Finite Group Databasebeta

← C5×#7611 #11930331

Subgroups — C5×#7611 #11930331

Order 1280.

408 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2295C211yesmaximal, characteristic
2C5×#1839C211yesmaximal, characteristic
3C5×#1745C211yesmaximal, characteristic
4C5×#1272C212yesmaximal
5C5×#1271C212yesmaximal
6C2×C4×C5×Q8C411yescharacteristic
7C2×C5×#97—21no—
8C5×#391C411yescharacteristic
9C5×#391C2211yescharacteristic
10C5×#389C411yescharacteristic
11C5×#389C2211yescharacteristic
12C5×#387—21no—
13C5×#387—21no—
14C4×C5×C4⋊C4—21no—
15C4×C5×C4⋊C4C411yescharacteristic
16C5×#376—21no—
17C43×C5C2211yescharacteristic
18C5×#336—21no—
19C5×#336—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7611C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×C5×C8—22no—
26C22×C5×C8—22no—
27C4×C5×Q8—22no—
28C4×C5×Q8—22no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C42×C5—21no—
36C2×C42×C5—21no—
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5C2×C411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C2×C42×C5D411yescharacteristic
41C2×C42×C5D411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5C2311yescharacteristic
44C5×#97—24no—
45C5×#95—21no—
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52#2295C2×C511yescharacteristic
53#1839C2×C511yescharacteristic
54#1745C2×C511yescharacteristic
55#1272C2×C512yes—
56#1271C2×C512yes—
57C2×C5×Q8—21no—
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×Q8M1612yes—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C2×C5×C8—24no—
73C2×C5×C8—42no—
74C2×C5×C8—42no—
75C2×C5×C8—42no—
76C2×C5×C8—42no—
77C2×C5×C8—42no—
78C5×C4⋊C4—24no—
79C5×C4⋊C4—21no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—42no—
83C5×C4⋊C4—42no—
84C5×C4⋊C4M1612yes—
85C42×C5—24no—
86C42×C5—22no—
87C42×C5—21no—
88C42×C5—21no—
89C42×C5—22no—
90C42×C5—22no—
91C42×C5—41no—
92C42×C5—41no—
93C42×C5—41no—
94C42×C5—42no—
95C2×C4×Q8C4×C511yescharacteristic
96C2×#97—21no—
97#391C4×C511yescharacteristic
98#391C22×C511yescharacteristic
99#389C4×C511yescharacteristic
100#389C22×C511yescharacteristic
101#387—21no—
102#387—21no—
103C4×C4⋊C4—21no—
104C4×C4⋊C4C4×C511yescharacteristic
105#376—21no—
106C43C22×C511yescharacteristic
107#336—21no—
108#336—21no—
109#336—21no—
110#336C22×C512yes—
111#336C22×C512yes—
112C23×C5C2×C22⋊C411yescharacteristic
113C5×Q8—42no—
114C5×Q8—42no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5#10412yes—
145C2×C4×C5C2×M1611yescharacteristic
146C2×C4×C5C2×M1611yescharacteristic
147C2×C4×C5#13512yes—
148C2×C4×C5#13712yes—
149C5×C8—44no—
150C5×C8—82no—
151C22×Q8C2×C4×C511yescharacteristic
152C22×C8—22no—
153C22×C8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×C4×C511yescharacteristic
160C2×C4⋊C4C2×C4×C511yescharacteristic
161C2×C4⋊C4C2×C4×C511yescharacteristic
162C2×C42—21no—
163C2×C42—21no—
164C2×C42C2×C4×C511yescharacteristic
165C2×C42C2×C4×C511yescharacteristic
166C2×C42C5×D411yescharacteristic
167C2×C42C5×D411yescharacteristic
168C2×C42C5×D411yescharacteristic
169C2×C42C5×D411yescharacteristic
170C2×C42C23×C511yescharacteristic
171#97—24no—
172#95—21no—
173#95—21no—
174#95—21no—
175#95—21no—
176#95—21no—
177#95—21no—
178#95—21no—
179C22×C5#40711yescharacteristic
180C22×C5#41011yescharacteristic
181C22×C5#41311yescharacteristic
182C22×C5#41611yescharacteristic
183C22×C5#41911yescharacteristic
184C22×C5C2×#10411yescharacteristic
185C22×C5#42111yescharacteristic
186C4×C5—21no—
187C4×C5—21no—
188C4×C5—22no—
189C4×C5—22no—
190C4×C5—22no—
191C4×C5—41no—
192C4×C5—42no—
193C4×C5—41no—
194C4×C5—42no—
195C4×C5—41no—
196C4×C5—81no—
197C4×C5—81no—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C5×M1612yes—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C5×C22⋊C411yescharacteristic
207C22×C4C5×C22⋊C411yescharacteristic
208C22×C4C5×C22⋊C411yescharacteristic
209C22×C4C5×C22⋊C411yescharacteristic
210C22×C4C22×C4×C511yescharacteristic
211C22×C4C2×C5×D411yescharacteristic
212C22×C4C2×C5×D411yescharacteristic
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—42no—
219C4⋊C4—24no—
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4C5×M1612yes—
226C42—24no—
227C42—21no—
228C42—21no—
229C42—22no—
230C42—22no—
231C42—22no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—42no—
236C2×C5#146411yescharacteristic
237C2×C5#148811yescharacteristic
238C2×C5#149111yescharacteristic
239C2×C5#150011yescharacteristic
240C2×C5#151511yescharacteristic
241C2×C5#152911yescharacteristic
242C2×C5#155411yescharacteristic
243C23C2×C5×C22⋊C411yescharacteristic
244Q8—42no—
245Q8—42no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4C5×#10412yes—
276C2×C4C2×C5×M1611yescharacteristic
277C2×C4C2×C5×M1611yescharacteristic
278C2×C4C5×#13512yes—
279C2×C4C5×#13712yes—
280C8—44no—
281C8—82no—
282C5#761111yescharacteristic, direct product factor, Sylow
283C22C5×#40711yescharacteristic
284C22C5×#41011yescharacteristic
285C22C5×#41311yescharacteristic
286C22C5×#41611yescharacteristic
287C22C5×#41911yescharacteristic
288C22C2×C5×#10411yescharacteristic
289C22C5×#42111yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—21no—
294C4—22no—
295C4—41no—
296C4—41no—
297C4—42no—
298C4—41no—
299C4—42no—
300C4—81no—
301C4—81no—
302C2C5×#146411yescharacteristic
303C2C5×#148811yescharacteristic
304C2C5×#149111yescharacteristic
305C2C5×#150011yescharacteristic
306C2C5×#151511yescharacteristic
307C2C5×#152911yescharacteristic
308C2C5×#155411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C43×C5 ◁ G

Complements

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

NH ≅ G/Ntype
23. #7611C5direct (N × H)
282. C5#7611direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#22952
C5×#18392
C5×#17452
C5×#12722
C5×#12712
#76115