Finite Group Databasebeta

← #14294915

Subgroups — #14294915

Order 1920.

544 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 166 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#11752335C211yesmaximal, characteristic
2C3×C42×AGL(1,𝔽5)C211yesmaximal, characteristic
3D5×#803C211yesmaximal, characteristic
4(C2×AGL(1,𝔽5))⋊(C3⋊C8)C214yesmaximal
5#10603878—31nomaximal, Hall
6C2×D5⋊(C3⋊C8)C2212yes—
7C2×C3×C4×AGL(1,𝔽5)C414yes—
8C2×C3×C4×AGL(1,𝔽5)C2212yes—
9C3×C42×D5C2211yescharacteristic
10C2×D5×C3⋊C8C2212yes—
11#91231C414yescomplemented
12#91087C411yescharacteristic, complemented
13C5×#803C411yescharacteristic, complemented
14#90952C412yescomplemented
15#69389—51nomaximal, Hall
16C42×AGL(1,𝔽5)D311yescharacteristic
17#65676—31no—
18D5×#97—31no—
19(C2×AGL(1,𝔽5))⋊C8—34no—
20C22×C3×AGL(1,𝔽5)C2×C414yes—
21C2×C3×C4×D5C2×C412yes—
22C2×C3×C4×D5C2311yescharacteristic
23C2×C3⋊#170C2×C414yes—
24D5⋊(C3⋊C8)—24no—
25C3×C4×AGL(1,𝔽5)—28no—
26C3×C4×AGL(1,𝔽5)—24no—
27C3×C42×C5C2×C411yescharacteristic
28C2×C3⋊#168C2×C412yes—
29C2×C5×C3⋊C8C2×C412yes—
30C3×C4×Dic5C2×C411yescharacteristic
31C3×C4×Dic5C2×C412yes—
32D5×C3⋊C8—24no—
33C3×C43—51no—
34C2×#803—51no—
35C2×#803—51no—
36#4524—54no—
37C2×C4×AGL(1,𝔽5)Dic314yes—
38C2×C4×AGL(1,𝔽5)C2×D312yes—
39C2×D5⋊C8—32no—
40C2×C8×D5—32no—
41C42×D5C2×D311yescharacteristic
42#4002—34no—
43C5×#97—31no—
44#3947—32no—
45#3935—31no—
46#1745—151noSylow
47C22×C3×D5C22×C411yescharacteristic
48C2×C3×AGL(1,𝔽5)—24no—
49C2×C3×AGL(1,𝔽5)—24no—
50C2×C3×AGL(1,𝔽5)M1618yes—
51C2×C3×C4×C5C4212yes—
52C2×C3×C4×C5C22×C411yescharacteristic
53C2×C3×Dic5C4212yes—
54C2×C3×Dic5C22×C411yescharacteristic
55C3×C4×D5—24no—
56C3×C4×D5#4114yes—
57C3⋊#170—24no—
58C3⋊#168—22no—
59C5×C3⋊C8—22no—
60C2×C3×C42—51no—
61C2×C3×C42—54no—
62C2×C3×C42—52no—
63C22×C3⋊C8—52no—
64C22×C3⋊C8—52no—
65#803—54no—
66#803—51no—
67#803—52no—
68#803AGL(1,𝔽5)11yescharacteristic, complemented
69C22×AGL(1,𝔽5)C2×Dic314yes—
70C2×C4×D5C2×Dic312yes—
71C2×C4×D5C22×D311yescharacteristic
72C2×#170—34no—
73C4×AGL(1,𝔽5)—28no—
74C4×AGL(1,𝔽5)—24no—
75D5⋊C8—64no—
76C2×C5×C8—32no—
77C42×C5C4×D311yescharacteristic
78C4×Dic5C4×D311yescharacteristic
79C4×Dic5C4×D312yes—
80C2×#168—32no—
81C8×D5—64no—
82C2×#97—151no—
83C2×#97—151no—
84C43—51no—
85#336—154no—
86C22×C3×C5C2×C4211yescharacteristic
87C2×C3×D5#11712yes—
88C2×C3×D5C2×M1614yes—
89C3×AGL(1,𝔽5)—28no—
90C3×C4×C5—22no—
91C3×C4×C5#11712yes—
92C3×Dic5—22no—
93C3×Dic5#11712yes—
94C22×C3×C4—51no—
95C22×C3×C4—54no—
96C22×C3×C4—52no—
97C3×C42—52no—
98C3×C42—51no—
99C3×C42—104no—
100C3×C42—108no—
101C3×C42C2×AGL(1,𝔽5)11yescharacteristic
102C2×C3⋊C8—54no—
103C2×C3⋊C8—52no—
104C2×C3⋊C8—104no—
105C2×C3⋊C8—104no—
106C2×C3⋊C8C2×AGL(1,𝔽5)12yes—
