Finite Group Databasebeta

← C5×#10521 #11933241

Subgroups — C5×#10521 #11933241

Order 1280.

420 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3246C211yesmaximal, characteristic
2C5×#1994C211yesmaximal, characteristic, complemented
3C5×#1962C211yesmaximal, characteristic
4C5×#1831C211yesmaximal, characteristic, complemented
5C5×#1550C211yesmaximal, characteristic, complemented
6C5×#1547C211yesmaximal, characteristic
7C5×#1292C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C5×#476—21no—
11C5×#475—21no—
12C5×#465—22no—
13C5×#461—21no—
14C5×#460—21no—
15C5×#423C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×C4⋊C8C2211yescharacteristic
19C2×C5×#104—21no—
20C2×C5×#104—21no—
21C43×C5C2211yescharacteristic
22C5×#339—21no—
23C5×#339—21no—
24C5×#336—22no—
25C5×#333—21no—
26C5×#332—21no—
27C5×#332—21no—
28C5×#331—21no—
29#10521C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C2×C5×SD16—22no—
32C2×C5×M16—21no—
33C2×C5×M16—21no—
34C22×C5×C8—21no—
35C22×C5×C8D412yes—
36C5×C4⋊Q8D411yescharacteristic
37C5×C4⋊Q8D411yescharacteristic
38C5×C4⋊Q8D411yescharacteristic
39C5×#127D411yescharacteristic
40C5×#125—21no—
41C5×#124—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×#121—21no—
45C5×#121—21no—
46C4×C5×Q8—21no—
47C4×C5×Q8—21no—
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C5×#117—21no—
51C2×C42×C5—21no—
52C2×C42×C5—21no—
53C2×C42×C5D411yescharacteristic
54C2×C42×C5D411yescharacteristic
55C2×C42×C5C2311yescharacteristic
56C5×#106—22no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×#104—42no—
66C5×#104—42no—
67C5×#103—22no—
68C5×#102—22no—
69#3246C2×C511yescharacteristic
70#1994C2×C511yescharacteristic, complemented
71#1962C2×C511yescharacteristic
72#1831C2×C511yescharacteristic, complemented
73#1550C2×C511yescharacteristic, complemented
74#1547C2×C511yescharacteristic
75#1292C2×C511yescharacteristic, complemented
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C2×C5×Q8—21no—
81C2×C5×Q8—21no—
82C2×C5×Q8—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—41no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—41no—
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5#4111yescharacteristic
93C5×SD16—82no—
94C5×M16—41no—
95C5×M16—41no—
96C5×M16—41no—
97C5×M16—41no—
98C2×C5×C8—22no—
99C2×C5×C8—42no—
100C2×C5×C8—42no—
101C2×C5×C8—41no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C5×C22⋊C4—41no—
115C42×C5—21no—
116C42×C5—21no—
117C42×C5—21no—
118C42×C5—41no—
119C42×C5—41no—
120C42×C5—42no—
121C42×C5—41no—
122C42×C5SD1612yescomplemented
123C42×C5C2×D411yescharacteristic
124C42×C5C2×D411yescharacteristic
125C42×C5#4111yescharacteristic
126C42×C5#4111yescharacteristic
127#533C22×C511yescharacteristic
128#532C22×C511yescharacteristic
129#476—21no—
130#475—21no—
131#465—22no—
132#461—21no—
133#460—21no—
134#423C22×C511yescharacteristic
135#423C22×C511yescharacteristic
136C2×C4⋊C8C22×C511yescharacteristic
137C2×C4⋊C8C22×C511yescharacteristic
138C2×#104—21no—
139C2×#104—21no—
140C43C22×C511yescharacteristic
141#339—21no—
142#339—21no—
143#336—22no—
144#333—21no—
145#332—21no—
146#332—21no—
147#331—21no—
148C23×C5—41no—
149C23×C5#12111yescharacteristic
150C5×Q8—41no—
151C5×Q8—41no—
152C5×Q8—41no—
153C5×Q8—41no—
154C5×Q8—81no—
155C5×D4—41no—
156C5×D4—41no—
157C5×D4—41no—
158C5×D4—41no—
159C5×D4—81no—
160C5×D4—81no—
161C5×D4—81no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—81no—
175C2×C4×C5—81no—
176C2×C4×C5#12011yescharacteristic
177C2×C4×C5#12111yescharacteristic
178C2×C4×C5#12111yescharacteristic
179C2×C4×C5#12311yescharacteristic
180C2×C4×C5#12311yescharacteristic
181C2×C4×C5#12411yescharacteristic
182C2×C4×C5C2×SD1611yescharacteristic
183C2×C4×C5#13511yescharacteristic
