Finite Group Databasebeta

← C5×#10484 #11933204

Subgroups — C5×#10484 #11933204

Order 1280.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#474C211yesmaximal, characteristic
2C5×#1956C211yesmaximal, characteristic, complemented
3C5×#1954C211yesmaximal, characteristic
4C5×#1802C211yesmaximal, characteristic
5C2×C5×#334C211yesmaximal, characteristic, complemented
6C2×C5×#332C211yesmaximal, characteristic, complemented
7C5×#1296C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C5×#474—22no—
11C5×#474—22no—
12C2×C5×#107—21no—
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×C4⋊C8C2211yescharacteristic
15C2×C5×C4⋊C8C2211yescharacteristic
16C2×C5×#103—21no—
17C2×C5×#103—21no—
18C2×C5×#102—21no—
19C2×C5×#102—21no—
20C2×C5×C22⋊C8—21no—
21C2×C5×C22⋊C8—21no—
22C2×C4×C5×C8C2211yescharacteristic
23C5×#384C2211yescharacteristic
24C5×#340—21no—
25C5×#334—22no—
26C5×#332—22no—
27#10484C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8—21no—
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C22×C5×C8—21no—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C22×C5×C8D411yescharacteristic
35C22×C5×C8D411yescharacteristic
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8—21no—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8D412yes—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4—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⋊C4D411yescharacteristic
50C2×C5×C22⋊C4—21no—
51C2×C42×C5C2311yescharacteristic
52C5×#107—24no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8D412yes—
59C5×#103—42no—
60C5×#103—42no—
61C5×#102—24no—
62C5×#102—42no—
63C5×C22⋊C8—42no—
64C5×C22⋊C8—42no—
65C4×C5×C8—21no—
66C4×C5×C8—21no—
67C2×#474C2×C511yescharacteristic
68#1956C2×C511yescharacteristic, complemented
69#1954C2×C511yescharacteristic
70#1802C2×C511yescharacteristic
71C2×#334C2×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×D4SD1612yes—
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
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—22no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—41no—
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×C8D812yes—
114C5×C4⋊C4—22no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—81no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—41no—
127C42×C5C2×D411yescharacteristic
128C42×C5C2×D411yescharacteristic
129C42×C5#4111yescharacteristic
130C42×C5#4111yescharacteristic
131C2×C4⋊Q8C22×C511yescharacteristic
132C2×C4×D4C22×C511yescharacteristic
133#474—22no—
134#474—22no—
135C2×#107—21no—
136C2×C4⋊C8C22×C511yescharacteristic
137C2×C4⋊C8C22×C511yescharacteristic
138C2×C4⋊C8C22×C511yescharacteristic
139C2×#103—21no—
140C2×#103—21no—
141C2×#102—21no—
142C2×#102—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×C4×C8C22×C511yescharacteristic
146#384C22×C511yescharacteristic
147#340—21no—
148#334—22no—
149#332—22no—
150C23×C5—22no—
151C23×C5—41no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5#12111yescharacteristic
158C5×Q8—42no—
159C5×Q8—42no—
160C5×Q8—81no—
161C5×Q8—81no—
162C5×D4—22no—
163C5×D4—22no—
164C5×D4—41no—
165C5×D4—41no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—41no—
169C2×C4×C5—42no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—81no—
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#12011yescharacteristic
182C2×C4×C5#12111yescharacteristic
183C2×C4×C5#12111yescharacteristic
184C2×C4×C5#12311yescharacteristic
185C2×C4×C5#12311yescharacteristic
186C2×C4×C5#12411yescharacteristic
187C2×C4×C5C2×D811yescharacteristic
188C2×C4×C5C2×SD1611yescharacteristic
189C2×C4×C5#13511yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C5#13711yescharacteristic
194C2×C4×C5#13711yescharacteristic
195C5×C8—22no—
196C5×C8—42no—
197C5×C8—41no—
198C5×C8—81no—
199C5×C8—81no—
200C22×Q8—21no—
201C22×D4C5×D411yescharacteristic
202C23×C4—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8C5×D411yescharacteristic
207C22×C8C5×D411yescharacteristic
