Finite Group Databasebeta

← C5×#10504 #11933224

Subgroups — C5×#10504 #11933224

Order 1280.

470 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×#3208C211yesmaximal, characteristic
2C5×#1986C211yesmaximal, characteristic, complemented
3C5×#1982C211yesmaximal, characteristic
4C5×#1965C211yesmaximal, characteristic
5C5×#1565C211yesmaximal, characteristic, complemented
6C5×#1550C211yesmaximal, characteristic, complemented
7C5×#1303C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C5×#127C2211yescharacteristic
10C5×#492—21no—
11C5×#486—21no—
12C5×#460—21no—
13C5×#460—21no—
14C5×#450—22no—
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×#102—22no—
19C2×C5×#100—21no—
20C2×C5×#100—21no—
21C4×C5×M16C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C5×#339—21no—
24C5×#339—21no—
25C5×#335—21no—
26C5×#334—21no—
27C5×#333—21no—
28C5×#332—21no—
29#10504C511yesmaximal, characteristic, direct product factor, Sylow
30C22×C5×D4—21no—
31C22×C5×D4—21no—
32C22×C5×D4D412yes—
33C2×C5×SD16—22no—
34C2×C5×SD16—22no—
35C2×C5×M16—21no—
36C2×C5×M16D411yescharacteristic
37C2×C5×M16D411yescharacteristic
38C22×C5×C8—21no—
39C5×C4⋊Q8D411yescharacteristic
40C5×C4⋊Q8D411yescharacteristic
41C5×#127—21no—
42C5×#127—21no—
43C5×#127—21no—
44C5×#127—21no—
45C5×#125—21no—
46C5×C22⋊Q8—21no—
47C5×C22⋊Q8—21no—
48C4×C5×Q8—21no—
49C4×C5×Q8—21no—
50C5×#117—21no—
51C2×C5×C4⋊C4—21no—
52C2×C42×C5—21no—
53C2×C42×C5C2311yescharacteristic
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8D411yescharacteristic
59C5×C4⋊C8D411yescharacteristic
60C5×#102—22no—
61C5×#102—22no—
62C5×#102—44no—
63C5×#100—42no—
64C5×#100—42no—
65C5×C22⋊C8—21no—
66C5×#97—21no—
67C4×C5×C8—21no—
68C4×C5×C8—21no—
69C5×#95—21no—
70#3208C2×C511yescharacteristic
71#1986C2×C511yescharacteristic, complemented
72#1982C2×C511yescharacteristic
73#1965C2×C511yescharacteristic
74#1565C2×C511yescharacteristic, complemented
75#1550C2×C511yescharacteristic, complemented
76#1303C2×C511yescharacteristic, complemented
77C24×C5—22no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×D4—22no—
81C2×C5×D4—22no—
82C2×C5×D4—42no—
83C2×C5×D4—42no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—41no—
87C2×C5×D4—41no—
88C2×C5×D4—41no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—82no—
93C22×C4×C5—41no—
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5#4111yescharacteristic
97C5×SD16—82no—
98C5×SD16—82no—
99C5×M16—21no—
100C5×M16—21no—
101C5×M16—21no—
102C5×M16—41no—
103C5×M16—41no—
104C5×M16SD1612yescomplemented
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8—21no—
108C2×C5×C8—21no—
109C2×C5×C8—42no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C22⋊C4—41no—
121C42×C5—41no—
122C42×C5—41no—
123C42×C5—41no—
124C42×C5C2×D411yescharacteristic
125C42×C5C2×D411yescharacteristic
126C42×C5#4111yescharacteristic
127C42×C5#4111yescharacteristic
128#533C22×C511yescharacteristic
129C2×#127C22×C511yescharacteristic
130#492—21no—
131#486—21no—
132#460—21no—
133#460—21no—
134#450—22no—
135#431C22×C511yescharacteristic
136#423C22×C511yescharacteristic
137C2×C4⋊C8C22×C511yescharacteristic
138C2×#102—22no—
139C2×#100—21no—
140C2×#100—21no—
141C4×M16C22×C511yescharacteristic
142C4×C4⋊C4C22×C511yescharacteristic
143#339—21no—
144#339—21no—
145#335—21no—
146#334—21no—
147#333—21no—
148#332—21no—
149C23×C5—42no—
150C23×C5—42no—
151C23×C5—42no—
152C23×C5—82no—
153C23×C5—82no—
154C23×C5#12111yescharacteristic
155C5×Q8—41no—
156C5×Q8—41no—
157C5×Q8—81no—
158C5×D4—44no—
159C5×D4—42no—
160C5×D4—42no—
161C5×D4—82no—
162C5×D4—82no—
163C5×D4—81no—
164C5×D4—81no—
165C5×D4—81no—
166C5×D4—81no—
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#12011yescharacteristic
176C2×C4×C5#12111yescharacteristic
177C2×C4×C5#12111yescharacteristic
178C2×C4×C5#12311yescharacteristic
