Finite Group Databasebeta

← #14277208

Subgroups — #14277208

Order 1920.

380 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 89 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
1D5⋊#830C212yesmaximal
2C3×#65415C211yesmaximal, characteristic
3#10598789—31nomaximal, Hall
4C22×C3×C4×D5C2211yescharacteristic
5C2×D5⋊(C3⋊C8)—22no—
6C2×C3×C5×M16C411yescharacteristic
7C2×C3×#681C411yescharacteristic
8#91241—22no—
9#91232C414yes—
10C3×#3952—22no—
11#67688—51nomaximal, Hall
12D5⋊(C22⋊C8)—32no—
13#65415D311yescharacteristic
14C23×C3×D5Q811yescharacteristic
15C22×C3×C4×C5C2×C411yescharacteristic
16C22×C3×Dic5D411yescharacteristic
17C2×C3×C4×D5—41no—
18C2×C3×C4×D5—41no—
19C2×C3×C4×D5C2×C412yes—
20C2×C3×C4×D5D412yes—
21C2×C3⋊#170—24no—
22D5⋊(C3⋊C8)—42no—
23D5⋊(C3⋊C8)—42no—
24C3×C5×M16—41no—
25C2×C3×C5×C8—21no—
26C3×#681—41no—
27C2×C3×#168—21no—
28C3×#407—51no—
29C2×#830—52no—
30C22×C4×D5C2×D311yescharacteristic
31C2×D5⋊C8—62no—
32C2×C5×M16Dic311yescharacteristic
33C2×#681Dic311yescharacteristic
34C22⋊#170—62no—
35#4003—34no—
36#3952—22no—
37#1298—151noSylow
38C23×C3×C5C4⋊C411yescharacteristic
39C22×C3×D5—24no—
40C22×C3×D5—41no—
41C22×C3×D5C4⋊C412yes—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C4211yescharacteristic
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C2×C3×Dic5—41no—
47C2×C3×Dic5C22⋊C412yes—
48C3×C4×D5—22no—
49C3×C4×D5—22no—
50C3×C4×D5—42no—
51C3⋊#170—44no—
52C3×C5×C8—41no—
53C3×#168—41no—
54C23×C3×C4—51no—
55C2×C3×M16—51no—
56C2×C3×M16AGL(1,𝔽5)11yescharacteristic
57C22×C3⋊C8—102no—
58C3×C22⋊C8—102no—
59#830—54no—
60#830—102no—
61C23×D5Dic611yescharacteristic
62C22×C4×C5C2×Dic311yescharacteristic
63C22×Dic5D1211yescharacteristic
64C2×C4×D5—41no—
65C2×C4×D5—41no—
66C2×C4×D5C4×D312yes—
67C2×C4×D5#6712yes—
68C2×#170—64no—
69D5⋊C8—122no—
70D5⋊C8—122no—
71C5×M16—41no—
72C2×C5×C8—21no—
73#681—41no—
74C2×#168—21no—
75#407—51no—
76C2×C22⋊C8—152no—
77C22×C3×C5—22no—
78C22×C3×C5—21no—
79C22×C3×C5#9511yescharacteristic
80C2×C3×D5—22no—
81C2×C3×D5—22no—
82C2×C3×D5—44no—
83C2×C3×D5#10814yes—
84C3×C4×C5—21no—
85C3×C4×C5#9911yescharacteristic
86C3×C4×C5#9911yescharacteristic
87C3×Dic5—22no—
88C24×C3—51no—
89C22×C3×C4—51no—
90C22×C3×C4—52no—
91C22×C3×C4—52no—
92C22×C3×C4—201no—
93C22×C3×C4—201no—
94C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
95C3×M16—41no—
96C3×M16—201no—
97C2×C3×C8—21no—
98C2×C3×C8—101no—
99C2×C3⋊C8—104no—
100C2×C3⋊C8—202no—
101C2×C3⋊C8—202no—
102C23×C5C4⋊Dic311yescharacteristic
103C22×D5—24no—
104C22×D5—41no—
105C22×D5Dic3⋊C412yes—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5C4×Dic311yescharacteristic
109C2×C4×C5#21711yescharacteristic
110C2×Dic5—41no—
111C2×Dic5(C2×D3)⋊C412yes—
112C4×D5—22no—
113C4×D5—22no—
114C4×D5—42no—
115#170—124no—
116C5×C8—41no—