107C22×D5C22×Dic311yescharacteristic
108C2×AGL(1,𝔽5)—24no—
109C2×AGL(1,𝔽5)—24no—
110C2×AGL(1,𝔽5)#20818yes—
111C2×C4×C5C4×Dic312yes—
112C2×C4×C5C2×C4×D311yescharacteristic
113C2×Dic5C4×Dic312yes—
114C2×Dic5C2×C4×D311yescharacteristic
115C4×D5—24no—
116C4×D5#23514yes—
117#170—64no—
118C5×C8—62no—
119#168—62no—
120C22×C8—152no—
121C22×C8—152no—
122C2×C42—51no—
123C2×C42—54no—
124C2×C42—52no—
125#97—31no—
126#97—152no—
127#97—154no—
128#97—151no—
129C2×C3×C5#37611yescharacteristic
130C2×C3×C5C4×M1612yes—
131C3×D5#43214yes—
132C23×C3—51no—
133C2×C3×C4—51no—
134C2×C3×C4—54no—
135C2×C3×C4—58no—
136C2×C3×C4—52no—
137C2×C3×C4—104no—
138C2×C3×C4—104no—
139C2×C3×C4—104no—
140C2×C3×C4C4×AGL(1,𝔽5)12yes—
141C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
142C3⋊C8—22no—
143C3⋊C8—104no—
144C3⋊C8—102no—
145C22×C5C2×C4×Dic311yescharacteristic
146C2×D5C2×#20814yes—
147C2×D5#92612yes—
148AGL(1,𝔽5)—28no—
149C4×C5—22no—
150C4×C5#87212yes—
151Dic5—22no—
152Dic5#87212yes—
153C22×C4—51no—
154C22×C4—54no—
155C22×C4—52no—
156C2×C8—32no—
157C2×C8—154no—
158C2×C8—152no—
159C2×C8—304no—
160C2×C8—304no—
161C42—52no—
162C42—51no—
163C42—104no—
164C42—108no—
165C42D3×AGL(1,𝔽5)11yescharacteristic
166C3×C5#174511yescharacteristic, complemented, Hall
167C22×C3—52no—
168C22×C3—54no—
169C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
170C3×C4—22no—
171C3×C4—52no—
172C3×C4—108no—
173C3×C4—102no—
174C3×C4#413012yes—
175C2×C5C4×#20812yes—
176C2×C5#493211yescharacteristic
177D5#492614yes—
178C23—51no—
179C2×C4—51no—
180C2×C4—54no—
181C2×C4—58no—
182C2×C4—52no—
183C2×C4—104no—
184C2×C4—104no—
185C2×C4—104no—
186C2×C4Dic3×AGL(1,𝔽5)12yes—
187C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
188C8—62no—
189C8—304no—
190C8—302no—
191C2×C3—54no—
192C2×C3#6568611yescharacteristic
193C2×C3M16×AGL(1,𝔽5)12yes—
194C5#6938911yescharacteristic, complemented, Sylow
195C22—54no—
196C22—52no—
197C22C2×Dic3×AGL(1,𝔽5)11yescharacteristic
198C4—22no—
199C4—52no—
200C4—108no—
201C4—102no—
202C4#9190912yes—
203C3#1060387811yescharacteristic, complemented, Sylow
204C2—54no—
205C2AGL(1,𝔽5)×#20812yes—
206C2#1175174811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C2×C42
FittingC3×C42×C5C2×C4
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1745
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
11. #91231C4semidirect
12. #91087C4semidirect
13. C5×#803C4semidirect
14. #90952C4semidirect
68. #803AGL(1,𝔽5)semidirect
166. C3×C5#1745semidirect
194. C5#69389semidirect
203. C3#10603878semidirect

Maximal subgroups

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

subgroupindex
#117523352
C3×C42×AGL(1,𝔽5)2
D5×#8032
(C2×AGL(1,𝔽5))⋊(C3⋊C8)2
#106038783
#693895