179C2×C4×C5#12311yescharacteristic
180C2×C4×C5#12411yescharacteristic
181C2×C4×C5C2×SD1611yescharacteristic
182C2×C4×C5#13511yescharacteristic
183C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C5#13711yescharacteristic
185C5×C8—22no—
186C5×C8—41no—
187C5×C8—41no—
188C5×C8—41no—
189C5×C8—81no—
190C5×C8—81no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4C5×D412yes—
194C2×SD16—22no—
195C2×SD16—22no—
196C2×M16—21no—
197C2×M16C5×D411yescharacteristic
198C2×M16C5×D411yescharacteristic
199C22×C8—21no—
200C4⋊Q8C5×D411yescharacteristic
201C4⋊Q8C5×D411yescharacteristic
202#127—21no—
203#127—21no—
204#127—21no—
205#127—21no—
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C42—21no—
214C2×C42C23×C511yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8C5×D411yescharacteristic
220C4⋊C8C5×D411yescharacteristic
221#102—22no—
222#102—22no—
223#102—44no—
224#100—42no—
225#100—42no—
226C22⋊C8—21no—
227#97—21no—
228C4×C8—21no—
229C4×C8—21no—
230#95—21no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—82no—
234C22×C5—82no—
235C22×C5—82no—
236C22×C5—162no—
237C22×C5—162no—
238C22×C5#39411yescharacteristic
239C22×C5#46111yescharacteristic
240C22×C5#46311yescharacteristic
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—21no—
244C4×C5—82no—
245C4×C5—81no—
246C4×C5—81no—
247C4×C5#45311yescharacteristic
248C4×C5#45511yescharacteristic
249C4×C5#46011yescharacteristic
250C4×C5#46411yescharacteristic
251C4×C5#46511yescharacteristic
252C4×C5#46811yescharacteristic
253C24—22no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—82no—
269C22×C4—41no—
270C22×C4C2×C5×D411yescharacteristic
271C22×C4C2×C5×D411yescharacteristic
272C22×C4C5×#4111yescharacteristic
273SD16—82no—
274SD16—82no—
275M16—21no—
276M16—21no—
277M16—21no—
278M16—41no—
279M16—41no—
280M16C5×SD1612yescomplemented
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—42no—
286C2×C8—41no—
287C2×C8—41no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C22⋊C4—41no—
297C42—41no—
298C42—41no—
299C42—41no—
300C42C2×C5×D411yescharacteristic
301C42C2×C5×D411yescharacteristic
302C42C5×#4111yescharacteristic
303C42C5×#4111yescharacteristic
304C2×C5—21no—
305C2×C5—21no—
306C2×C5—162no—
307C2×C5#203711yescharacteristic
308C2×C5#204811yescharacteristic
309C2×C5#205511yescharacteristic
310C23—42no—
311C23—42no—
312C23—42no—
313C23—82no—
314C23—82no—
315C23C5×#12111yescharacteristic
316Q8—41no—
317Q8—41no—
318Q8—81no—
319D4—44no—
320D4—42no—
321D4—42no—
322D4—82no—
323D4—82no—
324D4—81no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
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—22no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—81no—
351C8—81no—
352C5#1050411yescharacteristic, direct product factor, Sylow
353C22—21no—
354C22—21no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—162no—
359C22—162no—
360C22C5×#39411yescharacteristic
361C22C5×#46111yescharacteristic
362C22C5×#46311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4C5×#45311yescharacteristic
370C4C5×#45511yescharacteristic
371C4C5×#46011yescharacteristic
372C4C5×#46411yescharacteristic
373C4C5×#46511yescharacteristic
374C4C5×#46811yescharacteristic
375C2—21no—
376C2—21no—
377C2—162no—
378C2C5×#203711yescharacteristic
379C2C5×#204811yescharacteristic
380C2C5×#205511yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#127C22
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×#1986C2semidirect
5. C5×#1565C2semidirect
6. C5×#1550C2semidirect
7. C5×#1303C2semidirect
29. #10504C5direct (N × H)
71. #1986C2×C5semidirect
74. #1565C2×C5semidirect
75. #1550C2×C5semidirect
76. #1303C2×C5semidirect
104. C5×M16SD16semidirect
280. M16C5×SD16semidirect
352. C5#10504direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32082
C5×#19862
C5×#19822
C5×#19652
C5×#15652
C5×#15502
C5×#13032
#105045