Finite Group Databasebeta

← C5×#10520 #11933240

Subgroups — C5×#10520 #11933240

Order 1280.

440 conjugacy classes of subgroups.

The subgroup lattice has 382 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×#1842C211yesmaximal, 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⋊C8—22no—
18C2×C5×C4⋊C8C2211yescharacteristic
19C2×C5×C4⋊C8C2211yescharacteristic
20C2×C5×#104—21no—
21C2×C5×#104—21no—
22C43×C5C2211yescharacteristic
23C5×#339—21no—
24C5×#339—21no—
25C5×#333—21no—
26C5×#332—21no—
27C5×#332—21no—
28C5×#331—21no—
29#10520C511yesmaximal, 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×C4⋊C8—44no—
66C5×#104—42no—
67C5×#104—42no—
68C5×#103—22no—
69C5×#102—22no—
70#3246C2×C511yescharacteristic
71#1994C2×C511yescharacteristic, complemented
72#1962C2×C511yescharacteristic
73#1842C2×C511yescharacteristic, complemented
74#1550C2×C511yescharacteristic, complemented
75#1547C2×C511yescharacteristic
76#1292C2×C511yescharacteristic, complemented
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C5×#41—41no—
81C2×C5×Q8—21no—
82C2×C5×Q8—21no—
83C2×C5×Q8—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—41no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—41no—
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5#4111yescharacteristic
94C5×SD16—82no—
95C5×M16—41no—
96C5×M16—41no—
97C5×M16—41no—
98C5×M16—41no—
99C2×C5×C8—22no—
100C2×C5×C8—42no—
101C2×C5×C8—42no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
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×C22⋊C4—41no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—41no—
116C42×C5—22no—
117C42×C5—22no—
118C42×C5—21no—
119C42×C5—21no—
120C42×C5—21no—
121C42×C5—42no—
122C42×C5—41no—
123C42×C5SD1612yescomplemented
124C42×C5C2×D411yescharacteristic
125C42×C5C2×D411yescharacteristic
126C42×C5#4111yescharacteristic
127C42×C5#4111yescharacteristic
128#533C22×C511yescharacteristic
129#532C22×C511yescharacteristic
130#476—21no—
131#475—21no—
132#465—22no—
133#461—21no—
134#460—21no—
135#423C22×C511yescharacteristic
136#423C22×C511yescharacteristic
137C2×C4⋊C8—22no—
138C2×C4⋊C8C22×C511yescharacteristic
139C2×C4⋊C8C22×C511yescharacteristic
140C2×#104—21no—
141C2×#104—21no—
142C43C22×C511yescharacteristic
143#339—21no—
144#339—21no—
145#333—21no—
146#332—21no—
147#332—21no—
148#331—21no—
149C23×C5—41no—
150C23×C5#12111yescharacteristic
151C5×Q8—41no—
152C5×Q8—41no—
153C5×Q8—41no—
154C5×Q8—41no—
155C5×Q8—81no—
156C5×D4—41no—
157C5×D4—41no—
158C5×D4—41no—
159C5×D4—41no—
160C5×D4—81no—
161C5×D4—81no—
162C5×D4—81no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—22no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—81no—
176C2×C4×C5—81no—
177C2×C4×C5#12011yescharacteristic
178C2×C4×C5#12111yescharacteristic
179C2×C4×C5#12111yescharacteristic
180C2×C4×C5#12311yescharacteristic
181C2×C4×C5#12311yescharacteristic
182C2×C4×C5#12411yescharacteristic
183C2×C4×C5C2×SD1611yescharacteristic
184C2×C4×C5#13511yescharacteristic
185C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C5#13711yescharacteristic
187C5×C8—42no—
188C5×C8—81no—
189C5×C8—81no—
190C5×C8—81no—
191C2×#41—21no—
192C2×SD16—22no—
193C2×M16—21no—
194C2×M16—21no—
195C22×C8—21no—
196C22×C8C5×D412yes—
197C4⋊Q8C5×D411yescharacteristic
198C4⋊Q8C5×D411yescharacteristic
199C4⋊Q8C5×D411yescharacteristic
200#127C5×D411yescharacteristic
201#125—21no—
202#124—21no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205#121—21no—
206#121—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×D4—21no—
210C4×D4—21no—
211#117—21no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42C5×D411yescharacteristic
215C2×C42C5×D411yescharacteristic
216C2×C42C23×C511yescharacteristic
217#106—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—44no—
227#104—42no—
228#104—42no—
229#103—22no—
230#102—22no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—81no—
234C22×C5—81no—
235C22×C5—81no—
236C22×C5#39411yescharacteristic
237C22×C5#46511yescharacteristic
238C22×C5#46811yescharacteristic
239C4×C5—24no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—42no—
244C4×C5—81no—
245C4×C5—81no—
246C4×C5—81no—
247C4×C5#45311yescharacteristic
248C4×C5#45611yescharacteristic
249C4×C5#46011yescharacteristic
250C4×C5#46111yescharacteristic
251C4×C5#46311yescharacteristic
252C4×C5#46411yescharacteristic
253#41—41no—
254#41—41no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4C2×C5×D411yescharacteristic
268C22×C4C2×C5×D411yescharacteristic
269C22×C4C5×#4111yescharacteristic
270SD16—82no—
271M16—41no—
272M16—41no—
273M16—41no—
274M16—41no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—22no—
293C42—22no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—42no—
298C42—41no—
299C42C5×SD1612yescomplemented
300C42C2×C5×D411yescharacteristic
301C42C2×C5×D411yescharacteristic
302C42C5×#4111yescharacteristic
303C42C5×#4111yescharacteristic
304C2×C5—21no—
305C2×C5—21no—
306C2×C5—161no—
307C2×C5#203911yescharacteristic
308C2×C5#205011yescharacteristic
309C2×C5#205511yescharacteristic
310C23—41no—
311C23C5×#12111yescharacteristic
312Q8—41no—
313Q8—41no—
314Q8—41no—
315Q8—41no—
316Q8—81no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4C5×#12011yescharacteristic
339C2×C4C5×#12111yescharacteristic
340C2×C4C5×#12111yescharacteristic
341C2×C4C5×#12311yescharacteristic
342C2×C4C5×#12311yescharacteristic
343C2×C4C5×#12411yescharacteristic
344C2×C4C2×C5×SD1611yescharacteristic
345C2×C4C5×#13511yescharacteristic
346C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
347C2×C4C5×#13711yescharacteristic
348C8—42no—
349C8—81no—
350C8—81no—
351C8—81no—
352C5#1052011yescharacteristic, direct product factor, Sylow
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22C5×#39411yescharacteristic
359C22C5×#46511yescharacteristic
360C22C5×#46811yescharacteristic
361C4—24no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4C5×#45311yescharacteristic
370C4C5×#45611yescharacteristic
371C4C5×#46011yescharacteristic
372C4C5×#46111yescharacteristic
373C4C5×#46311yescharacteristic
374C4C5×#46411yescharacteristic
375C2—21no—
376C2—21no—
377C2—161no—
378C2C5×#203911yescharacteristic
379C2C5×#205011yescharacteristic
380C2C5×#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×#1842C2semidirect
5. C5×#1550C2semidirect
7. C5×#1292C2semidirect
29. #10520C5direct (N × H)
71. #1994C2×C5semidirect
73. #1842C2×C5semidirect
74. #1550C2×C5semidirect
76. #1292C2×C5semidirect
123. C42×C5SD16semidirect
299. C42C5×SD16semidirect
352. C5#10520direct (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×#18422
C5×#15502
C5×#15472
C5×#12922
#105205