Finite Group Databasebeta

← C5×#10426 #11933146

Subgroups — C5×#10426 #11933146

Order 1280.

444 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2820C211yesmaximal, characteristic
2C5×#1992C211yesmaximal, characteristic, complemented
3C5×#1959C211yesmaximal, characteristic
4C5×#1836C211yesmaximal, characteristic, complemented
5C2×C5×#330C211yesmaximal, characteristic, complemented
6C2×C5×#329C211yesmaximal, characteristic
7C5×#1295C211yesmaximal, characteristic, complemented
8C2×C5×#125C2211yescharacteristic
9C2×C5×#124C2211yescharacteristic
10C2×C5×#103—21no—
11C2×C5×#102—21no—
12C2×C5×#97C2211yescharacteristic
13C2×C5×#97C2211yescharacteristic
14C2×C5×#97C2211yescharacteristic
15C5×#399—21no—
16C5×#397—21no—
17C5×#396—21no—
18C5×#396—21no—
19C5×#395—21no—
20C5×#394—21no—
21C5×#384C2211yescharacteristic
22C5×#382C2211yescharacteristic
23C5×#340—21no—
24C5×#340—21no—
25C5×#340—21no—
26C5×#340—21no—
27C5×#330—22no—
28C5×#329—22no—
29#10426C511yesmaximal, characteristic, direct product factor, Sylow
30C22×C5×Q8D411yescharacteristic
31C22×C5×D4D411yescharacteristic
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C22×C5×C8—21no—
35C5×#125—21no—
36C5×#125—21no—
37C5×#125—21no—
38C5×#125—21no—
39C5×#124—21no—
40C5×#124—21no—
41C5×#124—21no—
42C5×#124—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4D411yescharacteristic
51C2×C5×C4⋊C4D411yescharacteristic
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C4⋊C4D411yescharacteristic
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C42×C5C2311yescharacteristic
61C5×#103—42no—
62C5×#102—42no—
63C5×#97—21no—
64C5×#97—21no—
65C5×#97—21no—
66C5×#97—21no—
67C5×#97—21no—
68C5×#97D412yes—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73#2820C2×C511yescharacteristic
74#1992C2×C511yescharacteristic, complemented
75#1959C2×C511yescharacteristic
76#1836C2×C511yescharacteristic, complemented
77C2×#330C2×C511yescharacteristic, complemented
78C2×#329C2×C511yescharacteristic
79#1295C2×C511yescharacteristic, complemented
80C24×C5—21no—
81C2×C5×Q8—21no—
82C2×C5×Q8—21no—
83C2×C5×Q8—41no—
84C2×C5×Q8—41no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—41no—
88C2×C5×D4—41no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—41no—
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C2×C5×C8—22no—
99C2×C5×C8—22no—
100C2×C5×C8—22no—
101C2×C5×C8—41no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—41no—
113C5×C4⋊C4—42no—
114C5×C4⋊C4—42no—
115C5×C4⋊C4—41no—
116C5×C4⋊C4—41no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—81no—
122C5×C4⋊C4—81no—
123C5×C22⋊C4—41no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—41no—
127C5×C22⋊C4—81no—
128C5×C22⋊C4—81no—
129C5×C22⋊C4—81no—
130C5×C22⋊C4—81no—
131C42×C5C2×D411yescharacteristic
132C42×C5#4111yescharacteristic
133C42×C5#4111yescharacteristic
134C42×C5#4111yescharacteristic
135C2×#125C22×C511yescharacteristic
136C2×#124C22×C511yescharacteristic
137C2×#103—21no—
138C2×#102—21no—
139C2×#97C22×C511yescharacteristic
140C2×#97C22×C511yescharacteristic
141C2×#97C22×C511yescharacteristic
142#399—21no—
143#397—21no—
144#396—21no—
145#396—21no—
146#395—21no—
147#394—21no—
148#384C22×C511yescharacteristic
149#382C22×C511yescharacteristic
150#340—21no—
151#340—21no—
152#340—21no—
153#340—21no—
154#330—22no—
155#329—22no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5#12011yescharacteristic
164C5×Q8—42no—
165C5×Q8—81no—
166C5×D4—42no—
167C5×D4—81no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
