Finite Group Databasebeta

← #14298409

Subgroups — #14298409

Order 1920.

544 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×C3×#4023C211yesmaximal, characteristic
2#11752457C212yesmaximal
3#11746790C214yesmaximal, complemented
4#10604247—31nomaximal, Hall
5C23×C3×Dic5C2211yescharacteristic
6C2×#6762C2214yes—
7C2×C3×C5×C22⋊C4C411yescharacteristic
8C2×C3×C22⋊Dic5C411yescharacteristic
9C2×C3×#683C2212yes—
10C2×C3×C4×Dic5C412yes—
11C3×#4023—24no—
12#91241—24no—
13#71589—51nomaximal, Hall
14C2×#4023D311yescharacteristic
15#65798—32no—
16#64919—34no—
17C24×C3×C5C2×C411yescharacteristic
18C22×C3×C4×C5C2×C412yes—
19C22×C3×Dic5—24no—
20C22×C3×Dic5C2×C411yescharacteristic
21C22×C3×Dic5C2×C412yes—
22C22×C3×Dic5D414yes—
23C22×C3×Dic5C2311yescharacteristic
24#6762—28no—
25C2×C3⋊#170—24no—
26C3×C5×C22⋊C4—22no—
27C3×C22⋊Dic5—22no—
28C3×#683—24no—
29C3×C4×Dic5—24no—
30C2×C3×#117—51no—
31#5207—52no—
32#4530—54no—
33C23×Dic5C2×D311yescharacteristic
34C2×#704—34no—
35C2×C5×C22⋊C4Dic311yescharacteristic
36C2×C22⋊Dic5Dic311yescharacteristic
37C2×#683C2×D312yes—
38C2×C4×Dic5Dic312yes—
39#4023—24no—
40C22⋊#170—64no—
41#1822—151noSylow
42C23×C3×C5—22no—
43C23×C3×C5—42no—
44C23×C3×C5C22⋊C412yes—
45C23×C3×C5C22×C411yescharacteristic
46C2×C3×C4×C5—22no—
47C2×C3×C4×C5—42no—
48C2×C3×Dic5—22no—
49C2×C3×Dic5—28no—
50C2×C3×Dic5—22no—
51C2×C3×Dic5—42no—
52C2×C3×Dic5C22⋊C412yes—
53C2×C3×Dic5C2×D412yes—
54C2×C3×Dic5#4114yes—
55C3⋊#170—44no—
56C23×C3×C4—51no—
57C3×#117—104no—
58C2×C3×C4⋊C4—52no—
59C2×C3×C22⋊C4—51no—
60C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
61C2×C3×C42—52no—
62C2×#208—54no—
63#830—104no—
64C24×C5C2×Dic311yescharacteristic
65C22×C4×C5C2×Dic312yes—
66C22×Dic5—24no—
67C22×Dic5C2×Dic311yescharacteristic
68C22×Dic5C2×Dic312yes—
69C22×Dic5#6714yes—
70C22×Dic5C22×D311yescharacteristic
71#704—68no—
72C2×#170—64no—
73C5×C22⋊C4—22no—
74C22⋊Dic5—22no—
75#683—24no—
76C4×Dic5—24no—
77C2×#117—51no—
78#407—152no—
79#343—154no—
80C22×C3×C5—22no—
81C22×C3×C5—22no—
82C22×C3×C5—24no—
83C22×C3×C5—44no—
84C22×C3×C5C2×C22⋊C411yescharacteristic
85C22×C3×C5#11712yes—
86C3×C4×C5—42no—
87C3×Dic5—22no—
88C3×Dic5—42no—
89C3×Dic5#12314yes—
90C24×C3C2×AGL(1,𝔽5)11yescharacteristic
91C22×C3×C4—51no—
92C22×C3×C4—54no—
93C22×C3×C4—51no—
94C22×C3×C4—52no—
95C22×C3×C4—104no—
96C22×C3×C4C2×AGL(1,𝔽5)12yes—
97C3×C4⋊C4—104no—
98C3×C22⋊C4—22no—
99C3×C22⋊C4—102no—
100C3×C42—104no—
101#208—108no—
102C2×C3⋊C8—104no—
103C23×C5—22no—
104C23×C5—42no—
