12311yescharacteristic
371C8—44no—
372C8—82no—
373C5#908211yescharacteristic, direct product factor, Sylow
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22C5×#38611yescharacteristic
383C22C2×C5×C22⋊C811yescharacteristic
384C22C5×#40811yescharacteristic
385C22C5×#41011yescharacteristic
386C22C5×#41011yescharacteristic
387C22C2×C5×#10111yescharacteristic
388C22C5×#41311yescharacteristic
389C22C5×C8×D412yes—
390C22C5×#43512yes—
391C4—22no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—21no—
396C4—22no—
397C4—42no—
398C4—41no—
399C4—42no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2C5×#145811yescharacteristic
405C2C5×#146111yescharacteristic
406C2C5×#147011yescharacteristic
407C2C5×#147311yescharacteristic
408C2C5×#186911yescharacteristic
409C2C5×#189911yescharacteristic
410C2C5×#190111yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC23C22×C5×C8
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
25. #9082C5direct (N × H)
42. C2×C5×C4⋊C4C8semidirect
209. C2×C4⋊C4C5×C8semidirect
373. C5#9082direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4312
C2×C5×#3872
C5×#18172
C2×C5×#3242
C5×#12802
#90825