Finite Group Databasebeta

← #11994614

Subgroups — #11994614

Order 1280.

404 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 103 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#10615070C211yesmaximal, characteristic
2#10615063C211yesmaximal, characteristic
3C5×#1526C211yesmaximal, characteristic
4#10600649C212yesmaximal
5#10598158C212yesmaximal
6C5×#533C2211yescharacteristic
7#65804C2211yescharacteristic
8C4×C5×M16C2212yes—
9#65368C412yes—
10#65367C412yes—
11#65353—22no—
12#65313—22no—
13Q8×#168—22no—
14#65289—22no—
15#65287—22no—
16#65214C2212yes—
17C2×C4×#168C2211yescharacteristic
18C5×#330—22no—
19#64676—22no—
20#64676—22no—
21#9068—51nomaximal, Sylow
22C2×C5×M16—22no—
23C5×C4⋊Q8C2×C412yes—
24C5×#125D412yes—
25C5×C22⋊Q8—22no—
26C4×C5×Q8—22no—
27C5×#117D412yes—
28C2×C42×C5C2311yescharacteristic
29#4072—21no—
30#4070—22no—
31C22×#168—21no—
32#4016—21no—
33#4015C2×C412yes—
34C4×Dic10—22no—
35C5×#97—22no—
36C4×C5×C8—22no—
37C22⋊#168—22no—
38#3940—24no—
39#3939—24no—
40C4⋊#168—24no—
41C4⋊#168D412yes—
42C4⋊#168D412yes—
43#3935—22no—
44C4×#168—22no—
45C4×#168—22no—
46C4×#168—21no—
47C4×#168C2×C411yescharacteristic
48C4×#168C2×C411yescharacteristic
49#3160—51no—
50#2986—51no—
51#1526D511yescharacteristic
52#1485—52no—
53#1278—52no—
54C2×C5×Q8—22no—
55C22×C4×C5C2×D411yescharacteristic
56C22×C4×C5#4112yes—
57C2×Dic10—22no—
58C5×M16—24no—
59C5×M16—42no—
60C2×C5×C8—42no—
61C5×C4⋊C4—22no—
62C5×C4⋊C4—24no—
63C5×C4⋊C4C22⋊C414yes—
64C5×C22⋊C4—22no—
65C42×C5—22no—
66C42×C5C22×C411yescharacteristic
67C42×C5C2×D412yes—
68C42×C5C2×D411yescharacteristic
69C22⋊Dic5—41no—
70C4⋊Dic5—22no—
71C4⋊Dic5—22no—
72#683—42no—
73C4×Dic5—41no—
74C2×#168—24no—
75C2×#168—21no—
76C2×#168—21no—
77C2×#168—22no—
78C2×#168—22no—
79#533—51no—
80#533C2×D511yescharacteristic
81#500—52no—
82#499—102no—
83#498—52no—
84#446—102no—
85C8×Q8—102no—
86#433—102no—
87#431—52no—
88#427—102no—
89C4×M16C2×D512yes—
90C2×C4×C8—51no—
91#330—22no—
92Q8⋊C8—102no—
93Q8⋊C8—102no—
94C23×C5#12311yescharacteristic
95C5×Q8—42no—
96C5×Q8—42no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—22no—
100C2×C4×C5—24no—
101C2×C4×C5C2×C22⋊C411yescharacteristic
102C2×C4×C5C4×D412yes—
103C2×C4×C5#12011yescharacteristic
104C2×C4×C5#12112yes—
105C2×Dic5—42no—
106Dic10—42no—
107Dic10—42no—
108C5×C8—44no—
109#168—22no—
110#168—22no—
111#168—42no—
112#168—42no—
113C2×M16—22no—
114C22×C8—101no—
115C4⋊Q8—52no—
116C4⋊Q8C4×D512yes—
117#125—101no—
118#125C22⋊D512yes—
119C22⋊Q8—22no—
120C22⋊Q8—102no—
121C4×Q8—22no—
122C4×Q8—102no—
123#117—101no—
124#117D2012yes—
125C2×C42C22×D511yescharacteristic
126#107—104no—
127#106—104no—
128C4⋊C8—52no—
129C4⋊C8—52no—
130C4⋊C8—104no—
131C22⋊C8—102no—
132#97—22no—
133#97—102no—
134C4×C8—22no—
135C4×C8—51no—
136C4×C8—51no—
137C4×C8—102no—
138C4×C8—102no—
139C4×C8—101no—
140C22×C5—22no—
141C22×C5—21no—
142C22×C5#38611yescharacteristic
143C4×C5—22no—
144C4×C5—21no—
145C4×C5—44no—
146C4×C5#44312yes—
147C4×C5#44412yes—
148C4×C5#45612yes—
149Dic5—82no—
150C2×Q8—22no—
151C2×Q8—102no—
152C22×C4C2×D2011yescharacteristic
153C22×C4#71112yes—
154M16—24no—
155M16—42no—
156C2×C8—42no—
157C2×C8—104no—
158C2×C8—101no—
159C2×C8—101no—
160C2×C8—102no—
161C2×C8—102no—
162C4⋊C4—22no—
163C4⋊C4—24no—
164C4⋊C4—102no—
165C4⋊C4—102no—
166C4⋊C4—202no—
167C4⋊C4#68514yes—
168C22⋊C4—22no—
169C22⋊C4—201no—
170C42—22no—
171C42—201no—
172C42C2×C4×D511yescharacteristic
173C42D4×D512yes—
174C42C2×C22⋊D511yescharacteristic
175C2×C5—41no—
176C2×C5#187612yes—
177C2×C5#188611yescharacteristic
178C23#403211yescharacteristic
179Q8—42no—
180Q8—42no—
181Q8—202no—
182Q8—202no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—202no—
188C2×C4#402712yes—
189C2×C4#402811yescharacteristic
190C2×C4C2×#68511yescharacteristic
191C2×C4#408512yes—
192C8—44no—
193C8—102no—
194C8—102no—
195C8—202no—
196C8—202no—
197C5#906811yescharacteristic, complemented, Sylow
198C22—21no—
199C22—22no—
200C22#6524711yescharacteristic
201C4—21no—
202C4—22no—
203C4—44no—
204C4—402no—
205C4#6504112yes—
206C4#6511212yes—
207C4#6511312yes—
208C2—41no—
209C2#1060089611yescharacteristic
210C2#1060117012yes—
subgroupG/H
centerC2×C4#4028
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1526C2
socleC22×C5#386
prime radicalC23×C5#123
cosocleC2×C42×C5C23
hypercenter#1526D5
hypocenterC5#9068
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
197. C5#9068semidirect

Maximal subgroups

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

subgroupindex
#106150702
#106150632
C5×#15262
#106006492
#105981582
#90685