Finite Group Databasebeta

← #13018345

Subgroups — #13018345

Order 1280.

320 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 84 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#10604699C212yesmaximal
3#10604352C212yesmaximal
4#10598795C212yesmaximal
5#65851C2211yescharacteristic
6#65759C2214yes—
7C5×#424C411yescharacteristic
8#65411C411yescharacteristic
9#65407C2211yescharacteristic
10#65391C411yescharacteristic
11C2×C8×Dic5C2211yescharacteristic
12#65286C411yescharacteristic
13#65119—22no—
14#65117—22no—
15#64883—22no—
16#64882—22no—
17#64870—24no—
18#8631—51nomaximal, Sylow
19C2×C5×M16C2×C411yescharacteristic
20C22×C5×C8C2×C411yescharacteristic
21C5×#117C2×C411yescharacteristic
22#4072C2×C411yescharacteristic
23C2×C4×Dic5C2311yescharacteristic
24C2×#681C2×C411yescharacteristic
25C22×#168C2×C411yescharacteristic
26#4036D412yes—
27#4034Q812yes—
28#4024—22no—
29C4×Dic10—22no—
30C22⋊#170—24no—
31#4002—24no—
32C4⋊#170—24no—
33C5×C4⋊C8—22no—
34#3947—21no—
35#3946—22no—
36#3946—22no—
37C8×Dic5—21no—
38C8×Dic5D412yes—
39C8×Dic5D412yes—
40#3935—21no—
41C4×#168—21no—
42#2960—51no—
43#1568—52no—
44#1537—52no—
45#1307—52no—
46C22×C4×C5C22×C411yescharacteristic
47C22×Dic5#4112yes—
48C2×Dic10—22no—
49C2×#170—44no—
50C5×M16—41no—
51C2×C5×C8—21no—
52C2×C5×C8—41no—
53C2×C5×C8C22⋊C412yes—
54C5×C4⋊C4C4⋊C412yes—
55C5×C22⋊C4—21no—
56C42×C5—21no—
57C22⋊Dic5—21no—
58C4⋊Dic5—22no—
59C4⋊Dic5C4⋊C412yes—
60#683—22no—
61#683—22no—
62C4×Dic5—21no—
63C4×Dic5C2×D411yescharacteristic
64C4×Dic5C2×D412yes—
65C4×Dic5C2×Q811yescharacteristic
66#681—41no—
67C2×#168—22no—
68C2×#168—21no—
69C2×#168C22⋊C411yescharacteristic
70C2×#168C22⋊C411yescharacteristic
71#533—51no—
72#446—102no—
73C8×Q8—102no—
74#432—54no—
75#424—51no—
76#424AGL(1,𝔽5)11yescharacteristic
77#423—51no—
78#405—51no—
79#405—51no—
80C2×C4×C8—51no—
81#335—102no—
82#334—102no—
83#330—104no—
84C23×C5#11711yescharacteristic
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—22no—
88C2×C4×C5C2×C22⋊C411yescharacteristic
89C2×C4×C5C2×C4⋊C411yescharacteristic
90C2×Dic5—22no—
91C2×Dic5—42no—
92C2×Dic5#12112yes—
93C2×Dic5C22⋊Q812yes—
94Dic10—44no—
95#170—84no—
96C5×C8—22no—
97C5×C8—41no—
98#168—21no—
99#168—41no—
100#168#10112yes—
101C2×M16—51no—
102C2×M16C2×AGL(1,𝔽5)11yescharacteristic
103C22×C8—51no—
104C22×C8C2×AGL(1,𝔽5)11yescharacteristic
105C4⋊Q8—52no—
106#125—52no—
107C22⋊Q8—102no—
108C4×Q8—102no—
109#117—51no—
110#117C2×AGL(1,𝔽5)11yescharacteristic
111C2×C42—51no—
112C4⋊C8—22no—
113C4⋊C8—102no—
114C4⋊C8—104no—
115C4⋊C8—102no—
116C22⋊C8—104no—
117#97—101no—
118#97—104no—
119#97—101no—
120C4×C8—52no—
121C4×C8—52no—
122C4×C8—101no—
123C4×C8—101no—
124C22×C5—21no—
125C22×C5—22no—
126C22×C5#38011yescharacteristic
127C4×C5—21no—
128C4×C5—42no—
129C4×C5C2×#10111yescharacteristic
130C4×C5#41311yescharacteristic
131Dic5—22no—
132Dic5—22no—
133Dic5—42no—
134C2×Q8—102no—
135C22×C4—52no—
136C22×C4C22×AGL(1,𝔽5)11yescharacteristic
137M16—41no—
138M16—201no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—51no—
142C2×C8—51no—
143C2×C8—102no—
144C2×C8—101no—
145C2×C8—204no—
146C2×C8C22⋊AGL(1,𝔽5)12yes—
147C4⋊C4—52no—
148C4⋊C4—102no—
149C4⋊C4—102no—
150C4⋊C4—102no—
151C4⋊C4C4⋊AGL(1,𝔽5)12yes—
152C22⋊C4—21no—
153C22⋊C4—101no—
154C42—21no—
155C42—51no—
156C42—51no—
157C42—52no—
158C42—101no—
159C2×C5—41no—
160C2×C5#180111yescharacteristic
161C2×C5#181412yes—
162C23#413011yescharacteristic
163Q8—204no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—52no—
168C2×C4—52no—
169C2×C4—102no—
170C2×C4—202no—
171C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
172C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
173C8—22no—
174C8—41no—
175C8—52no—
176C8—101no—
177C8—201no—
178C8—404no—
179C5#863111yescharacteristic, complemented, Sylow
180C22—21no—
181C22—22no—
182C22#6576511yescharacteristic
183C4—21no—
184C4—42no—
185C4—102no—
186C4—102no—
187C4—202no—
188C4#6577711yescharacteristic
189C4D5⋊#10111yescharacteristic
190C2—41no—
191C2#1060433611yescharacteristic
192C2#1060478012yes—
subgroupG/H
centerC22#65765
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#424C4
socleC22×C5#380
prime radicalC23×C5#117
cosocleC2×C4×Dic5C23
hypercenter#424AGL(1,𝔽5)
hypocenterC5#8631
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
179. C5#8631semidirect

Maximal subgroups

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

subgroupindex
#106108072
#106046992
#106043522
#105987952
#86315