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C5×D412yes—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—21no—
215C4×D4—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×C22⋊C4—21no—
223C2×C42C23×C511yescharacteristic
224#107—24no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8C5×D412yes—
231#103—42no—
232#103—42no—
233#102—24no—
234#102—42no—
235C22⋊C8—42no—
236C22⋊C8—42no—
237C4×C8—21no—
238C4×C8—21no—
239C22×C5—42no—
240C22×C5—42no—
241C22×C5—42no—
242C22×C5—81no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5#39411yescharacteristic
247C22×C5#45911yescharacteristic
248C22×C5#46311yescharacteristic
249C22×C5#46511yescharacteristic
250C22×C5#47011yescharacteristic
251C22×C5#47111yescharacteristic
252C22×C5#47311yescharacteristic
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—81no—
256C4×C5—82no—
257C4×C5—161no—
258C4×C5#44811yescharacteristic
259C4×C5#45211yescharacteristic
260C4×C5#45911yescharacteristic
261C4×C5#46311yescharacteristic
262C4×C5#46611yescharacteristic
263C4×C5#46911yescharacteristic
264C4×C5#48311yescharacteristic
265C4×C5#48511yescharacteristic
266C24—21no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4C5×SD1612yes—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×C5×D411yescharacteristic
289C22×C4C2×C5×D411yescharacteristic
290C22×C4C5×#4111yescharacteristic
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8C5×D812yes—
306C4⋊C4—22no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42C2×C5×D411yescharacteristic
320C42C2×C5×D411yescharacteristic
321C42C5×#4111yescharacteristic
322C42C5×#4111yescharacteristic
323C2×C5—82no—
324C2×C5#166511yescharacteristic
325C2×C5#167911yescharacteristic
326C2×C5#168911yescharacteristic
327C2×C5#170311yescharacteristic
328C2×C5#203511yescharacteristic
329C2×C5#205211yescharacteristic
330C2×C5#205411yescharacteristic
331C23—22no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23C5×#12111yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343D4—22no—
344D4—22no—
345D4—41no—
346D4—41no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C5×#12011yescharacteristic
363C2×C4C5×#12111yescharacteristic
364C2×C4C5×#12111yescharacteristic
365C2×C4C5×#12311yescharacteristic
366C2×C4C5×#12311yescharacteristic
367C2×C4C5×#12411yescharacteristic
368C2×C4C2×C5×D811yescharacteristic
369C2×C4C2×C5×SD1611yescharacteristic
370C2×C4C5×#13511yescharacteristic
371C2×C4C5×#13511yescharacteristic
372C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
373C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
374C2×C4C5×#13711yescharacteristic
375C2×C4C5×#13711yescharacteristic
376C8—22no—
377C8—42no—
378C8—41no—
379C8—81no—
380C8—81no—
381C5#1048411yescharacteristic, direct product factor, Sylow
382C22—42no—
383C22—42no—
384C22—42no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C5×#39411yescharacteristic
390C22C5×#45911yescharacteristic
391C22C5×#46311yescharacteristic
392C22C5×#46511yescharacteristic
393C22C5×#47011yescharacteristic
394C22C5×#47111yescharacteristic
395C22C5×#47311yescharacteristic
396C4—21no—
397C4—21no—
398C4—81no—
399C4—82no—
400C4—161no—
401C4C5×#44811yescharacteristic
402C4C5×#45211yescharacteristic
403C4C5×#45911yescharacteristic
404C4C5×#46311yescharacteristic
405C4C5×#46611yescharacteristic
406C4C5×#46911yescharacteristic
407C4C5×#48311yescharacteristic
408C4C5×#48511yescharacteristic
409C2—82no—
410C2C5×#166511yescharacteristic
411C2C5×#167911yescharacteristic
412C2C5×#168911yescharacteristic
413C2C5×#170311yescharacteristic
414C2C5×#203511yescharacteristic
415C2C5×#205211yescharacteristic
416C2C5×#205411yescharacteristic
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×#1956C2semidirect
5. C2×C5×#334C2semidirect
6. C2×C5×#332C2semidirect
7. C5×#1296C2semidirect
27. #10484C5direct (N × H)
68. #1956C2×C5semidirect
71. C2×#334C2×C5semidirect
72. C2×#332C2×C5semidirect
73. #1296C2×C5semidirect
381. C5#10484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4742
C5×#19562
C5×#19542
C5×#18022
C2×C5×#3342
C2×C5×#3322
C5×#12962
#104845