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—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—81no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5#12111yescharacteristic
193C2×C4×C5#12111yescharacteristic
194C2×C4×C5#12111yescharacteristic
195C2×C4×C5#12311yescharacteristic
196C2×C4×C5#12311yescharacteristic
197C2×C4×C5#12411yescharacteristic
198C5×C8—42no—
199C5×C8—42no—
200C5×C8—42no—
201C22×Q8C5×D411yescharacteristic
202C22×D4C5×D411yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—21no—
210#124—21no—
211#124—21no—
212#124—21no—
213#124—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C5×D411yescharacteristic
222C2×C4⋊C4C5×D411yescharacteristic
223C2×C4⋊C4C5×D411yescharacteristic
224C2×C4⋊C4C5×D411yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C42C23×C511yescharacteristic
232#103—42no—
233#102—42no—
234#97—21no—
235#97—21no—
236#97—21no—
237#97—21no—
238#97—21no—
239#97C5×D412yes—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5—81no—
249C22×C5—81no—
250C22×C5—81no—
251C22×C5#39411yescharacteristic
252C22×C5#45311yescharacteristic
253C22×C5#45411yescharacteristic
254C22×C5#45411yescharacteristic
255C22×C5#45511yescharacteristic
256C22×C5#45511yescharacteristic
257C22×C5#45611yescharacteristic
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—81no—
265C4×C5—81no—
266C4×C5—81no—
267C4×C5—81no—
268C4×C5—81no—
269C4×C5—161no—
270C24—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4C2×C5×D411yescharacteristic
286C22×C4C2×C5×D411yescharacteristic
287C22×C4C2×C5×D411yescharacteristic
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—81no—
319C22⋊C4—81no—
320C22⋊C4—81no—
321C42C2×C5×D411yescharacteristic
322C42C5×#4111yescharacteristic
323C42C5×#4111yescharacteristic
324C42C5×#4111yescharacteristic
325C2×C5—161no—
326C2×C5#165711yescharacteristic
327C2×C5#166111yescharacteristic
328C2×C5#166211yescharacteristic
329C2×C5#166411yescharacteristic
330C2×C5#203711yescharacteristic
331C2×C5#203811yescharacteristic
332C2×C5#204011yescharacteristic
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C5×#12011yescharacteristic
341Q8—42no—
342Q8—81no—
343D4—42no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C5×#12111yescharacteristic
370C2×C4C5×#12111yescharacteristic
371C2×C4C5×#12111yescharacteristic
372C2×C4C5×#12311yescharacteristic
373C2×C4C5×#12311yescharacteristic
374C2×C4C5×#12411yescharacteristic
375C8—42no—
376C8—42no—
377C8—42no—
378C5#1042611yescharacteristic, direct product factor, Sylow
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C5×#39411yescharacteristic
387C22C5×#45311yescharacteristic
388C22C5×#45411yescharacteristic
389C22C5×#45411yescharacteristic
390C22C5×#45511yescharacteristic
391C22C5×#45511yescharacteristic
392C22C5×#45611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—161no—
405C2—161no—
406C2C5×#165711yescharacteristic
407C2C5×#166111yescharacteristic
408C2C5×#166211yescharacteristic
409C2C5×#166411yescharacteristic
410C2C5×#203711yescharacteristic
411C2C5×#203811yescharacteristic
412C2C5×#204011yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1992C2semidirect
4. C5×#1836C2semidirect
5. C2×C5×#330C2semidirect
7. C5×#1295C2semidirect
29. #10426C5direct (N × H)
74. #1992C2×C5semidirect
76. #1836C2×C5semidirect
77. C2×#330C2×C5semidirect
79. #1295C2×C5semidirect
378. C5#10426direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28202
C5×#19922
C5×#19592
C5×#18362
C2×C5×#3302
C2×C5×#3292
C5×#12952
#104265