Finite Group Databasebeta

← #13014769

Subgroups — #13014769

Order 1280.

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

normal subgroups only

This group has 408 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
1Dic5×#125C211yesmaximal, characteristic
2#10604185C212yesmaximal
3#10598713C214yesmaximal
4C2×C5×#125C411yescharacteristic
5C2×C4⋊#170—22no—
6#65274C2212yes—
7#65270—22no—
8C4⋊C4×Dic5—22no—
9C4⋊C4×Dic5C412yes—
10#65225C411yescharacteristic
11C42×Dic5C2211yescharacteristic
12#64918—22no—
13#64918C2214yes—
14#7602—51nomaximal, Sylow
15C22×#170—24no—
16C5×#125—22no—
17C5×#125C814yescomplemented
18C2×C5×C4⋊C4—22no—
19C2×C5×C4⋊C4C2×C412yes—
20C2×C42×C5C2×C411yescharacteristic
21C2×C4⋊Dic5—22no—
22C2×C4⋊Dic5C2×C412yes—
23C2×C4×Dic5—22no—
24C2×C4×Dic5C2×C411yescharacteristic
25C2×C4×Dic5D412yes—
26C2×C4×Dic5D412yes—
27C2×C4×Dic5C2311yescharacteristic
28C4⋊#170—44no—
29#3963—22no—
30#3963—22no—
31#3963—22no—
32C4×#125—51no—
33#1831—52no—
34#1271—54no—
35C22×C4×C5—22no—
36C22×C4×C5C22⋊C412yes—
37C22×C4×C5C22×C411yescharacteristic
38C22×Dic5—22no—
39C22×Dic5C22⋊C411yescharacteristic
40C22×Dic5C22⋊C411yescharacteristic
41C22×Dic5C2×D412yes—
42C2×#170—44no—
43C2×#170—44no—
44C2×#170—44no—
45C5×C4⋊C4—28no—
46C5×C4⋊C4—22no—
47C5×C4⋊C4C2×C814yes—
48C42×C5C2×C812yes—
49C42×C5M1612yes—
50C4⋊Dic5—42no—
51C4⋊Dic5—42no—
52C4⋊Dic5—42no—
53C4×Dic5—22no—
54C4×Dic5—22no—
55C4×Dic5—22no—
56C4×Dic5—42no—
57C4×Dic5—41no—
58C4×Dic5—44no—
59C2×#125AGL(1,𝔽5)11yescharacteristic
60C2×C4⋊C8—102no—
61#389—52no—
62#387—102no—
63#382—51no—
64C4×C4⋊C4—52no—
65C4×C4⋊C4—102no—
66C43—51no—
67#336—54no—
68#336—102no—
69C23×C5C2×C22⋊C411yescharacteristic
70C2×C4×C5—21no—
71C2×C4×C5—21no—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—24no—
75C2×C4×C5—42no—
76C2×C4×C5—42no—
77C2×C4×C5C22⋊C814yes—
78C2×C4×C5C22×C811yescharacteristic
79C2×C4×C5C2×M1611yescharacteristic
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—21no—
84C2×Dic5—22no—
85C2×Dic5—42no—
86C2×Dic5—42no—
87C2×Dic5—42no—
88C2×Dic5#10112yes—
89C2×Dic5AGL(1,ℤ/8)12yes—
90C2×Dic5#13712yes—
91#170—84no—
92C22×C8—104no—
93#125—22no—
94#125#17014yescomplemented
95C2×C4⋊C4—22no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—102no—
98C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
99C2×C42—52no—
100C2×C42—51no—
101C2×C42—52no—
102C2×C42—51no—
103C2×C42—102no—
104C2×C42C2×AGL(1,𝔽5)11yescharacteristic
105C4⋊C8—204no—
106#95—102no—
107#95—102no—
108#95—102no—
109C22×C5C2×C22⋊C811yescharacteristic
110C22×C5#41011yescharacteristic
111C22×C5C2×#10111yescharacteristic
112C22×C5#41712yes—
113C22×C5#42112yes—
114C4×C5—21no—
115C4×C5—21no—
116C4×C5—24no—
117C4×C5—44no—
118Dic5—22no—
119Dic5—22no—
120Dic5—22no—
121Dic5—41no—
122Dic5—82no—
123C22×C4—22no—
124C22×C4—52no—
125C22×C4—51no—
126C22×C4—51no—
127C22×C4—102no—
128C22×C4C22⋊AGL(1,𝔽5)12yes—
129C22×C4C22×AGL(1,𝔽5)11yescharacteristic
130C2×C8—204no—
131C2×C8—204no—
132C2×C8—204no—
133C4⋊C4—22no—
134C4⋊C4—28no—
135C4⋊C4—202no—
136C4⋊C4—202no—
137C4⋊C4—202no—
138C4⋊C4C2×#17014yes—
139C42—102no—
140C42—102no—
141C42—102no—
142C42—202no—
143C42—201no—
144C42—204no—
145C42C2×#17012yes—
146C42#70412yes—
147C2×C5#146111yescharacteristic
148C2×C5#147712yes—
149C2×C5#151212yes—
150C2×C5#153411yescharacteristic
151C2×C5#156111yescharacteristic
152C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—24no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—52no—
161C2×C4—52no—
162C2×C4—52no—
163C2×C4—102no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—102no—
167C2×C4—101no—
168C2×C4—202no—
169C2×C4—202no—
170C2×C4—202no—
171C2×C4C22⋊#17014yes—
172C2×C4C22×#17011yescharacteristic
173C2×C4C2×#70411yescharacteristic
174C8—404no—
175C5#760211yescharacteristic, complemented, Sylow
176C22#6578511yescharacteristic
177C22D5⋊#10111yescharacteristic
178C22#6579312yes—
179C22#6579512yes—
180C22C2×C22⋊#17011yescharacteristic
181C4—21no—
182C4—21no—
183C4—24no—
184C4—44no—
185C4—102no—
186C4—102no—
187C4—102no—
188C4—201no—
189C4—402no—
190C2#1060457512yes—
191C2#1060457911yescharacteristic
192C2#1060458611yescharacteristic
193C2#1060497611yescharacteristic
194C2#1060500112yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#125C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×#125AGL(1,𝔽5)
hypocenterC5#7602
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
17. C5×#125C8semidirect
94. #125#170semidirect
175. C5#7602semidirect

Maximal subgroups

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

subgroupindex
Dic5×#1252
#106041852
#105987132
#76025