Finite Group Databasebeta

← #12003462

Subgroups — #12003462

Order 1280.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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
1#10610800C211yesmaximal, characteristic
2C5×#1849C211yesmaximal, characteristic
3#10601303C212yesmaximal
4#10600594C212yesmaximal
5#10598207C211yesmaximal, characteristic
6#65804C2212yes—
7C2×C5×#108—22no—
8C5×#423C2211yescharacteristic
9C5×#423C2211yescharacteristic
10C2×C5×#97C2211yescharacteristic
11#65426—22no—
12#65215C2212yes—
13#65140—22no—
14#65138—22no—
15#64702—22no—
16#64701—22no—
17#64685—24no—
18#10528—51nomaximal, Sylow
19C2×C5×M16—21no—
20C2×C5×M16D412yes—
21C22×C5×C8—21no—
22C2×C42×C5C2311yescharacteristic
23#4072—22no—
24#4070—22no—
25#4070—22no—
26C2×Dic20—22no—
27#4016—22no—
28#4015D412yes—
29#4015D412yes—
30C4×Dic10—22no—
31C4×Dic10—22no—
32C5×#108—44no—
33C5×C4⋊C8—22no—
34C5×C4⋊C8—22no—
35C5×#97—21no—
36C5×#97D412yes—
37C22⋊#168—22no—
38#3949—22no—
39#3948—24no—
40C4⋊#168—22no—
41#3935—22no—
42#3255—51no—
43#1849D511yescharacteristic
44#1559—52no—
45#1531—52no—
46#1307—51no—
47C22×C4×C5C2×D411yescharacteristic
48C22×C4×C5#4112yes—
49C2×Dic10—22no—
50C2×Dic10—22no—
51C5×M16—42no—
52C5×M16—42no—
53C2×C5×C8—22no—
54C2×C5×C8—22no—
55C2×C5×C8—22no—
56C2×C5×C8—22no—
57C2×C5×C8—41no—
58C42×C5C2×D411yescharacteristic
59C42×C5C2×D412yes—
60C42×C5#4111yescharacteristic
61C22⋊Dic5—42no—
62C4⋊Dic5—22no—
63C4⋊Dic5—22no—
64C4⋊Dic5—22no—
65C4⋊Dic5—22no—
66#683—42no—
67#683—42no—
68C4×Dic5—42no—
69C2×#168—42no—
70Dic20—82no—
71#533—52no—
72#475—102no—
73#470—102no—
74#462—102no—
75#432—52no—
76C2×#108—22no—
77#423C2×D511yescharacteristic
78#423C2×D511yescharacteristic
79C2×#97C2×D511yescharacteristic
80#333—102no—
81#332—102no—
82#330—104no—
83C23×C5#12411yescharacteristic
84C2×C4×C5—21no—
85C2×C4×C5—21no—
86C2×C4×C5—42no—
87C2×C4×C5#12011yescharacteristic
88C2×C4×C5#12112yes—
89C2×C4×C5#12111yescharacteristic
90C2×C4×C5#12312yes—
91C2×Dic5—42no—
92C2×Dic5—42no—
93Dic10—42no—
94Dic10—42no—
95Dic10—82no—
96C5×C8—24no—
97C5×C8—42no—
98C5×C8—81no—
99#168—82no—
100C2×Q16—102no—
101C2×M16—21no—
102C2×M16C22⋊D512yes—
103C22×C8—21no—
104C4⋊Q8—52no—
105C4⋊Q8—52no—
106#125—102no—
107C22⋊Q8—102no—
108C22⋊Q8—102no—
109C4×Q8—102no—
110C4×Q8—102no—
111#117—102no—
112C2×C42C22×D511yescharacteristic
113#108—44no—
114#106—102no—
115C4⋊C8—22no—
116C4⋊C8—22no—
117C4⋊C8—102no—
118#103—104no—
119C22⋊C8—102no—
120#97—21no—
121#97—102no—
122#97D2012yes—
123C22×C5—22no—
124C22×C5—21no—
125C22×C5#39411yescharacteristic
126C4×C5—22no—
127C4×C5—22no—
128C4×C5—21no—
129C4×C5#45311yescharacteristic
130C4×C5#45611yescharacteristic
131Dic5—82no—
132Dic5—82no—
133C2×Q8—102no—
134C2×Q8—102no—
135C22×C4#71312yes—
136C22×C4C2×C22⋊D511yescharacteristic
137Q16—402no—
138M16—42no—
139M16—42no—
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—202no—
146C4⋊C4—102no—
147C4⋊C4—102no—
148C4⋊C4—102no—
149C4⋊C4—102no—
150C4⋊C4—202no—
151C4⋊C4—202no—
152C22⋊C4—202no—
153C42—202no—
154C42C2×D2011yescharacteristic
155C42#70911yescharacteristic
156C42D4×D512yes—
157C2×C5—41no—
158C2×C5#203911yescharacteristic
159C2×C5#204912yes—
160C23#409311yescharacteristic
161Q8—202no—
162Q8—202no—
163Q8—402no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—42no—
167C2×C4—202no—
168C2×C4—202no—
169C2×C4#404012yes—
170C2×C4#404112yes—
171C2×C4#407611yescharacteristic
172C2×C4#408311yescharacteristic
173C8—24no—
174C8—42no—
175C8—81no—
176C8—402no—
177C5#1052811yescharacteristic, complemented, Sylow
178C22—22no—
179C22—21no—
180C22#6528011yescharacteristic
181C4—22no—
182C4—22no—
183C4—21no—
184C4—402no—
185C4—402no—
186C4#6536611yescharacteristic
187C4#6538411yescharacteristic
188C2—41no—
189C2#1060038611yescharacteristic
190C2#1060153012yes—
subgroupG/H
centerC22#65280
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1849C2
socleC22×C5#394
prime radicalC23×C5#124
hypercenter#1849D5
hypocenterC5#10528
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
177. C5#10528semidirect

Maximal subgroups

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

subgroupindex
#106108002
C5×#18492
#106013032
#106005942
#105982072
#105285