105C23×C5#21712yes—
106C23×C5C22×Dic311yescharacteristic
107C2×C4×C5—22no—
108C2×C4×C5—42no—
109C2×Dic5—22no—
110C2×Dic5—28no—
111C2×Dic5—22no—
112C2×Dic5—42no—
113C2×Dic5#21712yes—
114C2×Dic5#23514yes—
115C2×Dic5C2×#6712yes—
116#170—124no—
117C23×C4—51no—
118C2×M16—154no—
119#117—104no—
120C2×C4⋊C4—52no—
121C2×C22⋊C4—51no—
122C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic
123C2×C42—52no—
124C22⋊C8—304no—
125C2×C3×C5—22no—
126C2×C3×C5—42no—
127C2×C3×C5#38111yescharacteristic
128C2×C3×C5#41312yes—
129C23×C3—22no—
130C23×C3—42no—
131C23×C3C22⋊AGL(1,𝔽5)12yes—
132C23×C3C22×AGL(1,𝔽5)11yescharacteristic
133C2×C3×C4—22no—
134C2×C3×C4—42no—
135C2×C3×C4—54no—
136C2×C3×C4—52no—
137C2×C3×C4—52no—
138C2×C3×C4—108no—
139C2×C3×C4—102no—
140C2×C3×C4—102no—
141C2×C3×C4—202no—
142C3⋊C8—204no—
143C22×C5—22no—
144C22×C5—22no—
145C22×C5—24no—
146C22×C5—44no—
147C22×C5#92612yes—
148C22×C5C2×#21711yescharacteristic
149C4×C5—42no—
150Dic5—22no—
151Dic5—42no—
152Dic5#92914yes—
153C24C2×ΓL(1,𝔽16)11yescharacteristic
154C22×C4—51no—
155C22×C4—54no—
156C22×C4—51no—
157C22×C4—52no—
158C22×C4—104no—
159C22×C4C2×ΓL(1,𝔽16)12yes—
160M16—308no—
161C2×C8—304no—
162C4⋊C4—104no—
163C22⋊C4—22no—
164C22⋊C4—102no—
165C42—104no—
166C3×C5#182211yescharacteristic, complemented, Hall
167C22×C3—22no—
168C22×C3—22no—
169C22×C3—24no—
170C22×C3—44no—
171C22×C3#413012yes—
172C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
173C3×C4—42no—
174C3×C4—54no—
175C3×C4—102no—
176C3×C4—202no—
177C2×C5—22no—
178C2×C5—42no—
179C2×C5#521111yescharacteristic
180C2×C5#523712yes—
181C23—22no—
182C23—42no—
183C23#676312yes—
184C23C22×ΓL(1,𝔽16)11yescharacteristic
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—54no—
188C2×C4—52no—
189C2×C4—52no—
190C2×C4—108no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—202no—
194C8—604no—
195C2×C3—22no—
196C2×C3—42no—
197C2×C3#6576411yescharacteristic
198C2×C3#6577712yes—
199C5#7158911yescharacteristic, complemented, Sylow
200C22—22no—
201C22—22no—
202C22—24no—
203C22—44no—
204C22#9198912yes—
205C22C2×#676311yescharacteristic
206C4—42no—
207C4—54no—
208C4—102no—
209C4—202no—
210C3#1060424711yescharacteristic, complemented, Sylow
211C2—22no—
212C2—42no—
213C2#1175242311yescharacteristic
214C2#1175243612yes—
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
166. C3×C5#1822semidirect
199. C5#71589semidirect
210. C3#10604247semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40232
#117524572
#117467902
#106042473
#715895