Finite Group Databasebeta

← #12009849

Subgroups — #12009849

Order 1280.

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

normal subgroups only

This group has 292 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#10610308C211yesmaximal, characteristic
2C5×#2166C211yesmaximal, characteristic
3#10600688C211yesmaximal, characteristic
4#10598028C212yesmaximal
5#10598027C212yesmaximal
6#65852—21no—
7C5×#405C2211yescharacteristic
8#65426C2212yes—
9#65405—21no—
10#65390—21no—
11#65005C412yescomplemented
12#64992—21no—
13#64988C411yescharacteristic, complemented
14C4×Dic20—21no—
15#64972C411yescharacteristic, complemented
16C5×#364—21no—
17C5×#349C2212yes—
18C5×#347—21no—
19#64780C2211yescharacteristic
20#64777C2211yescharacteristic
21#64751—21no—
22#11771—51nomaximal, Sylow
23C2×C5×M16C2311yescharacteristic
24C22×C5×C8D411yescharacteristic
25C5×#117D411yescharacteristic
26#4072—21no—
27#4070—22no—
28C2×#681—21no—
29C2×Dic20—21no—
30C2×Dic20C2×C412yes—
31#4035—42no—
32#4025—42no—
33#4016—21no—
34#4015—21no—
35C4×Dic10—22no—
36C5×M32—22no—
37C5×#97C2×C411yescharacteristic
38C5×#97D411yescharacteristic
39C4×C5×C8C2×C411yescharacteristic
40C4×C5×C8D411yescharacteristic
41#3950—21no—
42#3949C2×C412yes—
43#3948—22no—
44#3948—22no—
45#3947—22no—
46C8×Dic5—22no—
47#3177—51no—
48#2166D511yescharacteristic
49#1747—51no—
50#1342—52no—
51#1340—52no—
52C22×C4×C5C2×D411yescharacteristic
53C2×Dic10—22no—
54C5×M16—41no—
55C2×C5×C8—21no—
56C2×C5×C8—21no—
57C2×C5×C8C22⋊C411yescharacteristic
58C2×C5×C8C22⋊C411yescharacteristic
59C2×C5×C8C22×C411yescharacteristic
60C2×C5×C8C2×D411yescharacteristic
61C5×C4⋊C4—21no—
62C5×C22⋊C4—21no—
63C42×C5C22⋊C411yescharacteristic
64C42×C5C22⋊C411yescharacteristic
65C22⋊Dic5—42no—
66C22⋊Dic5—41no—
67C4⋊Dic5—22no—
68C4⋊Dic5—42no—
69C4⋊Dic5—41no—
70#683—42no—
71#683—42no—
72#683—42no—
73C4×Dic5—22no—
74C4×Dic5—42no—
75#681—41no—
76#681—41no—
77C2×#168—22no—
78Dic20—42no—
79Dic20—41no—
80Dic20—41no—
81C5×C16—42no—
82#541—101no—
83#499—51no—
84#494—51no—
85#491—101no—
86#470—52no—
87#467—101no—
88#441—52no—
89C4×Q16—101no—
90#405—101no—
91#405C2×D511yescharacteristic
92#364—21no—
93#349C2×D512yes—
94#347—21no—
95#338—51no—
96H(3,ℤ/4)—51no—
97H(3,ℤ/4)—101no—
98C23×C5AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5C2×C22⋊C411yescharacteristic
104C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
105C2×Dic5—42no—
106C2×Dic5—42no—
107C2×Dic5—42no—
108Dic10—42no—
109Dic10—42no—
110C5×C8—21no—
111C5×C8—21no—
112C5×C8—21no—
113C5×C8#10411yescharacteristic
114C5×C8#10411yescharacteristic
115#168—42no—
116C2×Q16—52no—
117C2×Q16—101no—
118C2×M16—101no—
119C2×M16C22×D511yescharacteristic
120C22×C8D2011yescharacteristic
121C4⋊Q8—101no—
122#126—202no—
123#125—101no—
124#125—202no—
125C22⋊Q8—102no—
126C4×Q8—102no—
127#117—101no—
128#117D2011yescharacteristic
129M32—22no—
130#107—101no—
131#106—52no—
132#103—102no—
133#103—102no—
134#97—102no—
135#97C4×D511yescharacteristic
136#97C22⋊D511yescharacteristic
137C4×C8—102no—
138C4×C8C4×D511yescharacteristic
139C4×C8C22⋊D511yescharacteristic
140C22×C5—21no—
141C22×C5—41no—
142C22×C5#41811yescharacteristic
143C4×C5—21no—
144C4×C5—41no—
145C4×C5—41no—
146C4×C5#41011yescharacteristic
147C4×C5C2×#10411yescharacteristic
148Dic5—82no—
149Dic5—82no—
150Dic5—82no—
151C2×Q8—102no—
152C22×C4C2×D2011yescharacteristic
153Q16—202no—
154Q16—201no—
155Q16—201no—
156M16—41no—
157M16—201no—
158M16—201no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—102no—
162C2×C8#68511yescharacteristic
163C2×C8#68511yescharacteristic
164C2×C8C2×C4×D511yescharacteristic
165C2×C8C2×C22⋊D511yescharacteristic
166C4⋊C4—21no—
167C4⋊C4—102no—
168C4⋊C4—201no—
169C4⋊C4—202no—
170C4⋊C4—202no—
171C4⋊C4—202no—
172C4⋊C4—202no—
173C22⋊C4—21no—
174C22⋊C4—201no—
175C22⋊C4—202no—
176C42—102no—
177C42—202no—
178C42#68511yescharacteristic
179C42#68511yescharacteristic
180C16—42no—
181C2×C5—21no—
182C2×C5—41no—
183C2×C5#150511yescharacteristic
184C23#405411yescharacteristic
185Q8—202no—
186Q8—202no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—202no—
192C2×C4—202no—
193C2×C4—202no—
194C2×C4#405411yescharacteristic
195C2×C4C2×#68511yescharacteristic
196C8—21no—
197C8—21no—
198C8—21no—
199C8—202no—
200C8#395711yescharacteristic
201C8#395711yescharacteristic
202C5#1177111yescharacteristic, complemented, Sylow
203C22—21no—
204C22—41no—
205C22#6542011yescharacteristic
206C4—21no—
207C4—41no—
208C4—41no—
209C4—402no—
210C4—402no—
211C4—402no—
212C4#6529511yescharacteristic
213C4C2×#395711yescharacteristic
214C2—21no—
215C2—41no—
216C2#1060162511yescharacteristic
subgroupG/H
centerC2#10601625
commutatorC2×C5×C8C22×C4
FrattiniC2×M16C22×D5
FittingC5×#2166C2
socleC2×C5#1505
prime radicalC23×C5AGL(1,ℤ/8)
cosocleC2×C5×M16C23
hypercenter#2166D5
hypocenterC5#11771
LCSG ▷ C2×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
11. #65005C4semidirect
13. #64988C4semidirect
15. #64972C4semidirect
202. C5#11771semidirect

Maximal subgroups

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

subgroupindex
#106103082
C5×#21662
#106006882
#105980282
#105980272
#117715