Finite Group Databasebeta

← C5×#12862 #11935582

Subgroups — C5×#12862 #11935582

Order 1280.

566 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2310C211yesmaximal, characteristic
2C5×#1784C212yesmaximal
3C5×#1394C214yesmaximal, complemented
4C23×C5×Q8C2211yescharacteristic
5C2×C5×#117C411yescharacteristic
6C2×C5×#117C411yescharacteristic
7C2×C5×#101—22no—
8C2×C5×#101C2214yes—
9C5×#407—22no—
10C5×#391—22no—
11C5×#391C412yes—
12C5×#391C2212yes—
13C5×#381—22no—
14#12862C511yesmaximal, characteristic, direct product factor, Sylow
15C22×C5×Q8—24no—
16C22×C5×Q8—42no—
17C22×C5×Q8—42no—
18C22×C5×Q8C2×C411yescharacteristic
19C22×C5×Q8D412yes—
20C22×C5×Q8C2311yescharacteristic
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5D412yes—
23C2×C5×M16—24no—
24C5×#117—42no—
25C5×#117—42no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C412yes—
28C2×C5×C22⋊C4—21no—
29C2×C5×C22⋊C4—21no—
30C2×C42×C5—21no—
31C2×C42×C5C2×C412yes—
32C5×#101—28no—
33C5×#101—44no—
34C5×C22⋊C8—44no—
35C5×#95—24no—
36C5×#95—24no—
37#2310C2×C511yescharacteristic
38#1784C2×C512yes—
39#1394C2×C514yescomplemented
40C24×C5C22⋊C411yescharacteristic
41C2×C5×Q8—24no—
42C2×C5×Q8—22no—
43C2×C5×Q8—24no—
44C2×C5×Q8—41no—
45C2×C5×Q8—41no—
46C2×C5×Q8—42no—
47C2×C5×Q8—41no—
48C2×C5×Q8—41no—
49C2×C5×Q8—416no—
50C2×C5×Q8#4114yes—
51C22×C4×C5—22no—
52C22×C4×C5—22no—
53C22×C4×C5—22no—
54C22×C4×C5—24no—
55C22×C4×C5—24no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—42no—
59C22×C4×C5C22⋊C412yes—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22×C411yescharacteristic
62C22×C4×C5C2×D412yes—
63C5×M16—44no—
64C5×M16—44no—
65C2×C5×C8—44no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—42no—
68C5×C22⋊C4—42no—
69C5×C22⋊C4—42no—
70C42×C5—42no—
71C42×C5—42no—
72C23×Q8C22×C511yescharacteristic
73C2×#117C4×C511yescharacteristic
74C2×#117C4×C511yescharacteristic
75C2×#101—22no—
76C2×#101C22×C514yes—
77#407—22no—
78#391—22no—
79#391C4×C512yes—
80#391C22×C512yes—
81#381—22no—
82C23×C5—21no—
83C23×C5—21no—
84C23×C5—42no—
85C23×C5#9912yes—
86C23×C5C2×C22⋊C411yescharacteristic
87C5×Q8—44no—
88C5×Q8—48no—
89C5×Q8—44no—
90C2×C4×C5—28no—
91C2×C4×C5—21no—
92C2×C4×C5—21no—
93C2×C4×C5—22no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—48no—
101C2×C4×C5—44no—
102C2×C4×C5—44no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5#9912yes—
106C2×C4×C5#11712yes—
107C2×C4×C5#12314yes—
108C5×C8—84no—
109C22×Q8—24no—
110C22×Q8—42no—
111C22×Q8—42no—
112C22×Q8C2×C4×C511yescharacteristic
113C22×Q8C5×D412yes—
114C22×Q8C23×C511yescharacteristic
115C23×C4C2×C4×C511yescharacteristic
116C23×C4C5×D412yes—
117C2×M16—24no—
118#117—42no—
119#117—42no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4C2×C4×C512yes—
122C2×C22⋊C4—21no—
123C2×C22⋊C4—21no—
124C2×C42—21no—
125C2×C42C2×C4×C512yes—
126#101—28no—
127#101—44no—
128C22⋊C8—44no—
129#95—24no—
130#95—24no—
131C22×C5—22no—
132C22×C5—22no—
133C22×C5—24no—
134C22×C5—42no—
135C22×C5—42no—
136C22×C5#38111yescharacteristic
137C22×C5C2×#9911yescharacteristic
138C22×C5C2×#9911yescharacteristic
139C4×C5—24no—
140C4×C5—22no—
141C4×C5—22no—
142C4×C5—42no—
143C4×C5—82no—
144C4×C5—82no—
145C24C5×C22⋊C411yescharacteristic
146C2×Q8—22no—
147C2×Q8—24no—
148C2×Q8—24no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—42no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—416no—
155C2×Q8C5×#4114yes—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—42no—
164C22×C4C5×C22⋊C412yes—
165C22×C4C5×C22⋊C411yescharacteristic
166C22×C4C22×C4×C511yescharacteristic
167C22×C4C2×C5×D412yes—
168M16—44no—
169M16—44no—
170C2×C8—44no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—42no—
175C42—42no—
176C42—42no—
177C2×C5—21no—
178C2×C5—21no—
179C2×C5—42no—
180C2×C5#181911yescharacteristic
181C2×C5#213312yes—
182C23—21no—
183C23—21no—
184C23—42no—
185C23C5×#9912yes—
186C23C2×C5×C22⋊C411yescharacteristic
187Q8—44no—
188Q8—48no—
189Q8—44no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—48no—
201C2×C4—44no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4C5×#9912yes—
206C2×C4C5×#11712yes—
207C2×C4C5×#12314yes—
208C8—84no—
209C5#1286211yescharacteristic, direct product factor, Sylow
210C22—22no—
211C22—22no—
212C22—24no—
213C22—42no—
214C22—42no—
215C22C5×#38111yescharacteristic
216C22C2×C5×#9911yescharacteristic
217C22C2×C5×#9911yescharacteristic
218C4—24no—
219C4—22no—
220C4—22no—
221C4—42no—
222C4—82no—
223C4—82no—
224C2—21no—
225C2—21no—
226C2—42no—
227C2C5×#181911yescharacteristic
228C2C5×#213312yes—
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C23×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1394C2semidirect
14. #12862C5direct (N × H)
39. #1394C2×C5semidirect
209. C5#12862direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23102
C5×#17842
C5×#13942
#128625