Finite Group Databasebeta

← C5×#2758 #10616353

Subgroups — C5×#2758 #10616353

Order 640.

352 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×#400C211yesmaximal, characteristic
2C5×#400C211yesmaximal, characteristic
3C5×#400C211yesmaximal, characteristic
4C5×#400C211yesmaximal, characteristic
5C5×#400C211yesmaximal, characteristic
6C5×#395C211yesmaximal, characteristic
7C5×#391C211yesmaximal, characteristic
8C5×#391C211yesmaximal, characteristic
9C5×#389C211yesmaximal, characteristic
10C5×#387C211yesmaximal, characteristic
11C5×#387C211yesmaximal, characteristic
12C5×#387C211yesmaximal, characteristic
13C5×#387C211yesmaximal, characteristic
14C5×#383C211yesmaximal, characteristic
15C5×#383C211yesmaximal, characteristic
16C22×C5×Q8C2211yescharacteristic
17C2×C5×C4⋊C4C2211yescharacteristic
18C2×C5×C4⋊C4C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic
20C2×C5×C4⋊C4C2211yescharacteristic
21C2×C5×C4⋊C4C2211yescharacteristic
22C2×C5×C4⋊C4C2211yescharacteristic
23C2×C5×C4⋊C4C2211yescharacteristic
24C2×C5×C4⋊C4C2211yescharacteristic
25C2×C5×C4⋊C4C2211yescharacteristic
26C2×C42×C5C2211yescharacteristic
27C2×C42×C5C2211yescharacteristic
28C2×C42×C5C2211yescharacteristic
29C5×#95C2211yescharacteristic
30C5×#95C2211yescharacteristic
31C5×#95C2211yescharacteristic
32C5×#95C2211yescharacteristic
33C5×#95C2211yescharacteristic
34C5×#95C2211yescharacteristic
35C5×#95C2211yescharacteristic
36C5×#95C2211yescharacteristic
37C5×#95C2211yescharacteristic
38C5×#95C2211yescharacteristic
39C5×#95C2211yescharacteristic
40C5×#95C2211yescharacteristic
41C5×#95C2211yescharacteristic
42C5×#95C2211yescharacteristic
43C5×#95C2211yescharacteristic
44C5×#95C2211yescharacteristic
45C5×#95C2211yescharacteristic
46C5×#95C2211yescharacteristic
47C5×#95C2211yescharacteristic
48C5×#95C2211yescharacteristic
49C5×#95C2211yescharacteristic
50C5×#95C2211yescharacteristic
51#2758C511yesmaximal, characteristic, direct product factor, Sylow
52C2×C5×Q8—22no—
53C2×C5×Q8—22no—
54C2×C5×Q8—41no—
55C22×C4×C5C2311yescharacteristic
56C22×C4×C5C2311yescharacteristic
57C22×C4×C5C2311yescharacteristic
58C22×C4×C5C2311yescharacteristic
59C22×C4×C5C2311yescharacteristic
60C22×C4×C5C2311yescharacteristic
61C22×C4×C5C2311yescharacteristic
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C22×C4×C5C2311yescharacteristic
68C22×C4×C5C2311yescharacteristic
69C22×C4×C5C2311yescharacteristic
70C5×C4⋊C4—22no—
71C5×C4⋊C4—22no—
72C5×C4⋊C4—22no—
73C5×C4⋊C4—22no—
74C5×C4⋊C4—22no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C42×C5—22no—
80C42×C5—22no—
81C42×C5—41no—
82#400C2×C511yescharacteristic
83#400C2×C511yescharacteristic
84#400C2×C511yescharacteristic
85#400C2×C511yescharacteristic
86#400C2×C511yescharacteristic
87#395C2×C511yescharacteristic
88#391C2×C511yescharacteristic
89#391C2×C511yescharacteristic
90#389C2×C511yescharacteristic
91#387C2×C511yescharacteristic
92#387C2×C511yescharacteristic
93#387C2×C511yescharacteristic
94#387C2×C511yescharacteristic
95#383C2×C511yescharacteristic
96#383C2×C511yescharacteristic
97C23×C5C2411yescharacteristic
98C5×Q8—44no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
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—21no—
125C2×C4×C5—21no—
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—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5#4112yes—
142C2×C4×C5#4112yes—
143C2×C4×C5#4112yes—
144C22×Q8C22×C511yescharacteristic
145C2×C4⋊C4C22×C511yescharacteristic
146C2×C4⋊C4C22×C511yescharacteristic
147C2×C4⋊C4C22×C511yescharacteristic
148C2×C4⋊C4C22×C511yescharacteristic
149C2×C4⋊C4C22×C511yescharacteristic
