Finite Group Databasebeta

← #14294961

Subgroups — #14294961

Order 1920.

480 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C4×D5⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#65686C211yesmaximal, characteristic
3D5×#803C211yesmaximal, characteristic
4(C2×AGL(1,𝔽5))⋊(C3⋊C8)C214yesmaximal
5#10603879—31nomaximal, Hall
6C2×D5⋊(C3⋊C8)C2212yes—
7C2×C3×C4×AGL(1,𝔽5)C2212yes—
8C3×C42×D5C2211yescharacteristic
9C2×D5×C3⋊C8C2212yes—
10C4×C3⋊#170C414yescomplemented
11C3×(C2×AGL(1,𝔽5))⋊C4C414yes—
12#91087C411yescharacteristic, complemented
13C5×#803C411yescharacteristic, complemented
14#90952C412yescomplemented
15#69435—51nomaximal, Hall
16#65686D311yescharacteristic
17C4×D5⋊C8—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)—24no—
26C3×C42×C5C2×C411yescharacteristic
27C2×C3⋊#168C2×C412yes—
28C2×C5×C3⋊C8C2×C412yes—
29C3×C4×Dic5C2×C411yescharacteristic
30C3×C4×Dic5C2×C412yes—
31D5×C3⋊C8—24no—
32C3×#376—51no—
33C2×#803—51no—
34C2×C4×C3⋊C8—51no—
35#4524—54no—
36C2×C4×AGL(1,𝔽5)C2×D312yes—
37C2×D5⋊C8—32no—
38C2×C8×D5—32no—
39C42×D5C2×D311yescharacteristic
40(C2×AGL(1,𝔽5))⋊C4Dic314yes—
41C4×#170—34no—
42C5×#97—31no—
43#3947—32no—
44#3935—31no—
45#1746—151noSylow
46C22×C3×D5C22×C411yescharacteristic
47C2×C3×AGL(1,𝔽5)—24no—
48C2×C3×AGL(1,𝔽5)—28no—
49C2×C3×C4×C5C4212yes—
50C2×C3×C4×C5C22×C411yescharacteristic
51C2×C3×Dic5C4212yes—
52C2×C3×Dic5C22×C411yescharacteristic
53C3×C4×D5—24no—
54C3×C4×D5#4114yes—
55C3⋊#170—24no—
56C3⋊#168—22no—
57C5×C3⋊C8—22no—
58C2×C3×C42—51no—
59C2×C3×C42—52no—
60C22×C3⋊C8—52no—
61C22×C3⋊C8—52no—
62C3×#95—54no—
63#803—51no—
64#803—52no—
65#803AGL(1,𝔽5)11yescharacteristic, complemented
66C4×C3⋊C8—54no—
67C22×AGL(1,𝔽5)C2×Dic314yes—
68C2×C4×D5C2×Dic312yes—
69C2×C4×D5C22×D311yescharacteristic
70C2×#170—34no—
71C4×AGL(1,𝔽5)—24no—
72D5⋊C8—64no—
73C2×C5×C8—32no—
74C42×C5C4×D311yescharacteristic
75C4×Dic5C4×D311yescharacteristic
76C4×Dic5C4×D312yes—
77C2×#168—32no—
78C8×D5—64no—
79C2×#97—151no—
80C2×C4×C8—151no—
81#376—51no—
82#336—154no—
83C22×C3×C5C2×C4211yescharacteristic
84C2×C3×D5#11712yes—
85C2×C3×D5#13114yes—
86C3×AGL(1,𝔽5)—44no—
87C3×C4×C5—22no—
88C3×C4×C5#11712yes—
89C3×Dic5—22no—
90C3×Dic5#11712yes—
91C22×C3×C4—51no—
92C22×C3×C4—52no—
93C22×C3×C4—54no—
94C3×C42—52no—
95C3×C42—51no—
96C3×C42—104no—
97C3×C42C2×AGL(1,𝔽5)11yescharacteristic
98C2×C3⋊C8—54no—
99C2×C3⋊C8—52no—
100C2×C3⋊C8—104no—
101C2×C3⋊C8—104no—
102C2×C3⋊C8C2×AGL(1,𝔽5)12yes—
103C22×D5C22×Dic311yescharacteristic