184C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C5#13711yescharacteristic
186C5×C8—42no—
187C5×C8—81no—
188C5×C8—81no—
189C5×C8—81no—
190C2×#41—21no—
191C2×SD16—22no—
192C2×M16—21no—
193C2×M16—21no—
194C22×C8—21no—
195C22×C8C5×D412yes—
196C4⋊Q8C5×D411yescharacteristic
197C4⋊Q8C5×D411yescharacteristic
198C4⋊Q8C5×D411yescharacteristic
199#127C5×D411yescharacteristic
200#125—21no—
201#124—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204#121—21no—
205#121—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×D4—21no—
209C4×D4—21no—
210#117—21no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42C5×D411yescharacteristic
214C2×C42C5×D411yescharacteristic
215C2×C42C23×C511yescharacteristic
216#106—22no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225#104—42no—
226#104—42no—
227#103—22no—
228#102—22no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—81no—
232C22×C5—81no—
233C22×C5—81no—
234C22×C5#39411yescharacteristic
235C22×C5#46511yescharacteristic
236C22×C5#46811yescharacteristic
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—42no—
241C4×C5—42no—
242C4×C5—81no—
243C4×C5—81no—
244C4×C5—81no—
245C4×C5#45411yescharacteristic
246C4×C5#45511yescharacteristic
247C4×C5#46011yescharacteristic
248C4×C5#46111yescharacteristic
249C4×C5#46311yescharacteristic
250C4×C5#46411yescharacteristic
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4C2×C5×D411yescharacteristic
266C22×C4C2×C5×D411yescharacteristic
267C22×C4C5×#4111yescharacteristic
268SD16—82no—
269M16—41no—
270M16—41no—
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—41no—
294C42—41no—
295C42—42no—
296C42—41no—
297C42C5×SD1612yescomplemented
298C42C2×C5×D411yescharacteristic
299C42C2×C5×D411yescharacteristic
300C42C5×#4111yescharacteristic
301C42C5×#4111yescharacteristic
302C2×C5—21no—
303C2×C5—21no—
304C2×C5—161no—
305C2×C5#204011yescharacteristic
306C2×C5#205011yescharacteristic
307C2×C5#205511yescharacteristic
308C23—41no—
309C23C5×#12111yescharacteristic
310Q8—41no—
311Q8—41no—
312Q8—41no—
313Q8—41no—
314Q8—81no—
315D4—41no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321D4—81no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4C5×#12011yescharacteristic
337C2×C4C5×#12111yescharacteristic
338C2×C4C5×#12111yescharacteristic
339C2×C4C5×#12311yescharacteristic
340C2×C4C5×#12311yescharacteristic
341C2×C4C5×#12411yescharacteristic
342C2×C4C2×C5×SD1611yescharacteristic
343C2×C4C5×#13511yescharacteristic
344C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
345C2×C4C5×#13711yescharacteristic
346C8—42no—
347C8—81no—
348C8—81no—
349C8—81no—
350C5#1052111yescharacteristic, direct product factor, Sylow
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C5×#39411yescharacteristic
357C22C5×#46511yescharacteristic
358C22C5×#46811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—42no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4C5×#45411yescharacteristic
368C4C5×#45511yescharacteristic
369C4C5×#46011yescharacteristic
370C4C5×#46111yescharacteristic
371C4C5×#46311yescharacteristic
372C4C5×#46411yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2C5×#204011yescharacteristic
377C2C5×#205011yescharacteristic
378C2C5×#205511yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1994C2semidirect
4. C5×#1831C2semidirect
5. C5×#1550C2semidirect
7. C5×#1292C2semidirect
29. #10521C5direct (N × H)
70. #1994C2×C5semidirect
72. #1831C2×C5semidirect
73. #1550C2×C5semidirect
75. #1292C2×C5semidirect
122. C42×C5SD16semidirect
297. C42C5×SD16semidirect
350. C5#10521direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32462
C5×#19942
C5×#19622
C5×#18312
C5×#15502
C5×#15472
C5×#12922
#105215