Finite Group Databasebeta

← C5×#10476 #11933196

Subgroups — C5×#10476 #11933196

Order 1280.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#461C211yesmaximal, characteristic
2C5×#1990C211yesmaximal, characteristic, complemented
3C5×#1954C211yesmaximal, characteristic
4C5×#1802C211yesmaximal, characteristic
5C2×C5×#335C211yesmaximal, characteristic, complemented
6C2×C5×#332C211yesmaximal, characteristic, complemented
7C5×#1296C211yesmaximal, characteristic, complemented
8C22×C5×SD16—21no—
9C2×C5×C4⋊Q8C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#461—22no—
12C5×#461—22no—
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×C4⋊C8C2211yescharacteristic
15C2×C5×C4⋊C8C2211yescharacteristic
16C2×C5×#103—21no—
17C2×C5×#102—21no—
18C2×C5×C22⋊C8—21no—
19C2×C5×C22⋊C8—21no—
20C2×C4×C5×C8C2211yescharacteristic
21C5×#384C2211yescharacteristic
22C5×#340—21no—
23C5×#340—21no—
24C5×#340—21no—
25C5×#335—22no—
26C5×#332—22no—
27#10476C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8—21no—
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C2×C5×SD16—24no—
32C2×C5×SD16—42no—
33C2×C5×SD16—42no—
34C22×C5×C8—21no—
35C22×C5×C8—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⋊Q8D412yes—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C22⋊C4—21no—
54C2×C42×C5C2311yescharacteristic
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8D412yes—
61C5×#103—24no—
62C5×#102—42no—
63C5×C22⋊C8—42no—
64C5×C22⋊C8—42no—
65C4×C5×C8—21no—
66C4×C5×C8—21no—
67C2×#461C2×C511yescharacteristic
68#1990C2×C511yescharacteristic, complemented
69#1954C2×C511yescharacteristic
70#1802C2×C511yescharacteristic
71C2×#335C2×C511yescharacteristic, complemented
72C2×#332C2×C511yescharacteristic, complemented
73#1296C2×C511yescharacteristic, complemented
74C24×C5—21no—
75C2×C5×Q8—22no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4D812yes—
87C22×C4×C5—21no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5#4111yescharacteristic
99C5×SD16—48no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—22no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C2×C5×C8—41no—
114C2×C5×C8SD1612yescomplemented
115C5×C4⋊C4—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C5×C4⋊C4—81no—
126C5×C22⋊C4—41no—
127C5×C22⋊C4—41no—
128C42×C5C2×D411yescharacteristic
129C42×C5C2×D411yescharacteristic
130C42×C5#4111yescharacteristic
131C42×C5#4111yescharacteristic
132C22×SD16—21no—
133C2×C4⋊Q8C22×C511yescharacteristic
134C2×C4×D4C22×C511yescharacteristic
135#461—22no—
136#461—22no—
137C2×C4⋊C8C22×C511yescharacteristic
138C2×C4⋊C8C22×C511yescharacteristic
139C2×C4⋊C8C22×C511yescharacteristic
140C2×#103—21no—
141C2×#102—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×C4×C8C22×C511yescharacteristic
145#384C22×C511yescharacteristic
146#340—21no—
147#340—21no—
148#340—21no—
149#335—22no—
150#332—22no—
151C23×C5—22no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5#12111yescharacteristic
159C5×Q8—42no—
160C5×Q8—42no—
161C5×Q8—81no—
162C5×Q8—81no—
163C5×D4—22no—
164C5×D4—22no—
165C5×D4—41no—
166C5×D4—41no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—41no—
170C2×C4×C5—42no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—81no—
174C2×C4×C5—81no—
175C2×C4×C5—81no—
176C2×C4×C5—81no—
177C2×C4×C5—81no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5—81no—
181C2×C4×C5—81no—
182C2×C4×C5#12011yescharacteristic
183C2×C4×C5#12111yescharacteristic
184C2×C4×C5#12111yescharacteristic
185C2×C4×C5#12311yescharacteristic
186C2×C4×C5#12311yescharacteristic
187C2×C4×C5#12411yescharacteristic
188C2×C4×C5C2×D811yescharacteristic
189C2×C4×C5C2×SD1611yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5#13511yescharacteristic
192C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C5#13711yescharacteristic
195C2×C4×C5#13711yescharacteristic
196C5×C8—22no—
197C5×C8—42no—
198C5×C8—41no—
199C5×C8—81no—
200C5×C8—81no—
201C22×Q8—21no—
202C22×D4C5×D411yescharacteristic
203C23×C4—21no—
204C2×SD16—24no—
205C2×SD16—42no—
206C2×SD16—42no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8C5×D411yescharacteristic