104C2×AGL(1,𝔽5)—24no—
105C2×AGL(1,𝔽5)—28no—
106C2×C4×C5C4×Dic312yes—
107C2×C4×C5C2×C4×D311yescharacteristic
108C2×Dic5C4×Dic312yes—
109C2×Dic5C2×C4×D311yescharacteristic
110C4×D5—24no—
111C4×D5#23514yes—
112#170—64no—
113C5×C8—62no—
114#168—62no—
115C22×C8—152no—
116C22×C8—152no—
117C2×C42—51no—
118C2×C42—52no—
119#97—31no—
120#97—152no—
121#97—151no—
122C4×C8—154no—
123#95—54no—
124C2×C3×C5#37611yescharacteristic
125C2×C3×C5#40512yes—
126C3×D5#43314yes—
127C23×C3—51no—
128C2×C3×C4—51no—
129C2×C3×C4—54no—
130C2×C3×C4—52no—
131C2×C3×C4—104no—
132C2×C3×C4—104no—
133C2×C3×C4—108no—
134C2×C3×C4C4×AGL(1,𝔽5)12yes—
135C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
136C3⋊C8—22no—
137C3⋊C8—104no—
138C3⋊C8—102no—
139C22×C5C2×C4×Dic311yescharacteristic
140C2×D5#92612yes—
141C2×D5#94814yes—
142AGL(1,𝔽5)—44no—
143C4×C5—22no—
144C4×C5#87212yes—
145Dic5—22no—
146Dic5#87212yes—
147C22×C4—51no—
148C22×C4—52no—
149C22×C4—54no—
150C2×C8—32no—
151C2×C8—154no—
152C2×C8—152no—
153C2×C8—304no—
154C2×C8—304no—
155C42—52no—
156C42—51no—
157C42—104no—
158C42D3×AGL(1,𝔽5)11yescharacteristic
159C3×C5#174611yescharacteristic, complemented, Hall
160C22×C3—52no—
161C22×C3—54no—
162C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
163C3×C4—22no—
164C3×C4—52no—
165C3×C4—102no—
166C3×C4—204no—
167C3×C4#413012yes—
168C2×C5#493211yescharacteristic
169C2×C5#499712yes—
170D5#500014yes—
171C23—51no—
172C2×C4—51no—
173C2×C4—54no—
174C2×C4—52no—
175C2×C4—104no—
176C2×C4—104no—
177C2×C4—108no—
178C2×C4Dic3×AGL(1,𝔽5)12yes—
179C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
180C8—62no—
181C8—304no—
182C8—302no—
183C2×C3—54no—
184C2×C3#6568611yescharacteristic
185C2×C3#6572812yes—
186C5#6943511yescharacteristic, complemented, Sylow
187C22—54no—
188C22—52no—
189C22C2×Dic3×AGL(1,𝔽5)11yescharacteristic
190C4—22no—
191C4—52no—
192C4—102no—
193C4—204no—
194C4#9190912yes—
195C3#1060387911yescharacteristic, complemented, Sylow
196C2—54no—
197C2#1175169712yes—
198C2#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#1746
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
10. C4×C3⋊#170C4semidirect
12. #91087C4semidirect
13. C5×#803C4semidirect
14. #90952C4semidirect
65. #803AGL(1,𝔽5)semidirect
159. C3×C5#1746semidirect
186. C5#69435semidirect
195. C3#10603879semidirect

Maximal subgroups

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

subgroupindex
C4×D5⋊(C3⋊C8)2
C3×#656862
D5×#8032
(C2×AGL(1,𝔽5))⋊(C3⋊C8)2
#106038793
#694355