Finite Group Databasebeta

← #13017149

Subgroups — #13017149

Order 1280.

368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 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#10610807C211yesmaximal, characteristic
2#10604688C212yesmaximal
3#10604363C211yesmaximal, characteristic
4#10604350C211yesmaximal, characteristic
5#10598788C212yesmaximal
6#65851C2211yescharacteristic
7#65754C2212yes—
8C4×#704C2212yes—
9C5×#424C411yescharacteristic
10#65411C411yescharacteristic
11#65407C2211yescharacteristic
12#65391C411yescharacteristic
13C2×C8×Dic5C2211yescharacteristic
14#65286C411yescharacteristic
15#65119—22no—
16#65117—22no—
17#170⋊C8—22no—
18#64879—22no—
19#64873C414yes—
20#64870C414yes—
21#8244—51nomaximal, Sylow
22C2×#704—22no—
23C2×C5×M16C2×C411yescharacteristic
24C22×C5×C8C2×C411yescharacteristic
25C5×#117C2×C411yescharacteristic
26#4072C2×C411yescharacteristic
27C2×C4×Dic5C2311yescharacteristic
28C2×#681C2×C411yescharacteristic
29C22×#168C2×C411yescharacteristic
30#4036C2×C412yes—
31#4034C2×C412yes—
32#4024—22no—
33C4×Dic10—22no—
34C22⋊#170—22no—
35#4004C2×C414yes—
36#4002C2×C414yes—
37C4×#170—22no—
38C4×#170—22no—
39C5×C4⋊C8—22no—
40#3947—21no—
41#3946—22no—
42#3946—22no—
43C8×Dic5—21no—
44C8×Dic5D412yes—
45C8×Dic5D412yes—
46#3935—21no—
47C4×#168—21no—
48#2960—51no—
49#1544—51no—
50#1526—51no—
51#1451—52no—
52#1299—52no—
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5#4112yes—
55C2×Dic10—22no—
56#704—44no—
57C2×#170—24no—
58C2×#170—24no—
59C5×M16—41no—
60C2×C5×C8—21no—
61C2×C5×C8—41no—
62C2×C5×C8C22⋊C412yes—
63C5×C4⋊C4C4212yes—
64C5×C22⋊C4—21no—
65C42×C5—21no—
66C22⋊Dic5—21no—
67C4⋊Dic5—22no—
68C4⋊Dic5C4212yes—
69#683—22no—
70#683—22no—
71C4×Dic5—21no—
72C4×Dic5C22×C411yescharacteristic
73C4×Dic5C22×C411yescharacteristic
74C4×Dic5C2×D412yes—
75#681—41no—
76C2×#168—22no—
77C2×#168—21no—
78C2×#168C22⋊C411yescharacteristic
79C2×#168C22⋊C411yescharacteristic
80#533—51no—
81#446—102no—
82C8×Q8—102no—
83#431—52no—
84#424—51no—
85#424AGL(1,𝔽5)11yescharacteristic
86#423—51no—
87#405—51no—
88#405—51no—
89C4×M16—52no—
90C2×C4×C8—51no—
91#332—54no—
92#330—54no—
93#322—102no—
94#322—102no—
95C23×C5#11711yescharacteristic
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5C2×C4211yescharacteristic
100C2×C4×C5C2×C22⋊C411yescharacteristic
101C2×Dic5—24no—
102C2×Dic5—22no—
103C2×Dic5C4×D412yes—
104C2×Dic5C4×D412yes—
105Dic10—44no—
106#170—44no—
107#170—44no—
108C5×C8—22no—
109C5×C8—41no—
110#168—21no—
111#168—41no—
112#168#10112yes—
113C2×M16—51no—
114C2×M16—102no—
115C2×M16C2×AGL(1,𝔽5)11yescharacteristic
116C22×C8—51no—
117C22×C8C2×AGL(1,𝔽5)11yescharacteristic
118C4⋊Q8—52no—
119#125—52no—
120C22⋊Q8—102no—
121C4×Q8—102no—
122#117—51no—
123#117C2×AGL(1,𝔽5)11yescharacteristic
124C2×C42—51no—
125C4⋊C8—22no—
126C4⋊C8—54no—
127C4⋊C8—102no—
128C4⋊C8—102no—
129C22⋊C8—102no—
130#97—54no—
131#97—101no—
132#97—101no—
133C4×C8—52no—
134C4×C8—52no—
135C4×C8—101no—
136C4×C8—102no—
137C4×C8—102no—
138C4×C8—101no—
139C22×C5—21no—
140C22×C5—22no—
141C22×C5C4×C22⋊C411yescharacteristic
142C4×C5—21no—
143C4×C5—42no—
144C4×C5C2×#10111yescharacteristic
145C4×C5#41311yescharacteristic
146Dic5—22no—
147Dic5—42no—
148Dic5#44414yes—
149C2×Q8—102no—
150C22×C4—52no—
151C22×C4C22×AGL(1,𝔽5)11yescharacteristic
152M16—41no—
153M16—204no—
154M16—201no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8—51no—
158C2×C8—51no—
159C2×C8—102no—
160C2×C8—104no—
161C2×C8—104no—
162C2×C8—101no—
163C2×C8C22⋊AGL(1,𝔽5)12yes—
164C4⋊C4—52no—
165C4⋊C4—102no—
166C4⋊C4—102no—
167C4⋊C4—102no—
168C4⋊C4C4×AGL(1,𝔽5)12yes—
169C22⋊C4—21no—
170C22⋊C4—101no—
171C42—21no—
172C42—51no—
173C42—51no—
174C42—52no—
175C42—101no—
176C2×C5—41no—
177C2×C5C4×#10111yescharacteristic
178C2×C5#176512yes—
179C23#413011yescharacteristic
180Q8—204no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—52no—
185C2×C4—52no—
186C2×C4—104no—
187C2×C4—102no—
188C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
189C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
190C8—22no—
191C8—41no—
192C8—52no—
193C8—101no—
194C8—204no—
195C8—204no—
196C8—201no—
197C5#824411yescharacteristic, complemented, Sylow
198C22—21no—
199C22—22no—
200C22C4×C22⋊AGL(1,𝔽5)11yescharacteristic
201C4—21no—
202C4—42no—
203C4—54no—
204C4—102no—
205C4—202no—
206C4#6577711yescharacteristic
207C4D5⋊#10111yescharacteristic
208C2—41no—
209C2#1060433511yescharacteristic
210C2#1060477812yes—
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#424C4
socleC22×C5C4×C22⋊C4
prime radicalC23×C5#117
cosocleC2×C4×Dic5C23
hypercenter#424AGL(1,𝔽5)
hypocenterC5#8244
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
197. C5#8244semidirect

Maximal subgroups

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

subgroupindex
#106108072
#106046882
#106043632
#106043502
#105987882
#82445