117#168—41no—
118C23×C4—51no—
119C2×M16—51no—
120C2×M16ΓL(1,𝔽16)11yescharacteristic
121C22×C8—302no—
122C22⋊C8—102no—
123C22⋊C8—154no—
124C22⋊C8—302no—
125C2×C3×C5—41no—
126C2×C3×C5#34112yes—
127C2×C3×C5#34211yescharacteristic
128C3×D5—24no—
129C23×C3—52no—
130C23×C3—104no—
131C23×C3—201no—
132C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—52no—
136C2×C3×C4—102no—
137C2×C3×C4—102no—
138C2×C3×C4—202no—
139C2×C3×C4—201no—
140C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
141C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
142C3×C8—41no—
143C3×C8—201no—
144C3⋊C8—204no—
145C22×C5—21no—
146C22×C5—22no—
147C22×C5C3⋊#9511yescharacteristic
148C2×D5—22no—
149C2×D5—22no—
150C2×D5—44no—
151C2×D5#82214yes—
152C4×C5—21no—
153C4×C5#83411yescharacteristic
154C4×C5#83411yescharacteristic
155Dic5—22no—
156C24—51no—
157C22×C4—51no—
158C22×C4—52no—
159C22×C4—52no—
160C22×C4—201no—
161C22×C4—201no—
162C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
163M16—41no—
164M16—201no—
165C2×C8—21no—
166C2×C8—101no—
167C2×C8—304no—
168C2×C8—602no—
169C2×C8—602no—
170C3×C5#129811yescharacteristic, complemented, Hall
171C22×C3—22no—
172C22×C3—21no—
173C22×C3—54no—
174C22×C3—102no—
175C22×C3—102no—
176C22×C3—204no—
177C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
178C3×C4—21no—
179C3×C4—102no—
180C3×C4#399911yescharacteristic
181C3×C4#401111yescharacteristic
182C2×C5—41no—
183C2×C5#452611yescharacteristic
184C2×C5#455812yes—
185D5—24no—
186C23—52no—
187C23—104no—
188C23—201no—
189C23C4⋊ΓL(1,𝔽16)11yescharacteristic
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—52no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4—202no—
196C2×C4—201no—
197C2×C4C4×ΓL(1,𝔽16)11yescharacteristic
198C2×C4#676311yescharacteristic
199C8—41no—
200C8—201no—
201C8—604no—
202C2×C3—41no—
203C2×C3—104no—
204C2×C3#6490112yes—
205C2×C3#6491711yescharacteristic
206C5#6768811yescharacteristic, complemented, Sylow
207C22—22no—
208C22—21no—
209C22—54no—
210C22—102no—
211C22—102no—
212C22—204no—
213C22#9123511yescharacteristic
214C4—21no—
215C4—102no—
216C4#9122811yescharacteristic
217C4#9124011yescharacteristic
218C3#1059878911yescharacteristic, complemented, Sylow
219C2—41no—
220C2—104no—
221C2#1174677212yes—
222C2#1174678811yescharacteristic
subgroupG/H
centerC2×C4#6763
commutatorC2×C3×C4×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC2×C3×C5×M16C4
socleC22×C3×C5#95
prime radicalC23×C3×D5Q8
cosocleC22×C3×C4×D5C22
hypercenterC2×M16ΓL(1,𝔽16)
hypocenterC3×C5#1298
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
170. C3×C5#1298semidirect
206. C5#67688semidirect
218. C3#10598789semidirect

Maximal subgroups

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

subgroupindex
D5⋊#8302
C3×#654152
#105987893
#676885