211C22×C8C5×D411yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8C5×D412yes—
216C4×D4—21no—
217C4×D4—21no—
218C4×D4—21no—
219C4×D4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C5×D411yescharacteristic
226C2×C22⋊C4—21no—
227C2×C42C23×C511yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8C5×D412yes—
234#103—24no—
235#102—42no—
236C22⋊C8—42no—
237C22⋊C8—42no—
238C4×C8—21no—
239C4×C8—21no—
240C22×C5—42no—
241C22×C5—42no—
242C22×C5—42no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5—81no—
247C22×C5#39411yescharacteristic
248C22×C5#46111yescharacteristic
249C22×C5#46311yescharacteristic
250C22×C5#46611yescharacteristic
251C22×C5#46811yescharacteristic
252C22×C5#47111yescharacteristic
253C22×C5#47311yescharacteristic
254C4×C5—21no—
255C4×C5—21no—
256C4×C5—81no—
257C4×C5—82no—
258C4×C5—161no—
259C4×C5#44711yescharacteristic
260C4×C5#45211yescharacteristic
261C4×C5#46011yescharacteristic
262C4×C5#46411yescharacteristic
263C4×C5#46511yescharacteristic
264C4×C5#46811yescharacteristic
265C4×C5#48011yescharacteristic
266C4×C5#48211yescharacteristic
267C24—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4C5×D812yes—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4C2×C5×D411yescharacteristic
290C22×C4C2×C5×D411yescharacteristic
291C22×C4C5×#4111yescharacteristic
292SD16—48no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—22no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8C5×SD1612yescomplemented
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—81no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C42C2×C5×D411yescharacteristic
322C42C2×C5×D411yescharacteristic
323C42C5×#4111yescharacteristic
324C42C5×#4111yescharacteristic
325C2×C5—82no—
326C2×C5#167311yescharacteristic
327C2×C5#168111yescharacteristic
328C2×C5#169111yescharacteristic
329C2×C5#169911yescharacteristic
330C2×C5#203311yescharacteristic
331C2×C5#205211yescharacteristic
332C2×C5#205511yescharacteristic
333C23—22no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C5×#12111yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4C5×#12011yescharacteristic
365C2×C4C5×#12111yescharacteristic
366C2×C4C5×#12111yescharacteristic
367C2×C4C5×#12311yescharacteristic
368C2×C4C5×#12311yescharacteristic
369C2×C4C5×#12411yescharacteristic
370C2×C4C2×C5×D811yescharacteristic
371C2×C4C2×C5×SD1611yescharacteristic
372C2×C4C5×#13511yescharacteristic
373C2×C4C5×#13511yescharacteristic
374C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
375C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C5×#13711yescharacteristic
377C2×C4C5×#13711yescharacteristic
378C8—22no—
379C8—42no—
380C8—41no—
381C8—81no—
382C8—81no—
383C5#1047611yescharacteristic, direct product factor, Sylow
384C22—42no—
385C22—42no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C5×#39411yescharacteristic
392C22C5×#46111yescharacteristic
393C22C5×#46311yescharacteristic
394C22C5×#46611yescharacteristic
395C22C5×#46811yescharacteristic
396C22C5×#47111yescharacteristic
397C22C5×#47311yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—81no—
402C4—161no—
403C4C5×#44711yescharacteristic
404C4C5×#45211yescharacteristic
405C4C5×#46011yescharacteristic
406C4C5×#46411yescharacteristic
407C4C5×#46511yescharacteristic
408C4C5×#46811yescharacteristic
409C4C5×#48011yescharacteristic
410C4C5×#48211yescharacteristic
411C2—82no—
412C2C5×#167311yescharacteristic
413C2C5×#168111yescharacteristic
414C2C5×#169111yescharacteristic
415C2C5×#169911yescharacteristic
416C2C5×#203311yescharacteristic
417C2C5×#205211yescharacteristic
418C2C5×#205511yescharacteristic
subgroupG/H
center, socleC23×C5#121
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×#1990C2semidirect
5. C2×C5×#335C2semidirect
6. C2×C5×#332C2semidirect
7. C5×#1296C2semidirect
27. #10476C5direct (N × H)
68. #1990C2×C5semidirect
71. C2×#335C2×C5semidirect
72. C2×#332C2×C5semidirect
73. #1296C2×C5semidirect
114. C2×C5×C8SD16semidirect
307. C2×C8C5×SD16semidirect
383. C5#10476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4612
C5×#19902
C5×#19542
C5×#18022
C2×C5×#3352
C2×C5×#3322
C5×#12962
#104765