Finite Group Databasebeta

← C5×#8735 #11931455

Subgroups — C5×#8735 #11931455

Order 1280.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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×#2274C211yesmaximal, characteristic
2C2×C5×#324C212yesmaximal
3C5×#1282C214yesmaximal
4C2×C5×#117C411yescharacteristic
5C2×C5×#117C411yescharacteristic
6C22×C5×C4⋊C4C2211yescharacteristic
7C2×C5×C22⋊C8C2214yes—
8C4×C5×C4⋊C4—22no—
9C4×C5×C4⋊C4—22no—
10C4×C5×C22⋊C4C412yes—
11C4×C5×C22⋊C4C2212yes—
12C5×#324—22no—
13C5×#324—22no—
14#8735C511yesmaximal, characteristic, direct product factor, Sylow
15C23×C4×C5C2×C411yescharacteristic
16C23×C4×C5C2×C411yescharacteristic
17C23×C4×C5C2311yescharacteristic
18C22×C5×C8—24no—
19C5×#117—22no—
20C5×#117—24no—
21C5×#117C814yescomplemented
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4—24no—
25C2×C5×C4⋊C4D412yes—
26C2×C5×C4⋊C4D412yes—
27C2×C5×C22⋊C4C2×C412yes—
28C2×C5×C22⋊C4C2×C412yes—
29C2×C42×C5—21no—
30C2×C42×C5—21no—
31C2×C42×C5—22no—
32C2×C42×C5—22no—
33C5×C22⋊C8—24no—
34C5×C22⋊C8—24no—
35C5×#95—22no—
36C5×#95—22no—
37#2274C2×C511yescharacteristic
38C2×#324C2×C512yes—
39#1282C2×C514yes—
40C24×C5C22×C411yescharacteristic
41C22×C4×C5—22no—
42C22×C4×C5—22no—
43C22×C4×C5—22no—
44C22×C4×C5—22no—
45C22×C4×C5—22no—
46C22×C4×C5—81no—
47C22×C4×C5—81no—
48C22×C4×C5C22⋊C411yescharacteristic
49C22×C4×C5C22⋊C411yescharacteristic
50C22×C4×C5C22⋊C412yes—
51C22×C4×C5C2×C812yes—
52C22×C4×C5M1612yes—
53C22×C4×C5C2×D412yes—
54C22×C4×C5#4114yes—
55C2×C5×C8—44no—
56C2×C5×C8—84no—
57C5×C4⋊C4—24no—
58C5×C4⋊C4—24no—
59C5×C4⋊C4—24no—
60C5×C4⋊C4—24no—
61C5×C22⋊C4—22no—
62C5×C22⋊C4—22no—
63C5×C22⋊C4C2×C814yes—
64C5×C22⋊C4M1614yes—
65C42×C5—24no—
66C42×C5—24no—
67C42×C5—82no—
68C42×C5—82no—
69C2×#117C4×C511yescharacteristic
70C2×#117C4×C511yescharacteristic
71C22×C4⋊C4C22×C511yescharacteristic
72C2×C22⋊C8C22×C514yes—
73C4×C4⋊C4—22no—
74C4×C4⋊C4—22no—
75C4×C22⋊C4C4×C512yes—
76C4×C22⋊C4C22×C512yes—
77#324—22no—
78#324—22no—
79C23×C5—41no—
80C23×C5—41no—
81C23×C5C2×C22⋊C411yescharacteristic
82C23×C5#11712yes—
83C23×C5C22×C811yescharacteristic
84C23×C5C2×M1611yescharacteristic
85C23×C5C2×M1612yes—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—24no—
91C2×C4×C5—24no—
92C2×C4×C5—22no—
93C2×C4×C5—24no—
94C2×C4×C5—24no—
95C2×C4×C5—42no—
96C2×C4×C5—44no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5—42no—
102C2×C4×C5—82no—
103C2×C4×C5C22⋊C812yes—
104C2×C4×C5C22⋊C812yes—
105C2×C4×C5#12314yes—
106C5×C8—84no—
107C23×C4C2×C4×C511yescharacteristic
108C23×C4C2×C4×C511yescharacteristic
109C23×C4C23×C511yescharacteristic
110C22×C8—24no—
111#117—22no—
112#117—24no—
113#117C5×C814yescomplemented
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—24no—
117C2×C4⋊C4C5×D412yes—
118C2×C4⋊C4C5×D412yes—
119C2×C22⋊C4C2×C4×C512yes—
120C2×C22⋊C4C2×C4×C512yes—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—22no—
124C2×C42—22no—
125C22⋊C8—24no—
126C22⋊C8—24no—
127#95—22no—
128#95—22no—
129C22×C5—21no—
130C22×C5—22no—
131C22×C5—21no—
132C22×C5—22no—
133C22×C5—41no—
134C22×C5—41no—
135C22×C5—42no—
136C22×C5#38111yescharacteristic
137C22×C5C2×C22⋊C811yescharacteristic
138C22×C5#40711yescharacteristic
139C22×C5#43112yes—
140C22×C5#43212yes—
141C4×C5—22no—
142C4×C5—22no—
143C4×C5—24no—
144C4×C5—44no—
145C4×C5—44no—
146C4×C5—42no—
147C24C22×C4×C511yescharacteristic
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—81no—
154C22×C4—81no—
155C22×C4C5×C22⋊C411yescharacteristic
156C22×C4C5×C22⋊C411yescharacteristic
157C22×C4C5×C22⋊C412yes—
158C22×C4C2×C5×C812yes—
159C22×C4C5×M1612yes—
160C22×C4C2×C5×D412yes—
161C22×C4C5×#4114yes—
162C2×C8—44no—
163C2×C8—84no—
164C4⋊C4—24no—
165C4⋊C4—24no—
166C4⋊C4—24no—
167C4⋊C4—24no—
168C22⋊C4—22no—
169C22⋊C4—22no—
170C22⋊C4C2×C5×C814yes—
171C22⋊C4C5×M1614yes—
172C42—24no—
173C42—24no—
174C42—82no—
175C42—82no—
176C2×C5—21no—
177C2×C5—21no—
178C2×C5—22no—
179C2×C5—22no—
180C2×C5#181711yescharacteristic
181C2×C5#182811yescharacteristic
182C2×C5#183011yescharacteristic
183C23—41no—
184C23—41no—
185C23C2×C5×C22⋊C411yescharacteristic
186C23C5×#11712yes—
187C23C22×C5×C811yescharacteristic
188C23C2×C5×M1611yescharacteristic
189C23C2×C5×M1612yes—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—82no—
207C2×C4C5×C22⋊C812yes—
208C2×C4C5×C22⋊C812yes—
209C2×C4C5×#12314yes—
210C8—84no—
211C5#873511yescharacteristic, direct product factor, Sylow
212C22—21no—
213C22—22no—
214C22—21no—
215C22—22no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22C5×#38111yescharacteristic
220C22C2×C5×C22⋊C811yescharacteristic
221C22C5×#40711yescharacteristic
222C22C5×#43112yes—
223C22C5×#43212yes—
224C4—22no—
225C4—22no—
226C4—24no—
227C4—44no—
228C4—44no—
229C4—42no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2C5×#181711yescharacteristic
235C2C5×#182811yescharacteristic
236C2C5×#183011yescharacteristic
subgroupG/H
center, socleC22×C5#381
commutatorC23C22×C5×C8
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
14. #8735C5direct (N × H)
21. C5×#117C8semidirect
113. #117C5×C8semidirect
211. C5#8735direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#22742
C2×C5×#3242
C5×#12822
#87355