Finite Group Databasebeta

← C5×#7644 #11930364

Subgroups — C5×#7644 #11930364

Order 1280.

402 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2295C211yesmaximal, characteristic
2C5×#1839C211yesmaximal, characteristic
3C5×#1831C211yesmaximal, characteristic
4C5×#1272C212yesmaximal
5C5×#1271C212yesmaximal
6C2×C4×C5×Q8C411yescharacteristic
7C2×C5×C4⋊C8—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#7644C511yesmaximal, 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×C4⋊C8—42no—
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#1831C2×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—42no—
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—21no—
87C42×C5—21no—
88C42×C5—22no—
89C42×C5—41no—
90C42×C5—41no—
91C42×C5—41no—
92C42×C5—41no—
93C42×C5—42no—
94C42×C5SD1612yes—
95C42×C5Q1612yes—
96C2×C4×Q8C4×C511yescharacteristic
97C2×C4⋊C8—21no—
98#391C4×C511yescharacteristic
99#391C22×C511yescharacteristic
100#389C4×C511yescharacteristic
101#389C22×C511yescharacteristic
102#387—21no—
103#387—21no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4C4×C511yescharacteristic
106#376—21no—
107C43C22×C511yescharacteristic
108#336—21no—
109#336—21no—
110#336—21no—
111#336C22×C512yes—
112#336C22×C512yes—
113C23×C5C2×C22⋊C411yescharacteristic
114C5×Q8—42no—
115C5×Q8—42no—
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—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
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#10312yes—
145C2×C4×C5#10312yes—
146C2×C4×C5C2×M1611yescharacteristic
147C2×C4×C5C2×M1611yescharacteristic
148C2×C4×C5C2×SD1611yescharacteristic
149C2×C4×C5C2×Q1611yescharacteristic
150C2×C4×C5#13512yes—
151C5×C8—82no—
152C5×C8—82no—
153C22×Q8C2×C4×C511yescharacteristic
154C22×C8—22no—
155C22×C8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4C2×C4×C511yescharacteristic
162C2×C4⋊C4C2×C4×C511yescharacteristic
163C2×C4⋊C4C2×C4×C511yescharacteristic
164C2×C42—21no—
165C2×C42—21no—
166C2×C42C2×C4×C511yescharacteristic
167C2×C42C2×C4×C511yescharacteristic
168C2×C42C5×D411yescharacteristic
169C2×C42C5×D411yescharacteristic
170C2×C42C5×D411yescharacteristic
171C2×C42C5×D411yescharacteristic
172C2×C42C23×C511yescharacteristic
173C4⋊C8—42no—
174#95—21no—
175#95—21no—
176#95—21no—
177#95—21no—
178#95—21no—
179#95—21no—
180#95—21no—
181C22×C5#40711yescharacteristic
182C22×C5#41011yescharacteristic
183C22×C5#41311yescharacteristic
184C22×C5C2×#10311yescharacteristic
185C22×C5#41611yescharacteristic
186C22×C5#42111yescharacteristic
187C22×C5#42111yescharacteristic
188C4×C5—22no—
189C4×C5—21no—
190C4×C5—21no—
191C4×C5—22no—
192C4×C5—21no—
193C4×C5—21no—
194C4×C5—22no—
195C4×C5—42no—
196C4×C5—41no—
197C4×C5—42no—
198C4×C5—41no—
199C4×C5—81no—
200C4×C5—81no—
201C2×Q8—21no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8C5×M1612yes—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C5×C22⋊C411yescharacteristic
210C22×C4C5×C22⋊C411yescharacteristic
211C22×C4C5×C22⋊C411yescharacteristic
212C22×C4C5×C22⋊C411yescharacteristic
213C22×C4C22×C4×C511yescharacteristic
214C22×C4C2×C5×D411yescharacteristic
215C22×C4C2×C5×D411yescharacteristic
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C4⋊C4—24no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4C5×M1612yes—
229C42—24no—
230C42—21no—
231C42—21no—
232C42—22no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42—42no—
238C42C5×SD1612yes—
239C42C5×Q1612yes—
240C2×C5#146411yescharacteristic
241C2×C5#148711yescharacteristic
242C2×C5#148811yescharacteristic
243C2×C5#151811yescharacteristic
244C2×C5#152111yescharacteristic
245C2×C5#153511yescharacteristic
246C2×C5#154211yescharacteristic
247C23C2×C5×C22⋊C411yescharacteristic
248Q8—42no—
249Q8—42no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4C5×#10312yes—
279C2×C4C5×#10312yes—
280C2×C4C2×C5×M1611yescharacteristic
281C2×C4C2×C5×M1611yescharacteristic
282C2×C4C2×C5×SD1611yescharacteristic
283C2×C4C2×C5×Q1611yescharacteristic
284C2×C4C5×#13512yes—
285C8—82no—
286C8—82no—
287C5#764411yescharacteristic, direct product factor, Sylow
288C22C5×#40711yescharacteristic
289C22C5×#41011yescharacteristic
290C22C5×#41311yescharacteristic
291C22C2×C5×#10311yescharacteristic
292C22C5×#41611yescharacteristic
293C22C5×#42111yescharacteristic
294C22C5×#42111yescharacteristic
295C4—21no—
296C4—21no—
297C4—22no—
298C4—22no—
299C4—21no—
300C4—21no—
301C4—22no—
302C4—41no—
303C4—42no—
304C4—41no—
305C4—42no—
306C4—81no—
307C4—81no—
308C2C5×#146411yescharacteristic
309C2C5×#148711yescharacteristic
310C2C5×#148811yescharacteristic
311C2C5×#151811yescharacteristic
312C2C5×#152111yescharacteristic
313C2C5×#153511yescharacteristic
314C2C5×#154211yescharacteristic
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. #7644C5direct (N × H)
287. C5#7644direct (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×#18312
C5×#12722
C5×#12712
#76445