150C2×C4⋊C4C22×C511yescharacteristic
151C2×C4⋊C4C22×C511yescharacteristic
152C2×C4⋊C4C22×C511yescharacteristic
153C2×C4⋊C4C22×C511yescharacteristic
154C2×C42C22×C511yescharacteristic
155C2×C42C22×C511yescharacteristic
156C2×C42C22×C511yescharacteristic
157#95C22×C511yescharacteristic
158#95C22×C511yescharacteristic
159#95C22×C511yescharacteristic
160#95C22×C511yescharacteristic
161#95C22×C511yescharacteristic
162#95C22×C511yescharacteristic
163#95C22×C511yescharacteristic
164#95C22×C511yescharacteristic
165#95C22×C511yescharacteristic
166#95C22×C511yescharacteristic
167#95C22×C511yescharacteristic
168#95C22×C511yescharacteristic
169#95C22×C511yescharacteristic
170#95C22×C511yescharacteristic
171#95C22×C511yescharacteristic
172#95C22×C511yescharacteristic
173#95C22×C511yescharacteristic
174#95C22×C511yescharacteristic
175#95C22×C511yescharacteristic
176#95C22×C511yescharacteristic
177#95C22×C511yescharacteristic
178#95C22×C511yescharacteristic
179C22×C5C2×#4111yescharacteristic
180C22×C5C2×#4111yescharacteristic
181C22×C5C2×#4111yescharacteristic
182C22×C5H(5,𝔽2)11yescharacteristic
183C22×C52−1+411yescharacteristic
184C22×C52−1+411yescharacteristic
185C22×C52−1+411yescharacteristic
186C4×C5—22no—
187C4×C5—22no—
188C4×C5—22no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5—41no—
194C4×C5—41no—
195C4×C5—41no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C5—41no—
199C4×C5—41no—
200C4×C5—41no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—41no—
204C22×C4C23×C511yescharacteristic
205C22×C4C23×C511yescharacteristic
206C22×C4C23×C511yescharacteristic
207C22×C4C23×C511yescharacteristic
208C22×C4C23×C511yescharacteristic
209C22×C4C23×C511yescharacteristic
210C22×C4C23×C511yescharacteristic
211C22×C4C23×C511yescharacteristic
212C22×C4C23×C511yescharacteristic
213C22×C4C23×C511yescharacteristic
214C22×C4C23×C511yescharacteristic
215C22×C4C23×C511yescharacteristic
216C22×C4C23×C511yescharacteristic
217C22×C4C23×C511yescharacteristic
218C22×C4C23×C511yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C42—22no—
229C42—22no—
230C42—41no—
231C2×C5#54111yescharacteristic
232C2×C5#54111yescharacteristic
233C2×C5#54211yescharacteristic
234C2×C5#55111yescharacteristic
235C2×C5#55211yescharacteristic
236C2×C5#55611yescharacteristic
237C2×C5#56311yescharacteristic
238C23C24×C511yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
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—21no—
256C2×C4—21no—
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—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4C5×#4112yes—
283C2×C4C5×#4112yes—
284C2×C4C5×#4112yes—
285C5#275811yescharacteristic, direct product factor, Sylow
286C22C2×C5×#4111yescharacteristic
287C22C2×C5×#4111yescharacteristic
288C22C2×C5×#4111yescharacteristic
289C22C5×H(5,𝔽2)11yescharacteristic
290C22C5×2−1+411yescharacteristic
291C22C5×2−1+411yescharacteristic
292C22C5×2−1+411yescharacteristic
293C4—22no—
294C4—22no—
295C4—22no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C2C5×#54111yescharacteristic
309C2C5×#54111yescharacteristic
310C2C5×#54211yescharacteristic
311C2C5×#55111yescharacteristic
312C2C5×#55211yescharacteristic
313C2C5×#55611yescharacteristic
314C2C5×#56311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C5C24
commutator, Frattini, cosocleC23C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

Complements

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

NH ≅ G/Ntype
51. #2758C5direct (N × H)
285. C5#2758direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#4002
C5×#3952
C5×#3912
C5×#3892
C5×#3872
C5×#3832
#27585