Finite Group Databasebeta

← C5×#7824 #11930544

Subgroups — C5×#7824 #11930544

Order 1280.

418 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2724C211yesmaximal, characteristic
2C5×#2100C212yesmaximal, complemented
3C5×#2094C211yesmaximal, characteristic
4C5×#1271C212yesmaximal, complemented
5C5×#1270C211yesmaximal, characteristic
6C2×C5×#123—21no—
7C2×C5×#106—21no—
8C2×C5×#102—21no—
9C5×#398—21no—
10C5×#397—22no—
11C5×#390C2211yescharacteristic
12C5×#389C2212yes—
13C5×#385—22no—
14C5×#384C2211yescharacteristic
15C5×#340—22no—
16C5×#340—22no—
17C5×#336C2211yescharacteristic
18C5×#336C2212yes—
19#7824C511yesmaximal, characteristic, direct product factor, Sylow
20C22×C5×D4D411yescharacteristic
21C23×C4×C5—21no—
22C22×C5×C8—21no—
23C22×C5×C8—22no—
24C5×#123—42no—
25C5×#123—42no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4D412yes—
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4—22no—
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—22no—
36C2×C42×C5C2311yescharacteristic
37C5×#106—42no—
38C5×#102—42no—
39C5×#95—22no—
40C5×#95—21no—
41C5×#95—22no—
42#2724C2×C511yescharacteristic
43#2100C2×C512yescomplemented
44#2094C2×C511yescharacteristic
45#1271C2×C512yescomplemented
46#1270C2×C511yescharacteristic
47C24×C5—21no—
48C2×C5×D4—21no—
49C2×C5×D4—41no—
50C2×C5×D4—41no—
51C2×C5×D4SD1612yes—
52C22×C4×C5—22no—
53C22×C4×C5—21no—
54C22×C4×C5—22no—
55C22×C4×C5—42no—
56C22×C4×C5—41no—
57C22×C4×C5—81no—
58C22×C4×C5—81no—
59C22×C4×C5C2×D411yescharacteristic
60C22×C4×C5C2×D412yes—
61C2×C5×C8—22no—
62C2×C5×C8—41no—
63C2×C5×C8—41no—
64C2×C5×C8—42no—
65C2×C5×C8—42no—
66C2×C5×C8—42no—
67C5×C4⋊C4—22no—
68C5×C4⋊C4—22no—
69C5×C4⋊C4—42no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—44no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—81no—
77C5×C22⋊C4—42no—
78C5×C22⋊C4—44no—
79C5×C22⋊C4—42no—
80C5×C22⋊C4—42no—
81C42×C5—41no—
82C2×#123—21no—
83C2×#106—21no—
84C2×#102—21no—
85#398—21no—
86#397—22no—
87#390C22×C511yescharacteristic
88#389C22×C512yes—
89#385—22no—
90#384C22×C511yescharacteristic
91#340—22no—
92#340—22no—
93#336C22×C511yescharacteristic
94#336C22×C512yes—
95C23×C5—22no—
96C23×C5—42no—
97C23×C5—41no—
98C23×C5—42no—
99C23×C5—41no—
100C23×C5#12011yescharacteristic
101C5×D4—42no—
102C5×D4—81no—
103C2×C4×C5—21no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—21no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—42no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—84no—
116C2×C4×C5—81no—
117C2×C4×C5—82no—
118C2×C4×C5C2×SD1611yescharacteristic
119C2×C4×C5#13512yes—
120C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C5#13712yes—
122C5×C8—42no—
123C5×C8—82no—
124C22×D4C5×D411yescharacteristic
125C23×C4—21no—
126C22×C8—21no—
127C22×C8—22no—
128#123—42no—
129#123—42no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4C5×D412yes—
135C2×C4⋊C4C5×D412yes—
136C2×C4⋊C4C5×D411yescharacteristic
137C2×C22⋊C4—22no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—22no—
140C2×C42C23×C511yescharacteristic
141#106—42no—
142#102—42no—
143#95—22no—
144#95—21no—
145#95—22no—
146C22×C5—42no—
147C22×C5—44no—
148C22×C5—82no—
149C22×C5—81no—
150C22×C5—81no—
151C22×C5#45011yescharacteristic
152C22×C5#45212yes—
153C22×C5#45311yescharacteristic
154C22×C5#45412yes—
155C22×C5#45811yescharacteristic
156C4×C5—21no—
157C4×C5—21no—
158C4×C5—22no—
159C4×C5—22no—
160C4×C5—82no—
161C4×C5—81no—
162C4×C5—82no—
163C4×C5—161no—
164C24—21no—
165C2×D4—21no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4C5×SD1612yes—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—41no—
174C22×C4—81no—
175C22×C4—81no—
176C22×C4C2×C5×D411yescharacteristic
177C22×C4C2×C5×D412yes—
178C2×C8—22no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—44no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C22⋊C4—42no—
195C22⋊C4—44no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C42—41no—
199C2×C5—82no—
200C2×C5#161311yescharacteristic
201C2×C5#161512yes—
202C2×C5#163011yescharacteristic
203C2×C5#163512yes—
204C2×C5#165711yescharacteristic
205C23—22no—
206C23—42no—
207C23—41no—
208C23—42no—
209C23—41no—
210C23C5×#12011yescharacteristic
211D4—42no—
212D4—81no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—84no—
226C2×C4—81no—
227C2×C4—82no—
228C2×C4C2×C5×SD1611yescharacteristic
229C2×C4C5×#13512yes—
230C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
231C2×C4C5×#13712yes—
232C8—42no—
233C8—82no—
234C5#782411yescharacteristic, direct product factor, Sylow
235C22—42no—
236C22—44no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22C5×#45011yescharacteristic
241C22C5×#45212yes—
242C22C5×#45311yescharacteristic
243C22C5×#45412yes—
244C22C5×#45811yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4—161no—
253C2—82no—
254C2C5×#161311yescharacteristic
255C2C5×#161512yes—
256C2C5×#163011yescharacteristic
257C2C5×#163512yes—
258C2C5×#165711yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2100C2semidirect
4. C5×#1271C2semidirect
19. #7824C5direct (N × H)
43. #2100C2×C5semidirect
45. #1271C2×C5semidirect
234. C5#7824direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#27242
C5×#21002
C5×#20942
C5×#12712
C5×#12702
#78245